VŠB - TECHNICAL UNIVERSITY OF OSTRAVA

FACULTY OF METALLURGY AND MATERIALS ENGINEERING

Power Engineering and Heat

Engineering Lecture notes

Doc. Ing. Zuzana Klečková, CSc.

Ostrava

2015

Title:

Code:

Author:

Edition: first, 2015

Number of pages:

Academic materials for the Economics and Management of Industrial Systems study

programme at the Faculty of Metallurgy and Materials Engineering.

Proofreading has not been performed.

Execution: VŠB - Technical University of Ostrava

1

STUDY REGULATIONS

Power Engineering and Heat Engineering

For the Quality Management branch within the scope of the consequential master’s study

and other branches you have obtained an educational packet including integrated lecture notes

for the full-time as well as distance study comprising also study regulations.

1. Prerequisites

Graduation from the subject Heat Transfer and Fluid Mechanics is a prerequisite for the

study of the subject Power Engineering and Heat Engineering.

2. The objective of the subject

is to broaden and deepen knowledge on energy resources, traditional and non-traditional

fuels, thermal energy obtaining, handling this energy in various selected types of power

engineering facilities. The intention is to show broader context of energy obtaining and

practical and environment-friendly utilization. After studying the subject, a student should be

able to categorize energy resources and energy equipment, to solve simple tasks of heat

energy transfer, to apply the findings on energy equipment including basic accessories.

For whom the subject is intended

The subject is included into the branch Quality Management at the Faculty of Metallurgy

and Materials Engineering and into the branch Economics and Management in Industry at the

Faculty of Metallurgy and Materials Engineering. The prerequisite is assumed, possibly the

use of the existing e-learning lecture notes for the subject Heat Transfer and Fluid Mechanics

(author doc. Ing. Adéla Macháčková, Ph. D.). These e-learning lecture notes can be also used

for bachelor’s degree study in the branch Thermal Engineering and Industrial Ceramics in the

study programme Metallurgical Engineering. These lecture notes can be also used by anyone

from other students to obtain concrete knowledge of the Thermal Engineering branch.

The lecture notes are divided to parts – chapters, which correspond to the logical dividing

of the studied subject matter, but they are not of the same volume. The assumed time for the

study of the chapter may differ significantly, therefore large chapters are further divided to

numbered subchapters and these correspond to the structure of the lecture notes described

below.

Recommended procedure for studying each chapter:

Time needed for the study:

In the beginning of the chapter the time needed for studying the subject matter is

suggested. The time is for information only and corresponds approximately to the number of

hours covering the lectures of the subject within the full-time study. This may be used as an

approximate guide for timetabling the study of the entire subject or a chapter. The time may

seem to be too long for someone, too short for someone else. There are students facing the

subject issues for the first time and those who have rich experience in this branch. It is

recommended to use the prescribed literature for the study, because these lecture notes cannot

cover the studied subject in detail considering its range.

Objective: After studying this chapter a student will be able to

2

Describe a process referred to in the chapter

Define basic terms

Solve simple practical tasks

Then there are given objectives to achieve after having studied this chapter – particular

skills, knowledge.

LECTURE

Presentation of the subject matter follows, introduction of new terms, their explanation,

all of this accompanied by figures, tables, solved example tasks.

Summary of terms

In the end of the chapter, the main terms for you to learn are repeated. If you do not

understand something, go back and go through the particular part once more.

Questions

In the very end of each main chapter, there are several theoretical questions for you to

verify you’ve managed the workload of the chapter successfully and completely.

Tasks to solve

As most of theoretical terms in this subject has a direct meaning and application in a

database practice, practical tasks to solve are also offered here. This is the heart of the matter

and your ability to apply the newly acquired knowledge for solving actual situations is the

main intent of this subject. Tasks to solve are always given in the end of each chapter.

KEY TO THE SOLUTION

The results of the given tasks are offered as a part of the solved tasks. You can make a

continuous control of the solution procedure, thus avoiding false steps.

A way to communicate with a lecturer:

A communication between students and the lecturer will be possible both personally and

through e-mail; the lecturer’s contact data is given on web pages of the workplace. At the

beginning of the semester you will obtain an individual computation programme, the check-

up of which will take part in arranged dates during the semester, in announced consultation

hours. More detailed instructions will be discussed with students at the beginning of the

course in which students will be present.

The author of these lecture notes wishes you successful and pleasant studies.

3

TABLE OF CONTENTS

1. INTRODUCTION ................. CHYBA! ZÁLOŽKA NENÍ DEFINOVÁNA.

2. ENERGY RESOURCES – FUELS AND THEIR PORPERTIES ........... 6 2.1 Basic properties of fuels ........................................................................................................... 7

2.2 Fuel combustion ................................................................. Chyba! Záložka není definována.

2.3 Combustion control ........................................................... Chyba! Záložka není definována.

Solved tasks .............................................................................. Chyba! Záložka není definována.

Summary of terms of Chapter 2 ................................................ Chyba! Záložka není definována. Questions for Chapter 2 ............................................................ Chyba! Záložka není definována.

3. HEATING OF MATERIALS ....................... 2CHYBA! ZÁLOŽKA NENÍ

DEFINOVÁNA. 3.1 External heat transfer ........................................................ 2Chyba! Záložka není definována.

3.2 Internal heat transfer ......................................................... Chyba! Záložka není definována.5

3.2.1 Classification of a charge as a thin or thick object ... Chyba! Záložka není definována.5

3.2.2 Heating of thin objects .............................................. Chyba! Záložka není definována.6

3.2.3 Heating of thick objects ............................................ Chyba! Záložka není definována.9

Solved tasks ............................................................................. Chyba! Záložka není definována.5

Summary of terms of Chapter 3 .............................................. Chyba! Záložka není definována.6 Questions for Chapter 3 .......................................................... Chyba! Záložka není definována.6

4 HEAT EXCHANGERS ...... CHYBA! ZÁLOŽKA NENÍ DEFINOVÁNA.7 4.1 Fuel saving ............................................................................................................................. 37

4.2 Flame temperature increase .................................................................................................... 39

4.3 Recuperators ........................................................................................................................... 39

4.4 Thermal calculation of a recuperator ...................................................................................... 39

4.5 Hydraulic calculation of a recuperator ........................... 41Chyba! Záložka není definována.

4.6 Types of recuperators ............................................................................................................. 42

4.7 Regenerators ........................................................................................................................... 43

Solved task .............................................................................. Chyba! Záložka není definována.4

Summary of terms of Chapter 4 .............................................. Chyba! Záložka není definována.5

Questions for Chapter 4 ........................................................... Chyba! Záložka není definována.6

5 FURNACES ......................... CHYBA! ZÁLOŽKA NENÍ DEFINOVÁNA.7 5.1 Classification of furnaces .................................................... Chyba! Záložka není definována.7 5.2 Furnace thermal work ....................................................... Chyba! Záložka není definována.8

5.3 Melting furnaces ..................................................................................................................... 49

5.4 Heating furnaces ..................................................................................................................... 51

5.5 Furnaces for heat treatment .................................................................................................... 52

Summary of terms of Chapter 5 .............................................. Chyba! Záložka není definována.5 Questions for Chapter 5 .......................................................... Chyba! Záložka není definována.5

Literature ................................................................................. Chyba! Záložka není definována.6

Úvod

4

1. INTRODUCTION

These e-learning lecture notes have been prepared for students studying subjects of the

Department of Thermal Engineering in branches of both bachelor’s and master’s studies.

Considering their content, they can be also used in other branches, possibly at other types of

schools concerning thermal engineering. They are divided into four main articles logically

following one after another, such as processes in furnace facilities follow one after another.

Thermal energy for realization of thermal technologies in furnaces is obtained from

energy resources. Most of furnace facilities work on the fuel burning principle. The obtained

thermal energy is consumed for the very technology in the furnace working area. The

heat transfer to the charge is performed here. After performing a particular technology there is

still a large portion of heat not used, therefore most of thermal facilities are complemented

with heat exchangers. The thermal device itself is arranged so that the technological action is

performed in optimal conditions as to the obtained product quality, as to the energy economic

efficiency and as to environmental aspects. A content of particular chapters is briefly

described below.

The chapter with a title Energy resources – fuels and their properties deals with

energy resources, assesses availability and utilization of these resources for heat engineering

technologies. It is focused on fuels used nowadays as thermal energy resources. Fuels are

evaluated according to their basic properties, such as the fuel chemical composition, gross

calorific value, net calorific value, flame temperature and a possibility to heat the fuel without

an oxidizer presence.

The next chapter with a title Heating of materials deals with working area of furnaces.

For heating of a charge, and thus for proper realization of a thermal technological process, an

amount of flue gas energy per the charge needs to be known. If this amount is known, the

particular process of heating of the charge can be assumed or determined. After its analysis,

solutions for particular charge heating regimes are evident.

A heating regime is not only a determination of temperatures in the charge during the

heating period, but also a determination of temperature and thermal regime of the furnace

equipment, which is mentioned in the final chapter Furnaces.

Outside the furnace workspace there are flue gasses leaving the thermal device, carrying

off a large amount of unutilized thermal energy, many times as high as 60%. For this reason,

this heat is returned back to the technological process by means of an exchanger, therefore a

chapter with a title Exchangers is included in these e-learning lecture notes.

The last chapter has a title Furnaces. This part categorizes furnace facilities in

accordance with selected parameters, such as technological specification, workspace shape, a

process of thermal energy obtaining and a method of flue gas waste heat utilization. Thermal-

technical characteristics of furnaces and basic furnace types are described here. We

recommend a student to gain knowledge from e-learning lecture notes from Macháčková A.,

Mrňková L. Industrial Furnaces in order to be able to answer all questions given in the end of

this chapter.

E-learning lecture notes in this scope cannot offer a detailed description of all the covered

procedures. However, they are essentials enabling to a student to comprehend the contents of

the subject Furnaces and Power Engineering. Then, this is a real support for a student’s

studies.

For better and more detailed studies, it is advisable for a student to use basic technical

literature given in the end of these lecture notes. If there are equations in the text, the

Úvod

5

denomination of quantities congruent with the original nomenclature in the given technical

literature is respected.

Energetické zdroje – paliva a jejich vlastnosti

6

2. ENERGY RESOURCES – FUELS AND THEIR PROPERTIES

Time needed for the study: 11 hours

Objective: After studying this chapter a student will be able to:

Define fuel and its basic properties

Describe incorporation of fuels into the national energy balance

Solve a selection of fuel as to its energy potential

Describe a transformation of the fuel chemical potential to thermal energy from the

static point of view

Understand a relation of combustion products and a temperature achieved in a

workspace

Understand a combustion control principle

Lecture

Energy management is nowadays a determining factor of the society development. For

the sustainable growth, the energy potential obtained from available energy resources needs to

be enhanced.

In the course of time, in relation with discovering and utilization of energy resources,

those have been categorized into 3 categories:

Primary (controlled nuclear reaction, fossil fuels, permanent resources, renewable

resources)

Secondary (waste fuels, waste heat, waste compression energy)

Derived (synthetic fuels)

Energy resources covered in the national energy mix can be divided into non-renewable

and renewable resources. Energy obtained from them:

Fossil fuel energy (brown coal, black coal, oil, natural gas)

Nuclear energy (nuclear fission, nuclear fusion)

Traditional fuel energy (wood, charcoal, bagasse) used in third world countries

Renewable resource energy (water, wind, Sun, biomass, Earth’s internal heat)

Fuels can be distinguished as fossil and synthetic as to their origination and as solid,

liquid and gaseous fuels as to their state of matter. A group of solid natural fuels includes

brown, black coal, synthetic fuels include coke, for example. Oil is a natural liquid fuel;

synthetic liquid fuels include for example gasoline, kerosene, petroleum, heating oils.

Gaseous natural fuels include natural or carboniferous gas. The synthetic fuel category may

cover an entire range of gases generated from gasification (generator gases), from various

production procedures (blast furnace gas, converter gas, coke-oven gas) or those generally

called process gases resulting from various technology processes, both as a main product (bio-

gas) or a by-product.

Fuels are characterized by selected basic characteristics, such as:

Fuel chemical composition

Energetické zdroje – paliva a jejich vlastnosti

7

Gross calorific value and net calorific value

Flame temperature

Fuel heating without the air intake

2.1. Basic properties of fuels

On the basis of the fuel chemical composition, basic properties of fuel determine a

released thermal energy amount, a possible achievable temperature of generated combustion

products (flue gasses) and determine whether the fuel can be subjected to heating (not

burning).

Fuel chemical composition

Fuel chemical composition is determined by an elementary complex analysis or a technical

analysis. For solid and liquid fuels, it applies that a sum of all chemical components in a fuel

must equal 100 %. Then, the sum of mass apportionments of carbon wC , hydrogen wH ,

sulfur wS (pyritic, sulfidic, organic), wN, wO and unburnable residue wA and total moisture

wwt equal 100 % (see Rédr, M., Příhoda, M. Basics of Heat Engineering).

