Typical Heat Exchange EquipmentEnergy balances

Heat flux and heat transfer coefficientsTemperature difference

Overall heat transfer coefficientHeat Exchanger Analysis

Heat transfer across a solid wall separating two liquids –latent heat (phase change) or sensible heat (∆T without phase change).

All such operations need heat transfer by conduction and convection

Simple tubular condenser

2

If vapour entering is single component (not a mixture), not superheated, and the condensate not sub cooled then shell side temp. is constant

T - point temperature difference (T1-inlet, T2 - outlet)

Terminal point temperature differences = approaches

Temperature range or range, Tcb – Tca

3

Counterflow or countercurrent flow

Tha – Temperature of hot fluid entering

Thb – Temperature of hot fluid leaving

Tca – Temperature of cold fluid entering Tca – Temperature of cold fluid leaving

4

Approaches : T1 = Tha – Tca T2 = Thb - Tcb

 

Warm fluid range = Tha - Thb Cold fluid range = Tcb - Tca   Parallel flow – Fluids enter same end & flow out

same end

Parallel flow: rarely used for single pass Thb >> Tca & Tha >> Tcb

5

H/E mechanical, potential & kinetic energies << enthalpy, hence for each fluid stream:

  m ( Hb – Ha ) = Q

q = Q/A

If the shell side fluid is hotter or colder than the ambient temperature then undesired heat loss/gain could result so lagging (insulation) is necessary. 6

  For the warm fluid, enthalpy balance: mh (Hhb – Hha) = Qh

heat lost = heat gained : Qc = - Qh

   Overall enthalpy balance   mc (Hcb - Hca ) = mh ( Hha – Hhb ) = Q     mh Cph( Tha – Thb ) =mc Cpc(Tcb - Tca ) = Q

7

  For condensers with phase change:   mh λ = mc Cpc(Tcb - Tca ) = Q

assuming no superheated vapour, no subcooled condensate

 Otherwise : mh [λ +Cph( Th – Thb )] =mc Cpc(Tcb - Tca )

HEAT FLUX = Rate of heat transfer per unit area [Wm-2], [Btuhr-1ft-2] 8

Important to specify whether internal or external surface areas being used (choice is arbitrary but order of magnitude different)

Heat flux across solid layers proportional to driving force T

 Q/A = ∆T/R also true for liquid layers   H/E driving force : Th -Tc

hot fluid avg. temp cold fluid avg. temp

9

∆T, hence heat flux, varies along length of H/E   dQ/dA = U∆T = U(Th – Tc)   Proportionality factor U, (overall heat

transfer coefficient) [Wm-2 oC-1]   For external tube area A = Ao , U = Uo

For internal tube area A = Ai , U = Ui

   Uo= Ai = Di

Ui Ao Do

10

Uo = dAi = Di

Ui dAo Do

For plate type H/E the areas for both sides are the same so there would be only one value for U.

Q = UA∆T Q = ∆T U A The value of U is important for designing any

cooling or heating system  

Inner diameter

Outter diameter

11

Assuming no accumulation of heat in the media:

Q = h1 A ∆ T1 Q = h2 A∆T2 Q = h3 A ∆ T3

  ∆T1 = Q/h1 A ∆T2 = Q/ h2 A ∆ T3 = Q/ h3 A     ∆T1 + ∆T2 + ∆ T3 = Q( 1 + 1 + 1)

A ( h1 h2 h3 )

∆T1 + ∆T2 + ∆T3 = ∆ T (Total temperature difference)

12

∆T = Q ( 1 + 1 + 1) but Q = ∆ T

A ( h1 h2 h3 ) U A

I = 1 + 1 + 1 U h1 h2 h3

Reciprocals of the heat transfer coefficients = resistances and are additive

 

13

In some cases the areas are not the same: A1, A2, A3  

∆T1+ ∆T2 + ∆ T3 = Q ( 1 + 1 + 1 ) (A1 h1 A2 h2 A3 h3)   Using one of the areas as the basis then U will

vary according to that area (say A1)   Q = U1 A1 ∆ T or ∆T = Q

U1 A 1 = 1 + A1 1 + A1 1

U h1 A2 h2 A3 h314

The U value depends on   Heat transfer mechanism

Fluid dynamics of both fluids

Properties of the H/E construction materials

Geometry of fluid paths

15

 Deposits & scale cause performance deterioration after a period of operation

Deposits from the flow streams increase thermal resistance and decrease heat transfer rate

Fouling factor or fouling resistance used to measure the overall effect of deposits on the heat transfer

Most common fouling is accumulation of solid deposits from the fluid onto the heating surfaces

16

Corrosion and chemical fouling also affect heat transfer

Glass coating and plastic pipes used to reduce chemical fouling

Algae growth in warm fluids lead to biological fouling

Chemical treatment is used to reduce biological fouling

17

Fouling factor is zero for new, clean heat exchangers, Rf =0

Rf depends operating temperature,fluid velocity and duration of service

Fluid R f , m2 oCw-1

Distilled water, sea water, T>50oC 0.0002

Distilled water, sea water, T<50oC 0.0001

Fuel Oil 0.0009

Steam (oil free) 0.0001

Refrigerants (liquid) 0.0002

Refrigerants (vapour) 0.0004

Alcohol vapours 0.000118

Fouling factors must be obtained experimentally from  the U values for both clean and dirty heat exchangers

 

Eg. Sea Water at 125.0 oC is used in a heat exchanger with fouling factor, Rf=0.0002 m2 oC/W. What is the percent reduction in the heat exchanger’s U value if in the clean state U=1961 W/m2 oC?

cleandirtyf UU

R11

WCmUU

R o

cleandirtyf /0002.0

11 2

%64.271001961

14191961%1419

099.7

1

099.70005099.00002.1961

10002.0

1

reductionU

U

dirty

dirty

19

Application determines hardware and configuration

Double pipe, tube in tube or concentric tube H/E is the simplest form & as the name implies consisting of two concentric tubes.

