Application of Mathematics in Chemical Engineering · 02/01/2014  · Engineering Heat Transfer...

Historical Background

Caloric theory: Heat is fluid like substance called caloric

that is mass-less, colorless, odorless, tasteless substance

that can be poured from one body into another)

James P. Joule: published in

1843 that heat was not a

substance after all

Heat: Perceived to be something that produces in us a

sensation of warmth

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Historical Background

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Thermodynamics?

Heat Transfer?

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Thermodynamics

It is the branch of engineering science which deals with

transformation of energy from one form to another.

The study of the relationship between heat, work and

energy.

It deals with the equilibrium and feasibility of process

and properties of system, direction of change etc.

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Work

The energy required to move an object against a force.

Work = force × distance

Energy

The capacity to do work or transfer heat.

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Energy can exist in various forms such as:

thermal

mechanical

kinetic

potential

electrical

magnetic

chemical

nuclear

Their sum constitutes the total

energy E of a system.

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Internal energy is the energy stored in a body.

It increases when the temperature of the body rises or

when the body changes from solid to liquid or from

liquid to gas.

Internal energy is the sum of kinetic and potential

energy of all particles in the body.

Unit of internal energy: joule (J)

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Heat

Heat is a form of energy.

It is energy in transit form which moves from high to low

temperature level.

Energy associated with the random motion of atoms and

molecules.

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When two bodies of different temperatures touch each

other, energy is transferred from the hot body to the cold

body until they reach the same temperature. (The bodies

are then said to be in thermal equilibrium.)

Heat is the energy transferred from one body to another as

a result of a temperature difference.

Heat is a form of energy which passes from a body at

higher temperature to a body at a lower temperature.

Unit of heat: joule (J)

Note: Heat cannot be measured directly by an instrument

as temperature is by a thermometer.

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• The transfer of energy as heat is always from the

higher-temperature medium to the lower-temperature

one.

• Heat transfer stops when the two mediums reach the

same temperature.

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Heat transfer: Science of thermodynamics and fluid

mechanics

Engineering Heat Transfer consists of the study of thermal

energy movement

Heat transfer is the science which predicts the rate of

energy transfer taking place between material bodies as a

result of temperature difference between them.

Heat transfer cannot be measure directly but the effects

produced by it can be observed and measured.

Heat Transfer

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Heat Temperature

It is a form of energy called

thermal energy.

It is a thermal state of a

body

It is measure of degree of

hotness or coldness of

system

Measured in kcal, BTU etc. Measured in 0C, 0F, K etc.

Colorimeter is used for

measurement.

Thermometer is used for

measurement.

Extensive property Intensive property

Extensive properties (i.e. mass) are dependent upon

the amount of a substance, while intensive

properties (i.e. density) are independent of quantity.

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• Zeroth law of Thermodynamics deals with thermal

equilibrium and establishes a concept of Temperature.

• First law of Thermodynamics throws light on concept of

internal energy.

• Second law of Thermodynamics indicates the limit of

converting heat into work and introduces the principle of

increase of entropy.

OR

It states that "Heat will flow naturally from one reservoir to

another at a lower temperature but not in opposite

direction without assistance.” (This law established the

direction of energy transport).

• Third law of Thermodynamics defines absolute zero of

entropy.

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Thermodynamics Heat Transfer

It is concerned with

equilibrium states and

precludes existence of

temperature gradient

It is concern with non-

equilibrium states.

Temperature gradient must

exist for exchange of heat

It helps to determine quantity

of heat and work interactions

when a system changes from

one equilibrium state to

another but do not provide

information on nature of

interaction and time rate at

which interaction occurs

∆u = ∆Q ± ∆W

It helps to predict rate at

which energy is exchanged

and also predicts temperature

distribution as a function of

coordinates and time within

regions of matter

We can not obtain

temperature profile

We can obtain temperature

profile

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• We are normally interested in how long it takes for the

hot coffee in a thermos bottle to cool to a certain

temperature which can not be determined from a

thermodynamic analysis alone.

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Consider the cooling of a hot steel bar placed in a pail of

water.

Thermodynamic analysis will predict the final equilibrium

temperature of the steel bar-water combination but it will not

predict how long it takes to reach this equilibrium condition or

what the temperature of bar will be after a certain length of

time before the equilibrium condition is attained.

But heat transfer study will predict the temperature of both the

bar and water as a function of time.

Heat transfer studies mainly require the knowledge of

thermodynamics, fluid mechanics, physics and mathematics.

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Energy can be transferred to or from

a given mass by two mechanisms:

heat transfer and work

Heat transfer rate: The amount of

heat transferred per unit time.

Heat flux: The rate of heat transfer

per unit area normal to the direction

of heat transfer.

Power: The work done per unit time.

when is constant:

The sensible and latent forms of internal energy can be transferred as a result of a

temperature difference and they are referred to as heat or thermal energy

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Application Areas of Heat Transfer

Energy production and conversion

For thermal design of boilers, steam turbines,

condensers, gas turbines, cooling towers, feed

heaters, internal combustion engine

Have to make a detailed heat transfer analysis.

Refrigeration and air conditioning:

The thermal design of compressors, evaporators,

incinerators involves an intensive study of heat

transfer.

Electric machines:

Insulations provide on electric wires need a heat

transfer analysis to avoid conditions which will cause

overheating.

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Application Areas of Heat Transfer

Civil Engineering

Design of buildings for the minimization of heat losses

need heat transfer study.

Construction of dams and other heavy structures,

calculation of thermal expansion of suspension bridge

and railway tracks.

Manufacturing process

The casting of metals, extrusion, metal cutting and

heat treatment of metals involve heat transfer study.

Chemical and Petrochemical operations

Environmental Engineering

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Application Areas of Heat Transfer

Earth Sciences

Astronomy

Agriculture and Food processing

Application:

The human body is constantly rejecting heat to its

surroundings and human comfort is closely tied to the rate

of this heat rejection.

We try to control this heat transfer rate by adjusting our

clothing to the environmental conditions.

Computer, TV, VCR, Freeze, Air-conditioning System

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Application Areas of Heat Transfer

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Engineering Heat Transfer

Heat transfer equipment such as heat exchangers, boilers,

condensers, radiators, heaters, furnaces, refrigerators, and

solar collectors are designed primarily on the basis of heat

transfer analysis.

The heat transfer problems encountered in practice can be

considered in two groups: (1) rating and (2) sizing

problems.

The rating problems deal with the determination of the

heat transfer rate for an existing system at a specifiedtemperature difference.

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Engineering Heat Transfer

The sizing problems deal with the determination of the

size of a system in order to transfer heat at a specified

rate for a specified temperature difference.

An engineering device or process can be studied either

experimentally (testing and taking measurements) or

analytically (by analysis or calculations).

The experimental approach has the advantage that we

deal with the actual physical system, and the desired

quantity is determined by measurement, within the limits

of experimental error. However, this approach is

expensive, time consuming, and often impractical.

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Questions1. The capacity to do work is _____________.

2. Heat is measured in _________.

3. The from of energy that produced feeling of hotness is

called________.

4. __________is neither created nor destroyed it can only

change one form to another.

5. What is the driving force for a heat transfer?

6. Heat transfer takes place according to __________law of

thermodynamics.

7. How does the science of heat transfer differ from the

science of thermodynamics?

8. How do rating problems in heat transfer differ from the

sizing problems?