Liquid fuel chemical composition is identical, only sulfur contained in the fuel can be

determined through different methods.

For gaseous fuels, chemical composition cannot be expressed in general, it depends on

what gaseous components are included. A gradual analysis is performed so that again the sum

of all volume percentage φi of particular components equals 100%.

In chemical composition, there are both flammable and non-flammable components, an

amount of flammable components is a rate of a released thermal potential.

A technical analysis of fuels determines a percentual apportionment of a combustible

matter, moisture and unburnable residue in a fuel.

Gross calorific value and net calorific value

Gross calorific value or net calorific value of fuel defines a real value of the released heat

energy.

Gross calorific value (Qs) is an amount of heat energy released at complete burning of a

fuel specific unit (kg, m3), whereas moisture contained in the fuel or generated during burning

remains in the liquid phase (condenses).

Net calorific value (Qi) is an amount of heat energy released at complete burning of a fuel

specific unit (kg, m3), whereas moisture contained in the fuel or generated during burning is in

the gaseous phase (evaporates).

Net calorific value is always lower by water evaporation heat. Qs and Qi values can be

determined in a laboratory (by a calorimeter) or by a calculation. Lattice equations, being so

simple, are used for calculations of gross calorific value and net calorific value of solid and

liquid fuels, see equation (2.1) and equation (2.2):

SO

HCs 1058

1440339 ww

wwQ

(kJ∙kg

-1) (2.1)

WSO

HCi 251058

1214339 www

wwQ

(kJ∙kg

-1) (2.2)

Energetické zdroje – paliva a jejich vlastnosti

8

Gross calorific value, or net calorific value, of gaseous fuels can be determined as a sum

of released heats at combustion of flammable components of a gaseous fuel under

corresponding conditions; in general, equation (2.3) and equation (2.4) can be written for

determination of gross calorific value Qs and net calorific value Qi.

i

n

i

i QrQ ,s

1

s

(J∙m-3

) (2.3)

i

n

i

i QrQ ,i

1

i

(J∙m-3

) (2.4)

where n is quantity of flammable components in gaseous fuel (1)

ri volume proportion of a defined component in 1 m3 of gas (m

3∙m

-3)

Qs,i, Qi,i gross calorific value, net calorific value of a defined component (J∙m-3

)

Values of gross calorific value and net calorific value of respective flammable

components, which may be contained in gaseous fuel, are specified in technical tables (e.g.

Rédr, M., Příhoda, M. Basics of Heat Engineering).

Values of net calorific value of fuels typically range between 3 to 40 MJ per the fuel

specific unit. For reference purposes a standard unit ’coal equivalent’ has been defined, for

which a value of 29.3 MJ has been determined as the net calorific value.

Flame temperature

Flame temperature characterizes fuel in term of its use in the heat equipment workspace.

The temperature of fresh flue gases, which are generated during burning, determines a heat

amount in a furnace workspace, and thus also a heat amount available for the thermal

technology itself. Flame temperature is not directly depending on net calorific value, but also

on other parameters, among them an amount of generated flue gasses, and possibly fuel

heating without air intake or just heating of used combustion air. It cannot be stated

unambiguously, that fuel with higher net calorific value has higher flame temperature.

Flame temperature characterizes the way the fuel is used in the furnace workspace. Flame

temperature determines the achievable temperature of a flame and this determines the

achievable temperature of the workspace and thus also the heat transfer intensity per charge.

Flame temperature can be derived from the thermal equilibrium equation of the particular

furnace device, expressing equality of heat components on the input side and output side in

the furnace workspace. Input components include fuel (Qch), possible pre-heating of this fuel

(Qp) and pre-heating of used combustion air (Qvzd). Heat output is a sum of heat of flue gasses

(Qsp), chemical and mechanical incompleteness of combustion (Qn,ch and Qn,m) and a

component of the so-called heat taken-out in the furnace workspace (Qod), which must

provide the effective heat to the charge and cover all heat losses of the workspace. In a case

that a dissociation of flue gas components is not considered (CO2, H2O), this balance equation

can be written as (2.5):

Qch + Qp + Qvzd = Qsp + Qn,ch + Qn,m + Qod (J∙kg-1

, J∙m-3

) (2.5)

As the balance equation is valid for the standard fuel unit (coal equivalent), the chemical

heat of the fuel is equal to net calorific value Qi. Heat of the preheated fuel and air is

determined by equation (2.6), resp. (2.8):

Energetické zdroje – paliva a jejich vlastnosti

9

Qp = Vp · cp,p · tp = Vp · ip = ip (J∙m-3

) (2.6)

n

i

iri1

iip (J∙m-3

) (2.7)

where Vp is gas volume (m3)

cp,p specific heat capacity of gas (J∙m-3

∙K-1

)

tp preheated gas temperature (°C)

ip preheated gas enthalpy (J∙m-3

)

ii gas component enthalpy (J∙m-3

)

ri volume proportion of a gas component (m3∙m

-3)

Qvzd = Lskut · cp,vzd · tvzd = Lskut · ivzd (J∙kg-1

) (J∙m-3

) (2.8)

where Lskut is actual amount of combustion air (m3∙kg

-1, m

3∙m

-3)

cp,vzd specific heat capacity of air (J∙m-3

∙K-1

)

tvzd preheated air temperature (°C)

ivzd preheated air enthalpy (J∙m-3

)

On the output side, there can be a heat loss as a result of dissociation of some flue gas

components at working temperatures above 1550 °C. The heat output components can be

determined according to relations (2.9, 2.10, 2.11).

Determination of heat of taken-out flue gasses Qsp (J∙kg-1

, J∙m-3

):

Qsp = Vsp . cp,sp . tsp (J.kg-1

, J.m-3

) (2.9)

where Vsp is flue gas volume (m3∙kg

-1, m

3∙m

-3)

cp,sp specific heat capacity of flue gas (J∙m-3

∙K-1

)

tsp flue gas temperature (°C)

Determination of chemical unburned carbon Qn,ch occurring at a lack of combustion air (n

< 1):

sp

CH

sp

H

sp

COspn,ch 423586,1074,126 VQ (J∙kg

-1, J∙m

-3) (2.11)

where is volume percentage of the respective component in flue gasses (%)

Determination of mechanical unburned carbon Qn,m (J∙kg-1

, J∙m-3

), occurring as a result of

a wrong contact of fuel and air:

Qn,m = 0.01 . Qi (J∙kg-1

, J∙m-3

) (2.12)

where is a mechanical loss coefficient (%).

The last component specified on the heat output side Qod cannot be expressed by a single

relation, therefore an analysis of the determination is not given here.

If relation (2.9) is substituted into the thermal equilibrium equation for the heat taken-out

in flue gasses, flame temperature can be calculated according to the equation mentioned

below (2.13):

Energetické zdroje – paliva a jejich vlastnosti

10

sp,sp

odmn,chn,vzdpi

sp

Q - Q-Q - Q Q Q

pcVt

(°C) (2.13)

Basic kinds of flame temperatures

Regarding the complexity of flame temperature determination, various types of flame

temperatures are derived based-on particular determined combustion conditions. There are

several types of flame temperatures. Three types are explained in these lecture notes:

1. Adiabatic flame temperature

2. Theoretical flame temperature

3. Actual flame temperature

Adiabatic flame temperature tad

The adiabatic flame temperature is a specific parameter of fuel, because it is determined

at adiabatic conditions and the combustion air amount always corresponds with a theoretical

value. Considering these conditions, the adiabatic flame temperature is generally defined as a

function of the following quantities:

),,( sp,

min

spchad pcVQft (°C) (2.14)

whereas n = 1, Qp = Qvzd = Qn,ch = Qn,m = Qod = 0

Theoretical flame temperature tt

The theoretical flame temperature respects the particular combustion conditions. The

particular value of the added combustion air (n>1) and preheating of combustion components

(fuel, air) are considered. It allows theoretical modelling of combustion conditions, so that

they meet the presupposed conditions of the combustion process. Therefore it is called

‘theoretical’ and can be expressed by a functional relation:

),,,,( p,spvzdpcht spcVQQQft (°C) (2.15)

whereas n > 1, Qn,ch = Qn,m = Qod = 0

Actual flame temperature tp

The so-called actual flame temperature is of the greatest importance in practice, as it

respects the actual burning conditions, such as the air excess 1n , possibly 1n (burn-out),

preheating of combustion components, heat transfer to the charge and covering of the

workspace losses. The definition relation for the actual flame temperature includes all

components contained in the balance equation:

),,,,,,,( sp,spodchn,mn,vzdpchp pcVQQQQQQft (°C) (2.16)

This temperature has the lowest value of the above mentioned temperatures and

corresponds with the achieved flue gas temperature in the furnace workspace demanded for the

proper technology process. As it is dependent on many factors (see equation 2. 16), it can be

also expressed as a function of a pyrometric effect ηpyr. The pyrometric effect is a value, which

can be included into characteristics of the thermal work of particular furnace devices, because

it expresses also actual heat losses of this equipment, as evident in relation (2.17):

Energetické zdroje – paliva a jejich vlastnosti

11

tp = tt · ηpyr (°C) (2.17)

Fuel heating without the air intake

Fuel heating without the air intake can lead to the combustion intensification, flame

temperature increase, fuel saving, shortening of the heating period, but also to origination of a

different kind of fuel etc. A reaction of fuel under the thermal load is a decisive factor. If it

changes its molecular structure, this is a thermally unstable fuel not applicable for preheating;

if it does not change its molecular structure (thermally stable fuel), preheating can be used.

Heating of thermally stable fuels without the air intake results in their improvement in the

case of solid fuels, reduction of their viscosity in the case of liquid fuels; gaseous fuels can be

heated in heat exchangers and it has a positive importance for the combustion process and the

heat transfer intensity in the furnace workspace.

2.2. Fuel combustion

Fuel combustion is rapid oxidation of the part of fuel, which reacts with an oxidizing agent.

As these are exothermic reactions, thermal energy is released during burning. For a proper

combustion process course, fuel needs to be supplied with a demanded ratio of an oxidizing

agent and an initial impulse for the combustion reaction process, i.e. the fuel and oxidizing

agent mixture must be heated to the ignition temperature (to initialize burning). An oxidizing

agent is generally meant a substance rich in oxygen. The best available is atmospheric air,

where O2 content reaches approximately 21 vol. % (see: Rédr, M., Příhoda, M. Basics of Heat

Engineering), oxygen enriched air, in some case pure oxygen.

Combustion product is flue gas, having an actual flame temperature and containing an

actual amount of thermal energy.

If combustion is considered as a static process, flue gas includes gaseous components,

which are a result of:

Oxidation reactions (CO, CO2, SO2)

Transfer of moisture and non-flammable part of fuel to a gaseous phase, (H2O, if fuels

contain an unburnable residue, fly ash may be present in flue gas)

Presence of air as an oxidizing agent (gaseous air nitrogen N2, excess

air oxygen O2)

If combustion is considered a dynamic process, in which fuel with a given chemical

structure plays a main part, the structure disintegration is accompanied by a number of

originating and disappearing intermediate products. These may in the given temperature area,

or after a reaction with components in the atmospheric air, create many new chemical

compounds (emissions, immissions) and phenomena in the air (albedo, smog, greenhouse

effect etc.).

According to the amount of the added oxidizing agent, three types of combustion may

occur – complete, incomplete and mixed.

Complete combustion: oxidation reactions have run completely, so flue gasses include

only non-flammable components CO2, SO2, H2O, N2, O2. In order to achieve this, the actual

amount of combustion air Lskut is increased by a specified percentage in accordance with a

type of fuel and combustion equipment. This percentage is expressed by a ratio of the actual

delivered combustion air Lskut to the theoretical needed Lmin (minimum) or by a ratio of the

actual consumed oxygen Oskut to the theoretical needed (minimum) Omin, see equation (2.18).

The ratio of these values is called an excess air factor and it is marked as n.

Energetické zdroje – paliva a jejich vlastnosti

12

min

skut

min

skut

O

O

L

Ln (1) (2.18)

Table 2.4 shows values for applicable excess air factors for some fuels.

The excess air factor values given in Table 2.1 are valid for fuel burning in furnace

devices. For burning gasoline, petroleum, gas in combustion engines or turbines and for waste

burning in incineration plants the range of the excess air factor values increases considerably.

At the incomplete combustion, flammable components occur in flue gasses. This condition

can be a result of a lack of the combustion air (the so-called chemical burn-out, n<1) or an

insufficient contact of fuel with an oxidizing agent (mechanical burn-out).

Table 2.1. Applicable range of the excess air factor for some fuels (Source: Rédr, M.,

Příhoda, M. Basics of Heat Engineering)

nopt Fuel type

1.05 to 1.10 Coke-oven gas, natural gas

1.10 to 1.15 Blast furnace gas, generator gas

1.10 to 1.30 Heating oil

1.15 to 1.35 Pulverized coal black, brown

1.30 to 1.50 Lump coal, mechanized furnace

1.50 to 2.00 Lump coal, hand-operated furnace

In practice, mixed combustion occurs usually, this means that products of the complete

combustion prevail in flue gasses, however, a certain amount e.g. of CO may occur in flue

gasses as a result of a local decrease in the excess air factor or a wrong contact with an

oxidizing agent.

For combustion, it is necessary to know the amount of added combustion air to the

standard fuel unit and the amount and composition of produced flue gasses. This can be

determined either from the elemental analysis of fuel or the use of empirical formulae.

Calculation of combustion – determination of an amount of generated flue gasses, their

composition, an amount of combustion air by a stoichiometric calculation (solid and

liquid fuels)

Dry atmospheric air is used as an oxidizing agent; its composition is considered only as a

content of oxygen and nitrogen in a ratio of 21 % to 79 % (volume). An error caused this way

is within a permissible tolerance.

The actual amount of flue gas Vsp is given by a sum of volumes of burning products:

VCO2 is in flue gasses as a result of burning of fuel carbon Cp

VH2O is in flue gasses as a result of burning of fuel hydrogen Hp; the moisture

contained in the fuel transfers into this volume, too

VSO2 is in flue gasses as a result of burning of fuel sulfur Sp

VN2 comprises fuel nitrogen Np and nitrogen contained in the used air - oxidizing agent

VO2 is the excess air oxygen as a result of burning with a value n>1

Energetické zdroje – paliva a jejich vlastnosti

13

The amount of needed combustion air Lskut, which needs to be added to the fuel specific

unit, depends on the oxygen amount needed for oxidation of flammable components of fuel.

The minimum value of this oxygen is determined by the oxygen amount needed for

combustion of particular flammable fuel components OminC

, OminH

, OminS

. If oxygen Op is

present in the fuel, it has a function of an oxidizing agent and it takes a priority part in the

burning process. So a less proportion of oxygen can be supplied by means of an external

oxidizing agent.

The above described can be summarized schematically as follows:

Fuel components Cp, H

p, S

p, O

p, N

p, W

p, A

p (kg∙kg

-1)

Oxidizing agent (air) N2 : O2 = 79 : 21 (% vol.)

Flue gasses Vsp: VCO2,VH2O,VSO2,VN2,VO2 (m3∙kg

-1)

Combustion air amount Lskut = Omin ·n ·100/21 (m3∙kg

-1)

Minimum oxygen amount Omin = OminC + Omin

H + Omin

S - O

P (m

3∙kg

-1)

For the calculation the following basic equations are used, which can be interpreted as

follows:

carbon

C + O2 = CO2 (2.19)

12 kg C + 22.4 m3 O2 = 22.4 m

3 CO2

for burning of 12 kg of carbon a minimum of 22.4 m3

of O2 is needed and 22.4 m

3 of CO2

are generated

for burning of Cp, Omin

C is needed and

C

COV 2 is generated

OminC

and C

COV 2 can be determined from this expression

hydrogen

H2 + 0.5 O2 = H2O (2.20)

2 kg H2 + 11.2 m3 O2 = 22.4 m

3 H2O

sulfur

S + O2 = SO2 (2.21)

32 kg S + 22.4 m3 O2 = 22.4 m

3 SO2

oxygen (recomputation of the mass amount to the volume amount)

O2 = O2 (2.22)

32 kg O2 = 22.4 m3 O2

nitrogen (recomputation of the mass amount to the volume amount)

N2 = N2 (2.23)

28 kg N2 = 22.4 m3 N2

moisture (recomputation of the mass amount to the volume amount)

H2O (l) = H2O (g) (2.24)

18 kg H2O (l) = 22.4 m3 H2O (g)

nitrogen from the air (oxidizing agent)

nON vzd 21

79min2 (2.25)

Energetické zdroje – paliva a jejich vlastnosti

14

oxygen excess from the air

1min2 nOOvzd (2.26)

For a better clarity, the calculation can be performed in a form of a combustion table, see

Table 2.2.

For gaseous fuel burning the procedure goes analogically. It is necessary to take into account

that the gaseous fuel specific unit is m3 and the calculation needs to be adapted to that.

Determination of an amount of generated flue gasses, their composition, an amount of

combustion air through application of empirical relations

If a total elemental analysis of fuel is not available, empirical relations can be used for

determination of a volume of generated flue gasses Vsp and an amount of combustion air Lskut,

because

Table 2.2. Combustion table for solid and liquid fuels

Energetické zdroje – paliva a jejich vlastnosti

15

there is a linear dependence of the fuel net calorific value and the combustion air theoretical

volume and the generated flue gas volume.

On the basis of this fact, the flue gas volume and the needed combustion air amount can

be determined by a simple equation (2.27):

VLnVsp min (m3·kg

-1, m

3·m

-3), (2.27)

where ΔV and Lmin quantities can be determined according to a fuel type and its net calorific

value from thermal – technical tables (Bálek, S. Thermal-technical tables and diagrams).

2.3. Combustion control

For the constant demanded heat transfer in the furnace workspace the constant burning is

needed, the result of which is a constant flame temperature. This can be maintained, if the

combustion ratio oxidizing agent – fuel is constant. The amount of the added combustion air

is determined by the excess air factor value n. Despite the fact that the combustion air amount

on the inlet into burners is adjusted to the appropriate value and it should not be changed, in

operation its value may be influenced by objective causes. By this reason an inspection of the

combustion process is performed, consisting in continuous monitoring of the excess air factor.

Volume proportions in selected gaseous components in dry flue gasses are monitored. Figure

2.1 shows how the volume proportions of carbon dioxide φCO2, carbon monoxide φCO, oxygen

φO2 change depending on n factor.

The excess air factor can be determined e.g. from monitoring of the carbon dioxide

volume proportion in dry flue gasses φCO2.

If the excess air factor equals one, φCO2 reaches its maximum value, which can be

expressed by a relation:

100V

s

min,

COmax 2

2

sp

coV

(%) (2.28)

Energetické zdroje – paliva a jejich vlastnosti

16

Fig. 2.1 Change in volume proportions of flue gas selected components on the excess air

factor

If the excess air factor increases, φCO2 decreases gradually, while the flue gas volume s

spV

increases. Its amount is determined by a relation

100V

s

sp

CO

co2

2

V (%) (2.29)

However, in both these relations (2.28), (2.29) the carbon dioxide volume remains

constant. If this equality is used and the dry flue gas volume is determined using the dry flue

gas volume at n = 1, for the complete combustion relation (2.30) can be derived, enabling to

determine the excess air factor value at the measured concentration φCO2. Then, this obtained

excess air factor value needs to be compared to the prescribed value and in a case they are

different, a correction must be made.

min

s

min,sp

CO

max,CO11

2

2

L

Vn

(1) (2.30)

Values φCO, φCH4 need to be determined by the relevant analyzers of gases.

In furnace systems, continuous monitoring of a selected gaseous component of flue gas

(mostly oxygen) is performed.

A change in the flue gas composition depending on the changing excess air factor for a

particular fuel is defined in the Ostwald combustion triangle. The design and the system of

use are described in details in the study literature given below.

Solved tasks

Task 2.1

Task

Determine the gross calorific value and net calorific value of brown coal with a

composition of 50.2 % C, 3.6 % H, 0.7 % S, 13.2 % O, 0.6 % N, 26.3 % W according to the

lattice equation.

Solution

The fuel chemical composition is substituted into equation (2.1) and (2.2)

SO

HC 1058

1440339 ww

wwQs

WSO

HC 251058

1214339 www

wwQi

3,899197,01058

2,136,314402,50339

sQ kJ∙kg

-1

Energetické zdroje – paliva a jejich vlastnosti

17

1,801183,26257,01058

2,136,312142,50339

iQ kJ∙kg

-1

Result

The brown coal gross calorific value is 19 899.3 kJ∙kg-1

, net calorific value is 18 801.1

kJ∙kg-1

.

The result is in the given units, despite the fact that percent are substituted into the

calculation. The numeric constants correspond to the relevant element net calorific value,

which is divided by 100.

Task 2.2

Task

Determine the gross calorific value and net calorific value of the blast furnace gas with

the composition: 10.6 % H2, 0.7 % O2, 54.0 % N2, 27.5 % CO, 1.4 % CH4, 0.4 % CnHm,

5.2 % CO2, 0.2 % C2H6.

Solution

Relations (2.3) and (2.4) are used; volume proportions of flammable components

according to the fuel chemical composition are substituted to them. Respective gross calorific

values, or net calorific values, of these components can be found in table 2.2. It respects

substituting in adequate units.

Result

The blast furnace gas gross calorific value is 5 779.82 kJ·m-3

, the net calorific value is

5 481.12 kJ·m-3

.

Task 2.3

Task

Coal with the composition of 79 % C, 4.5 % H, 1 % S, 5.6 % O, 1.4 % N, 2.5 % W is

burnt with 20% air excess. Determine the adiabatic flame temperature.

Solution

The procedure for the adiabatic flame temperature determination goes as follows:

a) determination of the fuel net calorific value

b) determination of the volume and composition of moist flue gasses for conditions n = 1

c) determination of fresh flue gas enthalpy

d) determination of a temperature interval in which the adiabatic flame temperature

occurs

e) specification of flue gas enthalpy depending on the flue gas chemical composition

f) interpolation in the specified interval and determination of the adiabatic flame

temperature

ad a)

The net calorific value is determined according to equation (2. 2). After proper substitution

and calculation, the net calorific value is 31 436 kJ∙kg-1

ad b)

Energetické zdroje – paliva a jejich vlastnosti

18

The calculation of combustion is performed on the basis of stoichiometric equations (2.10) to

(2.18) in accordance with Chapter 2.2

- a minimum amount of combustion oxygen Omin

OSHCmin32

4,22

32

4,22

2

2,11

12

4,22wwwwO

after substitution

056,032

4,2201,0

32

4,22045,0

2

2,1179,0

12

4,22min O = 1.694 m

3∙kg

-1

- determination of the particular components of flue gas

CO2 volume in the flue gas

CCO212

4,22wV

after substitution

4746,179,012

4,222 COV m

3∙kg

-1

H2O volume in the flue gas

5351,0025,018

4,22045,0

2

4,22

18

4,22

2

4,22WH2H2O wwV m

3∙kg

-1

SO2 volume in the flue gas

007,001,032

4,22

32

4,22SSO2 wV m

3∙kg

-1

N2 volume in the flue gas

3853,6176,3694,1014,028

4,22

21

79

28

4,22minNN2 nOwV m

3∙kg

-1

O2 volume in the flue gas

1minO2 nOV

because n=1, the oxygen volume in the flue gas is zero

- the total volume of the flue gas

402,8N2SO2H2OCO2

vlh

sp VVVVV m3∙kg

-1

The combustion calculation can be performed into the shown combustion table 2.2.

ad c)

The fresh flue gas enthalpy is defined by a ratio of the fuel net calorific value to the generated

flue gas volume:

57,3741402,8

436 31vlh

sp

i V

Qisp kJ∙m

-3

ad d)

The temperature interval, in which the flame temperature can be found, is specified in the

lecture notes Bálek, S. Thermal–technical tables and diagrams on page 26. The flue gas

enthalpy of 3 741.57 kJ∙m-3

value is between 2200 to 2300°C temperatures.

ad e)

Exact specification of the flue gas enthalpy for temperatures 2200 to 2300°C depending

on the chemical composition of the given fuel flue gas is necessary, because the used table is

Energetické zdroje – paliva a jejich vlastnosti

19

valid for the standard fuel, the composition of which can differ substantially from the

specified one.

Use the relation:

2200

N2N2

2200

SO2SO2

2200

H2OH2O

2200

CO2CO2vlh

sp

2200

sp

1iViViViV

Vi

After the substitution, when the values of the partial enthalpies of flue gas components

can be read in the same tables:

402,8

12200

sp i 68,37466,33083853.62,6439007,044105351,09,53894746,1 kJ.m-3

Having compared this obtained result with the fresh flue gas enthalpy in point c), it is

evident that the obtained result has a higher value than the fresh flue gas enthalpy isp,

therefore this value is considered a value limiting the interval for determination of the

adiabatic flame temperature from above. The lower limit of the interval is 2100 °C. For this

temperature the flue gas enthalpy is determined in the same way as for 2200 °C temperature.

The result is the value 2100

spi = 3560 kJ∙m-3

.

ad f)

The adiabatic flame temperature of the given coal occurs between temperatures 2100 °C

to 2200 °C. For both of these temperatures the related flue gas enthalpies 2100

spi and 2200

spi were

calculated. These values are used for interpolation within the specified temperature interval

and the flue gas enthalpy value isp = 3741.57 kJ∙m-3

is matched with a relevant temperature,

i.e. the adiabatic flame temperature.

Result

The adiabatic flame temperature of the coal of the given composition is 2197 °C.

Primary, secondary, synthetic fuel. Fossil fuel energy, traditional fuel energy, nuclear

energy, energy from renewable resources. Fuel chemical composition. Gross calorific value

and net calorific value of fuel. Lattice equations. Balance thermal equation. Adiabatic,

theoretical, actual flame temperature. Pyrometric effect. Complete, incomplete, mixed

combustion of fuel. Oxidizing agent. Oxidation. Exothermic reactions. Combustion air.

Excess air factor. Theoretical, actual consumption of the combustion air. Minimal

consumption of the combustion oxygen. Flue gas composition. Combustion control.

Questions for Chapter 2

1. What kinds of energy resources do you know?

2. What is fuel?

3. What are basic properties of fuels?

4. Which components do solid and liquid fuels contain, what is their specific unit?

5. Which components does gaseous fuel contain?

Summary of terms of Chapter 2

Energetické zdroje – paliva a jejich vlastnosti

20

6. Define gross calorific value and net calorific value. How do they differ, how can they be

determined?

7. At what conditions can the adiabatic, theoretical and actual flame temperature be determined?

What significance has a pyrometric effect?

8. Why is fuel heating without air intake performed? Which fuels are advisable for this process?

9. What kind of process is fuel combustion, what are necessary conditions for its course?

10. What can be considered an oxidizing agent? Which one is the most frequently used in operation?

11. What types of combustion processes can occur?

12. What does the excess air factor mean and what values can it take?

13. How can you determine the combustion air amount?

14. How can you determine the generated flue gas volume and composition?

15. What is the combustion control, what methods can be used and on what principle are they based?

Ohřev materiálu

21

3. HEATING OF MATERIALS

Time needed for the study: 9 hours

Objective: After studying this paragraph a student will be able to

Define the external and internal heat transfer, which occurs during material heating in

a furnace device, define a charge in term of temperature field formation

Describe modes of heating for thin and thick objects

Solve a heating period time, temperature distribution in an object, impacting thermal

flow and the furnace temperature

Lecture

The purpose of heating is to ensure demanded temperature in the heated material. At the

same time the allowable inhomogeneity of the temperature field across the material cross

section and minimal changes in the chemical composition (chemical composition e.g. in

surface layers) must be maintained and the material compactness must be preserved. The

economical point of view is of no less importance; heating has to run with an optimal amount

of the demanded energy for the given technological process and has to ensure observance of

emission factors pursuant to the current legislation at the same time.

Determination of technical possibilities and permissible heating velocities depends on

physical and mechanical properties of the heated material. Physical properties influence the

heat propagation through the material. Mechanical properties are important for calculations of

heating processes, where thermal stress can occur in materials.

Changes in temperature fields during heating initiate changes of these physical and

mechanical properties, volume propagation occurs, or changes in structure and phase occur in

some cases. An extent of these changes is determined by heating conditions.

Physical properties affecting a heating procedure are thermal conductivity coefficient

λ (W·m-1

·K-1

), specific heat capacity cp (J·kg-1

·K-1

), density ρ (kg·m-3

), temperature

conductivity coefficient a (m2·s

-1), heat absorbing capacity coefficient b (J·m

-2·s

-0.5·K

-1).

Mechanical properties include linear thermal expansion coefficient β (K-1

), modulus of

elasticity E (N·m-2

), tensile strength limit σpt (N·m-2

), relative elongation ε (%), relative

reduction φ (%).

Cooling is opposite to heating. Relations describing heating of materials can be also used

for cooling, however, this phenomenon runs in the opposite direction, thus from a higher

temperature to a lower one.

Heating is a non-stationary process. It is a complicated procedure, involving an external

heat transfer and internal heat transfer. The external heat transfer determines the thermal

energy amount from the surroundings (from flue gasses, from the brickwork, from the charge

around) impacting onto the heated charge surface. In furnaces, this is heat transfer from flue

gasses onto the heated material surface. Density of the thermal flow impacting onto the charge

needs to be solved. The internal heat transfer involves the thermal energy propagation through

the heated material. A relation of time to temperature, possibly a formed temperature field,

needs to be solved. The temperature distribution across the heated material cross section is

Ohřev materiálu

22

determined by the internal to external thermal resistance ratio. This ratio is the Biot Number.

Its actual numerical value determines the temperature distribution in a heated charge. Based

on this ratio value we can presume, whether the heated material temperature across the cross

section will change or not.

3.1 External heat transfer

The thermal energy transfer from the outer atmosphere (from the furnace brickwork

surface and from the surface of the charge around) onto the heated material surface is realized

through the external heat transfer. As to furnace systems, the atmosphere surrounding the

charge consists of flue gasses flowing around the charge and transferring heat to the charge

through a combination of convection and radiation.

The convection mode, which is assumed up to the work environment temperature 900 °C,

is characterized by a total heat transfer coefficient , which can be determined by a

calculation or application of empirical relations (according to a type and temperature of the

thermal equipment).

Radiation mode, which is assumed within a range of temperatures higher than 900 °C, is

characterized by a furnace constant pecc , which can be determined according to the following

relation:

)1(1

)1(..

mmm

mmm0pec0pec

CCC (1) (3.1)

where C0 is constant (W·m-2

·K-4

)

εpec integral emissivity of a furnace (1)

εm integral emissivity of a heated material (1)

φmm directional gain (1)

The radiation energy from flue gasses impacts not only the charge, but also the inner

surface of the furnace brickwork. In this case this is a heat exchange between two grey

surfaces, whereas a configuration of these surfaces also influences the resulting external

thermal flow. The impacting radiation energy is not only absorbed by these surfaces, but is

also reflected back into the furnace workspace, or more precisely to both of the grey surfaces.

A part of this energy is again kept in flue gasses. Partial thermal flows – impacting, reflected,

absorbed – of different intensities are gradually formed in the radiation process.

All thermal flows must be included in the thermal balance of the furnace atmosphere:

impacting, absorbed, reflected by flue gasses, brickwork, material, including the convective

thermal flow.

The relative position of grey surfaces (brickwork, material) is characterized by directional

gains. Their number can be derived from the number of grey surfaces. In the case of two grey

surfaces the number of directional gains is determined by number 4. These are φmm , φmz ,

φzm , φzz. These directional gains can be expressed by means of the so-called independent

directional gain, which in the case of 2 grey surfaces is only one and for availability of

determination this is particularly the directional gain φmm. The relation for its determination

is:

zm

mmm

SS

S

(1)

Ohřev materiálu

23

where Sm is material surface in a contact with flue gasses (m2)

Sz brickwork surface in a contact with flue gasses (m2)

If a reciprocity principle and a closeness principle are used in the expression of the other

three directional gains, the other directional gains take the following forms:

mmmz 1 (1) (3.2)

mm

z

mzm 1

S

S (1) (3.3)

mm

z

mzz 11

S

S (1) (3.4)

This way the configuration of both the grey surfaces is defined through a single one

independent directional gain φmm.

The external specific thermal flow, characterizing the external heat transfer, can be simply

written as a sum of the resulting radiative and convective specific thermal flows, then:

kzΣ qqq (W·m-2

) (3.5)

However, this simplicity is only apparent, since the relation for the resulting radiative

thermal flow and convective thermal flow is solved as described below:

Radiation in the furnace area

The radiative thermal flow impacting the charge is determined as the specific thermal

flow impacting on a unit of the charge surface, denominated as qz:

4

m

4

sp

m

sp

Σz100100

TTcq

(W·m

-2) (3.6)

mΣ 67,5c (W·m-2

·K-4

) (3.7)

where qz is specific radiative thermal flow (W·m-2

)

βsp, βm,, χ substitution members (1)

Tsp flue gas temperature (K)

Tm material temperature (K)

The substitution members include an influence of the configuration of surfaces (grey

surfaces) involved in the radiation heat transfer, their integral emissivity, magnitude and

integral emissivity of flue gasses. After adaptations, they can be expressed with the following

relations:

spmmspmm

sp

m 1111

(1)

Ohřev materiálu

24

spmm

sp

mmpm

mmmspm

111111

11

s

(1)

mmmmmspm

msp 11 (1)

where εsp is integral emissivity of flue gasses (1)

εm integral emissivity of material (1)

φmm directional gain (1)

ω surface ratio Sm /Sz (1)

The integral emissivity of material is determined by radiation properties of the material

surface. Integral emissivity values for various materials are given in the thermal–technical

tables. The integral emissivity of flue gas involves gaseous components of flue gas, which

have an asymmetrical molecule, such as CO, CO2, SO2, H2O etc. The integral emissivity of

these components is dependent on the partial pressure of the component, flue gas temperature

and the so-called radiative mean beam length (MBL). For an actual gaseous radiative

component of flue gas the related value is determined by means of the thermal-technical

tables. The mean beam length is a ratio of a flue gas volume to a surface determining this

volume. If partial integral emissivities of radiative components of flue gasses are determined

(e.g. εH2O, εCO2 …), the following relation (3.8) is one of possibilities for the flue gas integral

emissivity determination.

ΔH2OCO2sp (1) (3.8)

∆ε member is a correction factor for overlapping of spectral bands of particular gases. It

needs not to be determined in technical calculations, because its value does not affect the

result over the desired value of the calculation accuracy. The correction factor β makes

provision for an influence of a partial pressure of water vapour in flue gasses. This value is

also determined from the respective diagrams.

Convection in a furnace area

The convective thermal flow qk impacting on a charge is determined as the specific

thermal flow impacting on a unit of the charge surface:

mspkk ttq (W·m

-2) (3.9)

where qk is convective specific thermal flow (W·m-2

)

αk convective heat transfer coefficient (W·m-2

·K-1

)

tsp flue gas temperature (°C)

tm material temperature (°C)

The convective heat transfer coefficient can be determined from the criteria equation for

flue gas flowing in a furnace system. A form of criteria gives relation (3.10):

Nu = 0.032·Re0,8

(1) (3.10)

Ohřev materiálu

25

In this equation the Nusselt and Reynolds criterion is specified. If these criteria are

expressed through relevant physical quantities, the relation for the convective heat transfer

coefficient in flue gasses can be determined by the following expression (3.11):

0,2

h

0,8

tsp,

0,8

tsp,

tsp,

k 032,0d

w

(W·m

-2·K

-1) (3.11)

where λsp,t is flue gas thermal conductivity coefficient at the flue gas temperature

(W·m-1

·K-1

)

νsp,t flue gas kinematic viscosity at the flue gas temperature (m2·s

-1)

dh hydraulic diameter (m)

The resulting convective thermal flow equals to the product of a specific convective

thermal flow (see equation (3.9)) and a surface area of the charge being in a contact with flue

gas.

Resulting equation for the external heat transfer

The total external thermal flow impacting on the charge is determined by a sum of the

radiative and convective thermal flow. A total surface area Sm, coming into a contact with flue

gas, is considered, too. Such a determined external thermal flow is the thermal energy heating

the charge in a furnace and developing the demanded temperature distribution. Its value is

determined by relation (3.12):

mmspkm

4

mm

4

sp

spΣ100100

67,5 SttSTT

P

(W) (3.12)

In this equation two more members should be given, which result from the resulting

balance of partial thermal flows at heat transfer in a furnace area during heating. This is

convective heat, which transfers into the brickwork, and heat losses due to convection through

the brickwork. General experience have shown that these values, expressed as an absolute

value, are in principle the same size, therefore they are not given in equation (3.12).

3.2 Internal heat transfer

The internal heat transfer, which is realized in the charge through convection, can be

solved, if the external heat transfer is described. This also co-decides about a temperature

increase in a charge in the course of time. A fact of a temperature field occurring or not

occurring across the charge cross section decides about a selection of an ensuing

mathematical solution. In order to select a proper mathematical procedure for the convective

heat transfer in a charge, a ratio of the external to internal thermal resistance needs to be

known. According to a value of this ratio, a charge can be distinguished as a thin or thick

object from the thermal-technical point of view.

Then, the next step when solving a charge heating is to determine, whether the charge

will behave as a thin or thick object during heating.

3.2.1 Classification of a charge as a thin or thick object

A relation of temperature, possibly a temperature distribution in the area (temperature

field), and time is observed for a calculation of heating. Whether in the specified time in the

Ohřev materiálu

26

entire volume the temperature of the same value will be on the surface tp as well as inside the

centre tc, i.e.

t = tp – tc = 0

or a temperature gradient (temperature field), i.e.

t = tp – tc 0

this is determined by a ratio of the object thermal resistance b/ to the external thermal

resistance 1/αΣ. This ratio is the known Biot Number (Bi), expressed by equation (3.13):

Bib

b

Σ

Σ

1 (1) (3.13)

where αΣ is combined external heat transfer coefficient (W·m-2

·K-1

)

λ thermal conductivity coefficient (W·m-1

·K-1

)

b calculation thickness (m)

The calculation thickness b depends on an object physical thickness, its shape and a

heating method (single-sided, double-sided).

If the calculated value of Bi Number is lower than 0.25, the charge can be assessed as a

thin object, which will have within the entire volume only one temperature value in the

specified time during heating. If the calculated value of Bi Number is higher than 0.5, the

charge can be assessed as a thick object. In this case a temperature field will be formed in the

charge cross section during heating. The so-called transition region ranges between 0.25 to

0.5.

For furnaces, where radiative heat transfer (the so-called radiation mode) prevails, a

proportion of convection is very low, cannot be determined. In this case a charge type is

assessed using the Stark’s criterion. A relation for this criterion is given by equation (3.14):

bT

CSk 3

pec8

pec

10 (1) (3.14)

A furnace constant can be expressed e.g. by expression (3.1).

3.2.2 Heating of thin objects

Three types of heating are performed in operation:

A. The furnace temperature is constant

B. The thermal flow impacting on the heated material is constant

C. The furnace temperature is a linear function of time

A type of heating, when the furnace temperature is constant during the whole heating,

is used very often. To determine the time needed for heating it is assumed that the amount of

the heat energy supplied by the external heat transfer develops a respective enthalpy

increment in the charge. The determining factor is a work atmosphere temperature, whether

heating runs in the convection or radiation mode. If heating occurs in the convection region,

the equality between the impacting thermal energy per time interval dτ and the appropriate

enthalpy increment can be expressed by equation (3.15):

Ohřev materiálu

27

tcVStt dd)( pmmpecΣ (J) (3.15)

where αΣ is external heat transfer coefficient (W·m-2

·K-1

)

tpec work atmosphere temperature (°C)

t temperature of the heated material (°C)

Sm material surface in a contact with flue gasses (m2)

τ time (s)

Vm heated material volume (m3)

ρ heated material density (kg·m-3

)

cp specific heat capacity (J·kg-1

·K-1

)

As the solution goes in a very narrow interval, Σ, cp, can be considered a constant in

this interval and the equation can be solved by a separation of variables. A relation for a

calculation of the heating time can be determined by the subsequent integration:

kpec

0pec

Σ

p

1

k lntt

ttc

k

b

(s) (3.16)

where t0 is heated material temperature at the beginning of heating (°C)

tk heated material temperature at the end of heating in time τk (°C)

In formula (3.16) the ratio of Vm volume to Sm surface was replaced by:

1m

m

k

b

S

V

where k1 is the so-called shape coefficient, which takes values from 1 to 3, whereas value 1

applies for an object of a shape of a plate of unlimited dimensions, value 2 applies for a

cylinder of unlimited dimensions, value 3 for spherical shapes. For other charge shapes it is

determined on the basis of the thermal-technical tables depending on the heated object

geometry. Parameter b is the above mentioned calculation thickness of material.

Equation (3.16) is called a convection formula for a calculation of the heating time. This

is a base for a calculation of the temperature at the end of heating, equation (3. 17):

p

k

cb

k

pecpecketttt

..

..

0

1

.)(

(°C) (3.17)

For integration of equation (3.15), , cp, , were considered constant, as the solution

went in a very narrow temperature interval. Heating of material lasts for a substantially longer

time, therefore these parameters must be determined for a mean temperature of the heated

material during heating.

k

0k

d1

tt (°C) (3.18)

If we substitute equation (3.17) for tk in the equation (3.18), then the material mean

temperature is determined by a relation:

Ohřev materiálu

28

kpec

0pec

0kpec

lntt

tt

tttt

(°C) (3.19)

A more precise determination of the heating time is possible by dividing the whole

heating period to more intervals, in which partial heating times are determined. The resulting

heating time is a sum of these partial time periods.

If in equation (3.15) the impacting external thermal energy is expressed by a radiation

relation, this equation takes the form:

TcVSTT

C p dd100100

mm

44

pec

pec

(J) (3.20)

where Cpec is furnace constant (W·m-2

·K-4

)

Tpec work atmosphere temperature (K)

T temperature of the heated material (K)

Sm material surface in a contact with flue gasses (m2)

τ time (s)

Vm heated material volume (m3)

ρ heated material density (kg·m-3

)

cp specific heat capacity (J·kg-1

·K-1

)

Using the same assumption as for equation (3.15), a relation for the heating time called

also the radiation formula is determined:

0k3

pec

8

pec1

10

Tck

cb p

k (s) (3.21)

Function () has a form:

arctg

2

1

1

1ln.

4

1)(

For a type of heating, which is characterized by a constant impacting thermal flow q

onto the heated material surface, the total heating time is determined according to the relation:

0k

1

k ttqk

cb p

(s) (3.22)

The third method for heating a charge of a thin object type in operation is a heating

process with a constant increase of the furnace temperature, so the furnace temperature is a

linear function of time. The furnace temperature can be expressed by a relation:

tpec = tpec,0 + Z (°C) (3.23)

where tpec,0 is furnace temperature at the beginning of heating (°C)

tpec furnace temperature in time (°C)

Z temperature increase velocity (K·s-1

)

Ohřev materiálu

29

In this heating a charge temperature in the course of time is observed. To derive this

relation, equation (3.15) can be used, in which the given furnace temperature is replaced by

expression (3.23). After the adaptation, this equation can be re-written into a form:

d

d1Σpec,0

t

cb

ktZt

p

(K.s

-1) (3.24)

where t is charge temperature in time (°C)

If a substitution is implemented:

pcb

kA

1Σ (s-1

)

equation (3.24) takes the form:

0d

dpec,0

ZtAAt

t,

the solution of which is a relation

t = tpec,0 + Z · + A

Z – (tpec,0 - t0 + A

Z ) · exp (A·) (°C) (3.25)

Thermophysical parameters are determined for a material mean temperature during

heating (equation (3. 26)) by an iterative method:

k

0kkpec,0

2

A

ttZtt (°C) (3.26)

3.2.3 Heating of thick objects

In a charge, which refers to a thick object in its character, temperature fields across the

charge cross section occur during heating. A temperature change in space and time occurs.

This phenomenon is described by a Fourier equation of nonstationary heat conduction.

The equation has a shape (3.31):

2

2

2

2

2

2

z

t

y

t

x

ta

t

(K·s

-1) (3.27)

where τ is time (s)

t temperature (°C)

x, y, z coordinates (m)

a temperature conductivity coefficient (m2·s

-1)

For this equation to be solvable, conditions for the solution uniqueness has to be

defined and exactly specified. The uniqueness conditions involve a geometrical, physical,

initial and boundary condition (see e-learning lecture notes Macháčková A. Heat Transfer and

Fluid Mechanics).

Ohřev materiálu

30

According to the specified types of an initial and boundary condition, various heating

processes may occur. In operation, 4 heating methods for thick objects are performed the most

frequently.

A. The surface temperature is constant

B. The surface temperature is a linear function of time

C. The thermal flow on the material surface is constant

D. The furnace temperature is constant

To solve heating processes, the following has to be determined:

1. Temperature distribution in space and time

2. Related specific thermal flow

3. Related furnace temperature

Results of the solution of the particular heating, denominated as A, are shown in Figure

3.1. This heating is often realized in an equalization phase of heating in multi-zone furnaces.

The Figure shows a relation of temperature and a specific thermal flow on the heating time.

Curves marked as tc and Δt refer to the temperature distribution in the material. Curve tc refers

to the temperature change in the heated material centre, which increases gradually, while

decreasing a difference in a temperature gradient across the cross section down to a value

permissible for following procedures with the charge (for example forming). The time needed

for achieving the demanded temperature equalization is given on the horizontal axis.

In order to achieve the demanded temperature distribution in a heated charge, values of

the specific thermal flow q and related furnace temperatures tpec in the course of time have to

be determined by a calculation. The progression of these two quantities is shown in the upper

part of the graphic dependence (Fig. 3.1), the furnace temperature decreases according to the

external heat transfer laws (see Chapter 3.1).

Fig. 3. 1 Heating at the boundary condition of the 1st type

Ohřev materiálu

31

Calculations of heating can be performed by analytical methods or numerical methods.

To solve the heating shown in Fig 3.1, an analytical method is used, consisting in a solution of

the Fourier differential equation for one-way heat conduction in the direction of x axis with

particular conditions of uniqueness. The Fourier equation (3.27) has the following form:

2

2

x

ta

t

(K.s

-1) (3.28)

Uniqueness conditions for a solution of equation (3. 28)

The physical condition characterizes the physical principle of the heated material and it is

defined by temperature relations of the main physical parameters of the heated material, i.e.

thermal conductivity coefficient λ, specific heat capacity cp and density ρ. They are contained

in equation (3.28) in temperature conductivity coefficient a.

The geometrical condition defines an object shape. For this particular case a slab heated

from both sides has been chosen; its calculation thickness b is a half of its physical width. We

can assume that this is an object of a shape of a plate of unlimited dimensions.

The initial condition characterizes thermal conditions at the beginning of heating in the

chosen time τ = 0. For this case a parabolic temperature distribution across the cross section is

chosen, which can be expressed mathematically by the equation of a parabola 200

c

0 Δ ttt (°C)

η symbol denominates the so-called dimensionless coordinate, which localizes

geometrically a point in the direction of x axis, in which the particular temperature is

calculated. It is determined by x/b ratio.

The boundary condition is defined by a constant temperature on a surface of the heated

material (charge).

Fig. 3.2 shows this case schematically. The initial parabolic temperature distribution in

the material in time τ = 0 is depicted here. The surface temperature remains constant during

the whole heating phase. Fig. 3.2 depicts a demand for heating, i.e. the determination of a

time demanded for equalizing the

temperature in the centre to the prescribed temperature in relation to the surface temperature,

thus decreasing the initial temperature difference Δt0 to the temperature difference permissible

(Δt permissible) for subsequent technological operations.

After substituting the above mentioned uniqueness conditions into the equation of one-

way propagation of heat energy through a thick object depending on time and place (x axis)

into equation (3.28), this takes the following form (3.29):

Ohřev materiálu

32

Fig. 3. 2 Diagram for a solution of a heating procedure with a constant surface

temperature

Fob

xtttt nn

n

n n

2

1

13p

0

cp expcos14

(°C) (3.29)

where

2

12nn (1)

The given infinite line involves all members, the value of which is mostly higher than 10-

5. The Fourier criterion expresses the time in which the related temperature t is determined,

occurring in the direction of the heat energy propagation in a point x. This equation (3.29)

clearly specifies the demanded conditions for defining the uniqueness of the given heating.

For practical and fast calculations the infinite line is replaced by F function, in this case dF1 function

Fob

xfFFo

b

x d

nn

n

n n

;expcos14

1

2

1

13

(1) (3.30)

A combination of equation (3.29) and (3.30) results in equation (3.31):

Fo

b

xF

tt

tt;d

1

p

0

c

p (1) (3.31)

Again, equation (3.29) expresses the temperature distribution in time (Fo) and point (x/b).

Its graphic depiction is shown in Figure (3.3).

The above mentioned equations (3.29) and (3.31) are valid for objects of shapes of a

plate. The dependence of temperature to time for objects of cylindrical shapes can be derived

in the same way. The graphical depiction of this dependence is shown in Fig. 3.4.

Ohřev materiálu

33

Fig. 3. 3 Graphical expression of equation (3.35), function dF1 for an object of a shape of

a plate

Fig. 3. 4 Graphical expression of equation (3.35), function vF1 for an object of a

cylindrical shape

Determination of the thermal flow density (2nd

part of the calculation), which determines

this temperature distribution in the heated material, is based on equality of the external and

internal thermal flow on the heated material surface. For one-way propagation of the thermal

energy:

x

tq

(W·m

-2) (3.32)

Ohřev materiálu

34

Partial derivation is determined using relation (3.29). After substituting, equation (3. 32)

takes the form:

1

2

2

0

cp exp4

n

n

n

Fottb

q

(W·m

-2) (3.33)

If in equation (3.33) the infinite line is replaced by function dG1 , equation (3.33) can be

written in a form:

FoGttb

q d

1

0

cp

(W·m-2

) (3.34)

dG1 function is graphically processed in Fig. 3.5 and can be read from this graph for the

given time (Fo criterion value).

Fig. 3. 5 Function dG1 for a calculation of the thermal flow density (blue curve refers

to a charge of a cylindrical shape)

The last 3rd

part of the calculation determines the furnace temperature for ensuring the

demanded heating. Its determination is based on the known density of the thermal flow in the

course of time (2nd

part of the calculation). A decisive factor is a work atmosphere

temperature.

For the convection mode, relation (3.35) can be used:

ppecΣ ttq (W·m-2

) (3.35)

For the radiation mode, the following relation can be used:

4

p

4

pec

pec100100

TTcq (W·m

-2) (3.36)

If the calculation of heating is performed as described in the above mentioned procedure,

the calculated values can be graphically plotted as depicted in Figure 3.1.

Ohřev materiálu

35

Solved tasks

Task 3.1

Task

A plate of 40 mm thickness from carbon steel containing 0.1% C has to be annealed in a

chamber furnace with 760 °C temperature. The plate with an initial temperature of 20 °C is

placed on rests in the furnace. Determine the time demanded for heating of the plate to

temperature of 710 °C.

Solution

Considering the work atmosphere temperature, heating will be performed in the

convection mode. For the chosen calculation procedure, Bi criterion has to be determined in

order to assess the charge as a thick or thin object. For Bi criterion, the external heat transfer

coefficient needs to be known. Its value is determined from the empirical relation. Physical

parameters of steel containing 0.1% C can be found in thermal-technical tables. If Bi criterion

has a value lower than 0.25, a formula for a thin object can be used to calculate the heating

time.

The external heat transfer coefficient determination

5,175,11100

105,0

3

pec

kz ažT

= 0.105 [(273+760)/100]

3 +14 = 129.7 W·m

-2·K

-1

Determination of Bi criterion according to equation (3.13)

Thermophysical quantities are dependent on temperature, therefore they have to be

determined for the material mean temperature, see equation (3.19):

kpec

0pec

0kpec

lntt

tt

tttt

,

into which temperature values defined in the task are to be substituted, i.e. tpec = 760 °C,

tk = 710 °C, t0 = 20 °C. The mean temperature 504 °C is determined by the calculation. For

this temperature and steel chemical composition, the following values of thermophysical

parameters have been read in the thermal-technical tables:

λ = 40.3 W·m-1

·K-1

cp = 562 J·kg-1

·K-1

ρ = 7690 kg·m-3

Bi criterion

21044,63,40

02,07,129

bBi

Bi criterion value determines that this is heating of a thin object and the related formula

can be used – equation (3.16)

Heating time determination

Ohřev materiálu

36

s7961710760

20760ln

7,1291

562690702,0ln

pec

0pec

Σ1

k

p

ktt

tt

k

cb

Result

The plate in the chamber furnace with a constant temperature of 760 °C will be heated

from the initial temperature of 20 °C to the demanded temperature of 710 °C in 29.9 min.

Summary of terms of Chapter 3

Heating of a charge, physical properties, mechanical properties. External heat transfer,

furnace constant, integral emissivity, directional gain, radiation heat transfer, convection heat

transfer, convective mode, radiative mode. Total external heat transfer coefficient. Internal

heat transfer. Thin object, thick object, Bi criterion, Sk criterion, convection formula,

radiation formula, mean temperature of heating, heating modes, Fourier equation, solution

uniqueness conditions, temperature field in a charge, thermal flow density, furnace

temperature.

Questions for Chapter 3

16. What is a purpose of heating of a charge and what has to be respected during heating?

17. What is cooling of a charge and in which technologies does it occur?

18. Define the external heat transfer. Which thermal flows occur in the furnace external atmosphere

above a charge?

19. What does the external heat transfer coefficient express and which components does it consist of?

20. What is a characteristic of the convective heating mode and which quantities take a priority part?

21. What is a characteristic of the radiative heating mode and which quantities take a priority part?

22. What is a form of a resulting equation of the external thermal flow?

23. Define the internal heat transfer.

24. How do the so-called thin objects behave during heating? Which physical parameters are

decisive for it?

25. How do the so-called thick objects behave during heating? Which physical parameters are

decisive for it?

26. What heating modes are used for heating of thin objects?

27. Define a relation for heating time at a constant furnace temperature, constant thermal flow, at a

furnace temperature, which is a linear function of time.

28. What is a Fourier equation for a nonstationary heat transfer? Define its form and conditions of

uniqueness of a solution.

29. What are types of heating of the so-called thick objects used in operation?

30. Analytical solution of a temperature distribution in a charge depending on the heating time.

31. Analytical determination of the external thermal flow and furnace temperature during heating of

the so-called thick object.

Výměníky

37

4 HEAT EXCHANGERS

Time needed for the study: 7 hours

Objective After studying this paragraph a student will be able to

Define heat-saving due to implementation of a heat exchanger, the technology

effectiveness enhancement

Describe a heat exchanger function

Solve basic calculations related to an exchanger design

Lecture

Heat exchangers can utilize the so-called waste energy – a part of heat not used– going

out from a heat device workspace. The flue gas heat can be used for preheating of combustion

components (air, fuel), for heating of water, indoor heating, possibly for transformation to a

different kind of energy. Heat exchangers can be divided to two basic categories, namely

recuperative type and regenerative type exchangers.

Recuperators give the flue gas heat over to a colder heated medium through a partition

wall by a combined heat transfer. Both media – hot (flue gas) as well as cool, which will be

heated (air, water, fuel) flows through this device simultaneously.

Regenerators heat a cool medium (mostly air) by flue gasses by means of ceramic

refractory material, which is placed inside the exchanger. This is always a pair device.

Implementation of exchangers at furnaces results in fuel consumption reduction, flame

temperature increase and equipment efficiency increase.

4.1 Fuel saving

Determination of fuel saving is based on a balance equation of the particular thermal

equipment. If possible heat from exothermic reactions is neglected, then heat on the inlet side

comprises chemical heat of fuel Qch, preheating of combustion air Qvzd and preheating of

gaseous fuel Qvzd. This inlet heat is consumed in components, which are on the outlet side of

the balance equation. To be specific, this depends on realization of the given technology Quž,

a certain part of the heat is consumed by workspace losses Qztr and the rest of the heat leaves

in flue gasses Qsp. In this case the thermal balance equation has a form (4.1):

Qch + Qp + Qvzd = Quž + Qztr + Qsp (W) (4.1)

The balance equation is used for determination of fuel saving as a result of the

implementation of a heat exchanger. Chemical heat of fuel is expressed:

Qch = B·Qi (W) (4.2)

where B is fuel consumption (kg·s-1

, m3·s

-1)

Výměníky

38

Chemical heat chQ can be determined by solving equations (4.1) and (4.2), by solving

equation (4.3) in a case the thermal equipment is equipped with an exchanger, by equation

(4.4) in a case the equipment is not equipped with an exchanger.

spspvzdskutpi

ztružich

iViLiQ

QQQQ

(W) (4.3)

spspi

ztruži

´

chiVQ

QQQQ

(W) (4.4)

Saving is then determined by a relation:

100ch

ch

´

ch

Q

QQú (%) (4.5)

By substituting relations (4.3) and (4.4) into equation (4.5), the relation for calculating the

saving resulting from the implementation of heat recuperation takes a form (4.6):

100spspvzdskutpi

vzskutp

iViLiQ

iLiú (%) (4.6)

Equation (4.6) can be modified to a form:

100spr

č

sp

r

iii

iú (%) (4.7)

where č

spi is fresh flue gas enthalpy (J·m-3

)

ir recuperated flue gas enthalpy (J·m-3

)

The saving is only meaningful to the degree of recuperation 25% (see Fig. 4.1). Then

purchase costs exceed.

Fig. 4. 1 Relation between necessary costs for an exchanger, savings and a degree of

recuperation

1 – fuel saving, 2 – purchasing and operating costs

Výměníky

39

(Source: Příhoda, M., Hašek, P. Metallurgical furnaces)

4.2 Flame temperature increase

Thermal procedures occurring at elevated flame temperatures (e.g. in melting furnaces)

demand recuperation and enhancement of the actual temperature by gaining components Qp,

Qvzd, see equation (2.13).

Owing to preheating, fuels with low net calorific value, which are often a by-product of

particular technologies (e.g. blast furnace gas), can be also burnt successfully.

4.3 Recuperators

There are various types of recuperators. They are mostly categorized according to a partition

wall material between hot (flue gas) and heated medium (e.g. air) as metal and ceramic types,

according to a type of the prevailing heat transfer process (radiative, convective) and a system

of flowing (concurrent, countercurrent).

4.4 Thermal calculation of a recuperator

In order to determine a size of a heat-transfer surface S the basic equation for an

exchanger (4.18) can be used.

The hot medium is the flue gas letting-out of the furnace, which has to heat the combustion air

letting-in to the furnace burner.

S

0dΔ AtkQ (W) (4. 8)

where Q is amount of transferred heat in the exchanger (W)

k heat passage coefficient (W·m-2

·K-1

)

∆t temperature gradient between flue gas and air (K)

The temperature gradient between flue gas and air along the heat-transfer surface is

determined on the basis of knowledge of temperatures of flowing media as a mean

logarithmic temperature gradient, equation (4.9):

AtS

t dΔ1

Δ

S

0

(K) (4.9)

After substituting equation (4.9) into equation (4.8), the latter takes a form:

StkQ (W) (4.10)

Výměníky

40

concurrent

countercurrent

Fig. 4. 2 Change of temperatures of flue gas and air when passing through a recuperator

The following relation is a solution of equation (4.9)

S

0

S0

lnt

t

ttt

(K) (4.11)

where for the concurrent (see Figure 4.2): ´

vzd

´

sp0 ttt

´́´́

vzdspS ttt

and for countercurrent ´́

vzd

´

sp0 ttt

´

vzd

´́

spS ttt

If there is a crosscurrent flow, the mean logarithmic gradient determined by equation

(4.11) needs to be corrected.

The heat passage coefficient is a coefficient of the combined heat transfer. Heat from flue

gas propagates onto a heat-transfer surface by radiation and convection as described in

Chapter 3, through the heat-transfer surface according to convection laws and on the other

side of the heat-transfer surface the heat transfer is determined by a type of a flowing medium.

If air is preheated, then there is only the convective heat transfer.

If the heat-transfer surface is of a planar wall character, the thermal energy propagation

from flue gas to air can be written as follows

vzdsp

111

b

k (m

2·K·W

-1) (4.12)

where αsp is coefficient of heat transfer from flue gas onto a heat-transfer surface

(W·m-2

·K-1

)

αvzd coefficient of heat transfer from a heat-transfer surface into air (W·m-2

·K-1

)

b heat-transfer wall thickness (m)

λ coefficient of thermal conductivity of a heat-transfer wall (W·m-1

·K-1

)

For metallic recuperators it is determined by relation (4.13):

vzdsp

vzdsp

k (W·m

-1·K

-1) (4.13)

The heat passage coefficient value may be influenced by a shaped heat-transfer surface,

for example by ribbing.

A heat-transfer surface may be fouled, which decreases value k and this is corrected by a

corrective coefficient a value of which is determined in accordance with the exchanger

operation time. In operation, this coefficient ranges from 0.7 to 0.95.

Výměníky

41

To determine the total heat-transfer surface, the total amount of transferred heat energy in

the exchanger needs to be known. This can be understood as heat given over by flue gas in the

exchanger, or as heat taken by air in the exchanger. Theoretically, equality between these two

values should apply. In operation, due to leakage of exchangers a heat loss coefficient is

incorporated into the thermal equilibrium equation on the flue gas side:

zspspvzdvzdvzd iiViiV ´́´´́ (W) (4.14)

where Vvzd is volume of air flowing through the recuperator (m3·s

-1)

Vsp volume of flue gas flowing through the recuperator (m3·s

-1)

ivzd´´ air enthalpy on the outlet from the recuperator (J·m-3

)

ivzd´ air enthalpy on the inlet to the recuperator (J·m-3

)

isp´´ flue gas enthalpy on the outlet from the recuperator (J·m-3

)

isp´ flue gas enthalpy on the inlet to the recuperator (J·m-3

)

ηz loss coefficient (1)

The loss coefficient can take values ranging from 0.85 to 0.95.

If the flue gas temperature on the inlet to the exchanger is higher than the heat-transfer

wall material allows, the flue gas dilution must be performed, mostly by adding cool

combustion air Lch. The added air amount is governed by the so-called mixing rule and is

determined:

zřspch VL (m3·s

-1) (4.15)

The dilution coefficient is expressed:

´

vzd

zř

sp

zř

spsp

zřii

ii

(1)

where isp is original flue gas enthalpy (on the inlet to the recuperator) (J·m-3

)

zř

spi enthalpy of flue gas diluted to a permissible temperature (J·m-3

)

´

vzdi enthalpy of the air for dilution (J·m-3

)

4.5 Hydraulic calculation of a recuperator

The hydraulic calculation includes a determination of the total pressure losses of flowing

heat-transferring media and the related determination of actual flow velocities. An increase in

velocities increases the total heat passage coefficient. Therefore high flow velocities can be

desired as to the technological point of view. However, along with the increasing velocity the

pressure loss increases, thus increasing operating costs for the exchanger. A design and

arrangement of an exchanger has to find an optimal ratio between the pressure loss value and

the heat passage coefficient.

A heat exchanger features non-isothermal flow. By this reason, the total pressure loss is

determined by a sum of the pressure loss through local resistances, friction, non-isothermal

flow. A geometrical pressure influence is added due to the flow in vertical parts of an

exchanger. For the total pressure loss the following relation can be written:

pz = pz,t + pz,m + pz,n + pz,g (Pa) (4.16)

Výměníky

42

where pz is total pressure loss (Pa)

pz,t pressure loss by friction (Pa)

pz,m pressure loss through local resistances (Pa)

pz,n pressure loss due to non-isothermal flow (Pa)

pz,g geometrical pressure influence (Pa)

According to the equation of state, at heating of a gaseous heat-transferring medium pz,n >

0, at cooling pz,n <0.

4.6 Types of recuperators

In the industrial operation, there are various kinds of recuperative type exchangers.

Metallic recuperators are preferred for furnace equipment; if preheating to high temperatures

is demanded, ceramic recuperators are built.

Metallic recuperators can work in a convective, radiation – convective, as well as

radiative mode. A mode selection is determined by temperature of flue gas letting out from

the furnace and a requirement for preheating temperature. Metallic recuperators cover cast

iron and steel recuperators.

An example of a cast iron recuperator is shown in Fig. 4.3.

Fig. 4. 3 Cast iron needle type recuperator

(Source: Příhoda, M., Hašek, P. Metallurgical furnaces)

Due to high leakage, steel recuperators are more appropriate. They also incorporate

individual tube elements, which can include straight tubes, loop tubes and fields tubes. On the

basis of technical parameters the demanded number of tubes is assembled into sections of

varied arrangements. Tubes can be arranged in these sections either horizontally or vertically.

Preheating temperature reaches 700 °C, heat passage coefficient up to 45 W·m-2

·K-1

; as a

result of a lower pressure drop the flow velocities can reach 20 m·s-1

for air, 10 m·s-1

for flue

gas.

Cylindrical recuperators working in the radiative mode with an initial flue gas

temperature as high as 1500 °C preheat the combustion air to a range between 400 up to 950

°C. The inner cylinder of a diameter of 0.5 to 3 m is made of a heat-resistant plate. A length

of an exchanger can reach from 1.5 m up to tens of meters. Recuperators of longer lengths are

designed as a bottom part of a stack, where flue gas flows inside a heat-resistant cylinder and

air flows up to a particular height inside an annular area around this cylinder (stack).

Ceramic recuperators, in contrast to metallic ones, work with substantially higher flue gas

temperatures on the inlet. Ceramic elements are connected together to take a shape of tubular

parts. A high quantity of joints causes high untightness of this type of an exchanger. The flue

gas temperature on the inlet can be as high as 1500 °C, which enables combustion air

Výměníky

43

preheating up to 900 °C even at considerable untightness. Regarding the untightness, lower

flow velocities are used - for air 2 m·s-1

, for flue gas to 1 m·s-1

. The heat passage coefficient

reaches up to 5 W·m-2

·K-1

. The pressure loss is c. 100 Pa.

4.7 Regenerators

A type of regenerative exchangers has been implemented on grounds of required high

working temperatures in the furnace workspace. Therefore most of melting devices are at the

same time devices with regenerators, allowing preheating the combustion air to significantly

higher temperatures than with a recuperator. By this the theoretical flame temperature is

increased and actual flame temperature as well.

Despite the fact that there are regenerators with fixed as well as with movable internals –

a heat-transfer surface, the lecture is focused on classic regenerators with fixed grating. The

basic equation of a heat calculation considers a device periodical work and can be written in a

form:

StQ (J·cykl-1

) (4.33)

where QΣ is heat given over to a cool medium per one cycle (J·cykl-1

)

κ coefficient of heat transfer from a hot medium to a cool one (from flue gas to air)

(J·m-2

·K-1

·cykl-1

)

t mean temperature gradient between flue gas and air (K)

S heat-transfer surface (m2)

The heat calculation goes as with a countercurrent recuperator. Temperatures of heat-

transferring media are more or less constant on the inlet into the recuperator, however, they

change according to time (time of flowing) on the outlet. The heated medium – air – gradually

decreases its achieved preheating temperature during a period of grating cooling, while the

hot medium - flue gas – reacts adversely in a heating period. An average value of flue gas

temperature and air temperature on the outlet can be determined from relation (4.34a) and

(4.34b):

0

´́´́ 1dtt spsp (°C) (4.34a)

0

´́´́ 1dtt vzdvzd (°C) (4.34b)

where is a cooling period time (s)

heating period time (s)

Determination of heat transfer coefficient κ from the flue gas to the grating and then to

the air is a complicated thermal – technical calculation. For the determination the following

relation (4.35) can be accepted:

111

0,, mkm

pp

ttcb

tt (m

2·K·cykl·J

-1) (4.35)

where α is heat transfer coefficient from flue gas to grating (W·m-2

·K-1

)

Výměníky

44

α +

heat transfer coefficient from grating to air (W·m-2

·K-1

)

pt average temperature of the grating surface during heating (°C)

pt average temperature of the grating surface during cooling (°C)

kmt , grating temperature at the end of heating (°C)

0,mt grating temperature at the beginning of heating (°C)

b calculation thickness of grating (m)

ρ grating material density (kg·m-3

)

c specific heat capacity of grating material (J·kg-1

·K-1

)

After having performed the thermal calculation, a hydraulic calculation follows.

Solved task

Task 4.1

Task

Determine a heat-transfer surface of a recuperative type exchanger, which will heat

combustion air for a coke-oven gas fired furnace to 550 °C temperature. Flue gas on the inlet

to the exchanger has temperature of 920 °C, air on the inlet to the recuperator has temperature

of 20 °C. The heat passage coefficient has a value of 36 W·m-2

·K-1

, the loss coefficient

ηz = 0.85. The air flow volume in the recuperator is 9.13 m3·s-1, the flue gas flow volume is

10.07 m3·s

-1. The flow system is countercurrent.

Solution

In this case the flow volume of air and flue gas has been specified. Without this, a fuel

type should be known, its input to the furnace and the excess combustion air factor. Flow

volumes of flue gas and air can be determined from these values.

To solve a heat-transfer surface, relation (4.24) can be used

StkQ (W) (4.24)

The following needs to be determined one after another

a) amount of transferred heat in the exchanger Q

b) mean logarithmic temperature gradient t

c) heat-transfer surface

ad a)

The amount of transferred heat in the recuperator is determined from the left-hand side of

the exchanger balance equation (4.29), for which air enthalpy values for the specified

temperatures have to be found in the Thermal-technical tables and diagrams from Stanislav

Bálek, the author, on page 21

zspspspvzdvzdvzd iiViiV ´́´´´́ (W) (4.29)

´´́

vzdvzdvzd iiV 9.13 (774.80 – 26.38) = 6 833.1 kW

ad b)

Výměníky

45

A direct determination of a mean logarithmic gradient is not possible, since the flue gas

temperature on the outlet from the recuperator is not known. For its determination the right-

hand side of the exchanger balance equation is used (4.29). The flue gas enthalpy value on the

inlet into the recuperator is determined from the above mentioned tables, p. 25

3,59985,007,10

1,683368,1397´´́

zsp

vzdspsp

V

Qii

kJ·m-3

The enthalpy of flue gas of the coke-oven gas calculated this way has to be matched with

a related flue gas temperature value on the outlet from the recuperator; the value can be found

in the above mentioned tables. A value resulting from interpolation is 439.5 °C.

If temperatures of flowing media on the inlet into and outlet from the recuperator are

known, a scheme of the flow can be plotted, see Fig. 4.3 (countercurrent). The differences in

the media temperature on the beginning and at the end of the heat-transfer surface can be

determined from this scheme. ´́´

0 vzdsp ttt = 439.5 – 20 = 419.5 K

´´́

vzdspS ttt = 920 – 550 = 370 K

The obtained temperature differences are substituted into the relation for a mean

logarithmic temperature gradient (4.25)

396

370

5,419ln

3705,419

ln 0

0

S

S

t

t

ttt K

ad c)

Now everything is determined for equation (4.24) and after substituting we obtain a value

of the demanded heat-transfer surface

3,47939636

101,6833 3

tk

QS m

2

Result

The heat-transfer surface of the exchanger for combustion air heating to temperature of

550 °C must be of a size of 479.3 m2.

Summary of terms of Chapter 4

Heat recuperation. Fuel saving, flame temperature increase, equipment efficiency

enhancement. Recuperator. Dividing partition wall, heat-transfer surface, heat-transferring

media. Air preheating, gas preheating. Flow system, concurrent, countercurrent. Heat

calculation, amount of transferred heat, temperature of heat-transferring media and its change,

output capacity. Temperature gradient. Heat passage coefficient, coefficient of heat transfer

from flue gas, coefficient of heat transfer from air, thermal resistance, balance equation of a

recuperator. Flue gas dilution, dilution factor. Hydraulic calculation. Non-isometric flow, flow

velocity, total pressure loss of an exchanger. Metallic recuperator. Ceramic recuperator.

Regenerator. Heat transfer coefficient in a regenerator. Grating, heating period, cooling

period, heating time, cooling time. Cowper.

Výměníky

46

Questions for Chapter 4

32. What is heat recuperation?

33. In what devices the heat recuperation is performed?

34. What is a function of a heat exchanger?

35. What are basic types of exchangers?

36. What are purposes for heat recuperation?

37. How can savings resulting from implementation of an exchanger be determined? When is

advisable to implement it?

38. How does heat recuperation affect the fuel consumption? How is an ecological impact?

39. What is a heat-transfer surface and what types do you know?

40. Which components does a recuperator heat calculation comprise?

41. What is a relation for the heat passage coefficient?

42. What does a mean logarithmic temperature gradient express?

43. Write and describe an equation for a recuperator thermal equilibrium.

44. How can a heat-transfer surface be determined?

45. Which components does a hydraulic calculation of a recuperator comprise? What does it solve in

particular?

46. How does a recuperator differ from a regenerator?

47. What is a function of a regenerator?

48. Where can be a regenerator used?

49. When is it advisable to use a regenerator and when a recuperator?

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47

5 FURNACES

Time needed for the study: 9 hours

Objective: After studying this paragraph a student will be able to

Define a furnace device in term of a technological designation

Describe basic types of furnace devices, possibilities of application

In a combination with the foregoing chapters, to solve thermal work of a particular

equipment, determine a heating mode, a thermal energy consumption

Lecture

A furnace is a facility in which a particular technological thermal process is performed,

resulting in obtaining a new product, a product refinement, in some case a preparation of a

product for following technological operations that cannot be performed in a cold condition

state. A demanded thermal energy is provided through varied methods according to a furnace

type. It is always necessary for the process to run in conditions as optimal as possible, so with

maximal energy savings, with an adequate regard to the required product, respecting

environmental legislative standards.

5.1 Classification of furnaces

Furnaces occurring in metallurgy belong to a category of industrial furnaces. They are

classified according to various viewpoints. In operation, a categorization of furnaces

according to 4 basic features has been established. They are:

1. Technological purpose

2. Thermal energy source

3. Workspace shape

4. Method of utilization of outlet flue gas heat

The technological purpose divides furnaces into several groups in accordance with a type

of technology performed inside.

Melting furnaces serve for melting of materials (charge), such as blast furnace, cupola

furnace, glass furnace etc.

Heating furnaces heat materials to a formability temperature before subsequent forming

processes. This group covers for example forging furnaces, bogie-hearth furnaces, pusher

furnaces, rotary hearth furnace etc.; their shape and operating procedure depends on a charge

shape and weight.

Furnaces for heat treatment are, in principle, furnaces, where, as in heating furnaces, a

particular heating phase is solved, but also time dwelling on a specific temperature, as well as

cooling methods. Considering a technology requirement they have a different structural

design, they often work with different furnace atmospheres, therefore they belong to a

separate group of furnaces. This group covers e.g. quenching, annealing, tempering furnaces

etc.

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48

Baking kilns are used for baking of products, for example ceramics, lime etc.

Drying ovens remove humidity e.g. in foundry plants – drying of moulds and cores, as

well as in ceramic industry.

In distillation ovens products are obtained through distillation procedures, a coke-making

battery can be an example.

A heat source is very often fuel (see Chapter 2) or electric power. However, there are heat

facilities not requiring the so-called external heat source for producing their product, because

they can bring along a part of thermal energy from an immediately foregoing (upstream)

technological operation, a part of the needed thermal energy is produced during their own

technological process. Tandem furnaces or converters are examples of such equipment.

A workspace shape is selected with regard to a technology type performed in the furnace.

Particular shape types are shown in Figure 5.1.

Fig.5.1 Furnace workspace shapes (Source: Příhoda, M., Hašek, P. Metallurgical furnaces)

According to an utilization method of heat energy leaving the furnace through produced

flue gasses, furnaces are categorized as recuperative, regenerative (see Chapter 4) and

furnaces without an exchanger.

5.2 Furnace thermal work

The thermal work of a furnace device is characterized by a thermal regime, temperature

regime, output, efficiency and specific energy consumption.

The thermal regime determines the thermal input in dependence on time. It is governed

by a required temperature regime. It is given in Watt units (W).

The temperature regime is determined by the furnace workspace temperature. The

furnace temperature depends on a fuel type, burning conditions and very often on preheating

of combustion components (see Chapter 2). Many furnaces would not reach the required

working temperature without implemented recuperation (see the actual flame temperature,

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49

pyrometric effect). Melting furnaces require the highest working temperatures. Here a

difference between the charge temperature and the working temperature may be from 200 K

up to order-of-magnitude 103 K (plasma furnaces). From the point of view of economy

utilization of the energy potential, the work atmosphere temperature should not exceed the

charge temperature too much; it is particular for a particular furnace type. Furnaces can work

in a stationary and nonstationary mode, the furnace temperature may vary along the furnace

length (pusher-type furnaces), may have a constant value in a particular part (zone).

Output of a furnace specifies the amount of a manufactured production per a time unit. It

is given in kg·s-1

or t·h-1

. To compare the same type of furnaces of different sizes the specific

output is used, related to a unit of a hearth surface.

Efficiency of a furnace is an effective heat to furnace input ratio. The effective heat is heat

needed for realization of the technological process inside the furnace area.

The specific energy consumption is an amount of energy demanded for a manufacture of

a production unit. It is given in J·kg-1

.

5.3 Melting furnaces

A category of melting furnaces cover blast furnaces, cupola furnaces, converters, tandem

furnaces, electric arc furnaces, electric induction furnaces, electron-beam furnaces, plasma

furnaces. They serve for melting of materials, ores, concentrates, remelting for the purpose of

chemical composition modification.

The blast furnace for pig iron making is the largest melting furnace. It reaches a height of

25 up to 40 m. In the past, a large number of these furnaces were on the Czechoslovak

Republic territory. Along with a depression of metallurgy after 1989, their number was

decreasing gradually; at present they are active only in Třinec Iron and Steel Works and in

Ostrava metallurgical complex ArcelorMittal. A scheme of this furnace is shown in Figure

5.2.

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50

Fig. 5. 2 Blast furnace scheme (Source: Rédr, M. Heat Engineering)

Oxygen converters, tandem furnaces, arc furnaces, formerly also air converters, Siemens-

Martin furnaces are used for production of steel from pig iron.

The oxygen converter produces steel from melted liquid iron. This is furnace equipment,

which has replaced air converters. It works without an external heat energy source. A

significant part of heat needed for realization of the technology is delivered by the liquid iron

enthalpy; the rest is obtained by burning-out elements in liquid iron (e.g. carbon) and other

exothermic reactions of additives.

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51

Fig. 5. 3 Oxygen converter scheme (Source: Rédr, M. Heat Engineering)

1 – converter lining, 2 – converter shell, 3 – steel bath, 4 – upper part of the converter, 5 –

inspection hole, 6 – bearing structure, 7 – oxygen lance.

Descriptions of other above mentioned melting facilities are available in lecture notes

Metallurgical furnaces from authors Příhoda, M., Hašek, P. at the VŠB - Technical University

of Ostrava.

5.4 Heating furnaces

Heating furnaces provide charge heating before following mechanical hot processing –

forming. Heating time periods needed for heating of material to the specified formability

temperature are solved in Chapter 3.

Soaking pit furnaces are used for heating of very heavy ingots of weights higher than 2

tons. As these are thick objects, heating of the charge to the permissible temperature gradient

across the cross section as well as height is demanded. By this reason the soaking pit furnace

is designed as double-chamber. While in the 1st chamber intensive heating of ingots to the

required temperature is performed with a full heat input, the second chamber, which has

completed this heating phase, decreases heat supply - heat output and a phase of temperature

equalizing to the required value is performed here. According to a layout of burners and a flue

gas exhaust design, soaking pit furnaces are of single-pass or double-pass configuration.

After continuous steel casting having emerged, furnaces of this type of have lost their

significance.

Chamber furnaces heat a charge, which can vary both in a shape and in a size and can be

of various grades. They perform heating prior to subsequent forging or pressing. Considering

a wide assortment and varied charge size, chamber furnaces are designed either with a fixed

or movable hearth. If the hearth can drive out, the furnace is called a bogie-hearth furnace.

Furnaces are complemented with recuperators (see Chapter 4), which preheats the inlet

combustion air, or possibly fuel. The thermal mode is stationary for heating of a charge of

lesser dimensions and simpler shapes. Nonstationary thermal mode is performed for heating

of a charge of large dimensions. A type of lining depends on a working regime of the furnace

– continuous or non-continuous.

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52

Pusher furnaces provide heating of billets or slabs of weights from 50 kg to 40 tons prior

to following rolling. Pusher furnaces are usually divided to several zones, material is pushed

from the charge opening towards the discharge opening through particular zones by a pusher.

Charge is placed on water cooled skids and one piece touches the other. The furnace walls are

equipped with inspection windows for monitoring the move of the charge. Zones work with a

different thermal regime, which is derived from a zone function.

Walking beam furnaces provide heating of the same kind of charge as pusher furnaces.

As the structural design allows regular heating of a charge from all sides, the charge can

consist of blocks or slabs of higher thicknesses. These furnaces differ from pusher ones in a

way of moving the material. It is performed using fixed and moving beams. This way of

moving the charge is more regardful, allows heating of varied charges in term of chemical

composition, bottom as well as upper heating can be performed, the furnace hearth is not

damaged. This furnace can be divided to zones, too.

Rotary hearth furnaces are used for heating of semi-finished products of round cross

sections prior to subsequent rolling. They have a shape of an annulus, which forms a hearth of

the furnace. A charge is placed onto this rotary hearth and gradually moved-on around a circle

through regions with various thermal inputs. This way the charge passes through zones with a

different thermal mode between the charging and discharging opening. The thermal mode is

defined by the input of burners, which are placed in side walls of the furnace along its

perimeter. Furnaces are complemented with recuperators, efficiency reaches up to 60 % then.

Sectional furnaces are used for high-speed heating of tubular semi-finished products of

diameters less than 200 mm. The flue gas temperature above a charge can be by as much as

300 K higher than the charge temperature. Then the time needed for heating is shortened. A

sectional furnace incorporates individual separate sections of lengths of 0.8 to 1.7 m, which

are connected to one another by connecting links. In a connecting link an axially deviated

roller of a special shape is placed, allowing a move of round billets not only in a forward

direction, but also around their own horizontal axis at the same time. Burners are built-in in

the section wall; they provide side heating of a charge. Heat recuperation is necessary.

Fig. 5.4 shows a chamber furnace with a bogie hearth in a front view, from the side of the

charging opening fitted with a gate. In the bottom part the exchanger chambers are depicted.

Figure 5.5 shows a pusher furnace. Particular zones can be seen in the Figure – a

preheating zone, a main-heating zone, an equalizing zone. A recuperator is depicted in the

bottom part. Water-cooled skids pass through the furnace. The furnace is equipped with

working (monitoring) windows along its entire length.

5.5 Furnaces for heat treatment

Furnaces for heat treatment work as multi-phase furnaces in which heat treatment

particular phases are performed step by step. There is an exactly calculated heating mode in

which phases of heating to the required temperature alternate with phases of dwelling on a

constant value, including a regulated temperature decrease again to the particular value (in the

course of time). Respective time periods and

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53

Fig. 5. 4 Chamber furnace (Source: Rédr, M. Heat Engineering)

Fig. 5. 5 Pusher furnace (Source: Rédr, M. Heat Engineering)

required particular temperatures a materials can be selected according to a type of heat

treatment (tempering, annealing, quenching) and according to the chemical composition of the

given material.

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54

Fig. 5. 6 Rotary hearth furnace (Source: Rédr, M. Heat Engineering)

Furnaces for heat treatment can operate periodically or continuously. A particular design

is determined by a type of the entire production line, i.e. a type of technological operation

(heat treatment, surface finishing), by a charge shape, charge weight etc. They can be

designed as covered, chamber-type, pass-through (see Fig. 5.7).

Fig. 5. 7 Chamber furnace for heat treatment of Al ingots

(Source: http://www.ethermtz.cz/vyrobky/komorove-pece-pro-tepelne-zpracovani-svitku-al-

plechu)

More detailed descriptions of furnaces can be found in lecture notes Metallurgical

furnaces from authors Příhoda, M., Hašek, P. at the Department of Thermal Engineering of

the Faculty of Metallurgy and Materials Engineering. A student may also learn from e-

learning lecture notes Macháčková A., Mrňková L. Industrial Furnaces or from audiovisual

recordings on the website of the Department of Thermal Engineering of the Faculty of

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55

Metallurgy and Materials Engineering, VŠB - Technical University of Ostrava:

http://katedry.fmmi.vsb.cz/635/projekty.php (záložka Výzkum - Projekty).

The mentioned text is a summary for a basic orientation.

Summary of terms of Chapter 5

Classification of furnaces, classification aspects, technological purpose, thermal energy

source, workspace shape, waste heat utilization. Furnace thermal work. Temperature regime,

thermal regime. Furnace output, furnace efficiency, furnace energy consumption. Melting

furnaces. Blast furnace, charge, system of flow in a blast furnace, products of the blast furnace

production, blast furnace thermal mode. Converter. Heating furnaces, particular types.

Chamber furnaces and bogie-hearth furnaces, charge type, heating methods. Pusher and

walking-beam furnaces, principle of moving the material, thermal and temperature regime.

Rotary hearth furnace principle, a way of the use. Sectional furnaces, assortment of sectional

furnaces. Furnaces for heat treatment.

Questions for Chapter 5

50. According to which selected aspects are industrial furnaces classified?

51. How can a furnace workspace shape look like? Specify particular types including designation of

the type of the furnace.

52. Which quantities determine thermal work of furnaces?

53. What is characteristic for thermal mode of furnaces?

54. What is characteristic for temperature mode of furnaces?

55. Give examples of melting furnaces and their principles.

56. Describe the blast furnace and the technological process.

57. What are input charge materials for the blast furnace?

58. What are blast furnace process products? Describe their following utilization and possible

processing.

59. What ensures high temperatures of the blast furnace workspace?

60. What does oxygen converter serve for?

61. Describe a converter process principle.

62. What are thermal demands of a converter and how are they ensured?

63. How does a tandem furnace work?

64. What do heating furnaces serve for and what types of heating furnaces do you know?

65. Compare chamber furnaces and bogie-hearth furnaces, define their advantages and disadvantages.

66. How does a pusher furnace operate, what does it serve for, how does charge heating run?

67. Why are pass-through furnaces designed as multi-zone? By what can heating be intensified?

68. Describe a technology principle and operating procedure of a pusher furnace.

69. What is a difference between a pusher furnace and a walking-beam furnace?

70. For what type of charge rotary hearth furnaces are used? Describe a working scheme of this

furnace.

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56

71. What are furnaces for heat treatment?

72. What is a protective atmosphere, when is it used?

73. How can be direct heating in furnaces for heat treatment performed?

74. When and by what reasons indirect heating in furnaces for heat treatment is used?

75. What types of surface finishing in term of chemical composition do you know?

Literature

RÉDR, M., PŘÍHODA, M., Základy tepelné techniky (Basics of Heat

Engineering), Prague: SNTL, 1991, 675 p. 1st edition, ISBN 80-03-00366-0,

PŘÍHODA, M., RÉDR, M., Sdílení tepla a proudění (Heat Transfer and Flow),

Ostrava: VŠB – TUO 1998, 180 p., 1st edition, ISBN 80-7078-549-7, lecture

notes,

PŘÍHODA, M., HAŠEK, P., Hutnické pece (Metallurgical Furnaces), Ostrava:

VŠB – TUO, 1983, 1st edition, lecture notes,

MACHÁČKOVÁ, A., KOCICH, R., Sdílení tepla a proudění (Heat Transfer

and Fluid Mechanics), Ostrava: VŠB-TUO, 2012. 180 p. ISBN 978-80-248-

2576-2. e-learning lecture notes,

KLEČKOVÁ, Z., MACHÁČKOVÁ, A., Minimalizace emisí při energetickém

využití odpadů (Minimization of Emissions in Energy Utilization of Wastes).

Ostrava: Marionetti, 2011, 147 p. ISBN 978-80-260-1279-5, 1st edition.

MACHÁČKOVÁ A., MRŇKOVÁ L. Průmyslové pece (Industrial Furnaces),

e-learning lecture notes. Available on http://katedry.fmmi.vsb.cz/635/

KLEČKOVÁ Z. Audiovisual recordings.

Available on http://katedry.fmmi.vsb.cz/635/projekty.php (bookmark Research -

Projects).

More actual sources are available at the guarantor of the subject.