Compact H/E are designed where there is strict limitations regarding weight and volume so as to give large heat transfer area per unit volume. The area density (ratio of area to volume) β> 700 m2 m-3.

Examples are car radiators (β=600 m2 m-3) and glass ceramic gas turbine H/E (β=15000 m2 m-3)

20

The most common type of H/E used in industrial applications.

Tube count can reach several hundreds with baffles.

Classifies by tube passes as, one shell pass and two tube passes, or two shell passes and four tube passes.

Fouling can be severe and the H/E must be taken out of service periodically to labourously clean the tubes.

21

22

23

Corrugated parallel plates facing each other and held firmly together by head frames with hot and cold fluids flowing between alternate plates.

Gap between plates 1.3-1.5 mm with large surface area to volume ratio.

Increasing demand for heat transfer can be met by simply increasing the number of plates.

Application prevalent in the diary and brewing industries with stainless steel the popular material of construction with rubber seal gaskets.

24

25

26

27

High degree of turbulence even at low flow rates

Very high heat transfer coefficients typical

Heat transfer Water U

Per plate Flow rate Value

W/K gal/h kW/m2K

1580 550 3.70

2110 850 4.94

2640 1250 6.13

Easy to dismantle and clean

28

Sheets of metal are coiled to enclose a spiral annulus in the construction in this H/E with the advantage of good fouling characteristics and ease of cleaning.

Application confined to fluids with high solids concentration.

Velocities as high as 2.1 m/s and U values of 2.8 kW/m2K are achievable.

29

SHEs are usually relatively small in size.

30

H/Es are usually selected to satisfy a particular temperature range or to predict outlet temperatures under conditions of known flow rates.

Two methods are normally used to analyze H/E performance:

LMTD method

NTU method31

Counterflow or countercurrent flowTha

Th vs q

Tc vs qThb

Tca

ΔT1

Q QT

ΔT2

Tcb

ΔT1

ΔT2

ΔT vs q

ΔT

Assumptions:

i) Overall coefficient is constant

ii) The specific heats of the hot & cold fluids are constant

iii) Heat loss to the surroundings is negligible

iv) The flows are steady and either counter current or parallel (not both)

Te

mp

era

ture

32

Based on the assumptions the temperatures of the hot and cold streams are expected to vary linearly with the heat rate.

Similarly ΔT will vary linearly with q resulting in a line of constant gradient

ΔT1 & ΔT2 are the temperature approaches then the gradient of the ΔT vs. q line is given by:

TQ

TT

dQ

Td 12

33

1

2

12

1

2

12

12

1

2

0

12

12

lnln

ln

:

)tan(

2

1

TTTT

LMTDLMTDUA

TTTT

UAQ

AQ

TTU

T

T

dAQ

TTU

T

Td

exchangerheattheofareaentiretheovergIntegratin

UtconsQ

TT

TdAU

Td

TUAdQTUA

dQbut

TTT

TT

A

T

T

T

T

34

When ΔT1 ~ ΔT2 ΔLMTD ~ ΔTavg

With condensing fluids ΔLMTD is the same for all types of flow patterns

For non-condensing fluids in counter current flow pattern:

ΔT2 = warm end approach ΔT1 = cold end approach

35

For variable U values:

Where U1, U2 are the U values at the ends of the H/E

Other researchers proposed other methods of determining a representative temperature change across the H/E. According to Underwood:

21

12

2112

lnTUTUTUTU

AQ TT

3

1

231

13

1

21)( TTTm

36

A heat exchanger is required to cool 20.0 kg/s of water from 360.0 K to 340.0 K using 25.0 kg/s of water at 300.0 K. If the overall heat transfer coefficient is constant at 2.0 kW/m2K what is the required surface area using;

(a) counter current concentric tube heat exchanger

(b) co-current concentric tube heat exchanger

37

For multi pass H/E flow pattern is counter current in some tubes (passes) and parallel flow in others

Finding the actual temperature difference would be very difficult due to complex flow patterns

Underwood and Bowman et al introduced use of a correction factor based on graphical methods of modifying the ΔLMTD.

38

Depending on equipment geometry and inlet and outlet temperatures a correction factor may be applied to the counter current flow ΔLMTD to compensate for the complex flow.

ΔTm =F*ΔLMTD CF

F<1 For cross flow & multi-pass shell & tube H/Es F=1 Limiting value corresponds to counter flow H/Es Charts of F vs P & R

39

sideshell

tubesideP

P

Cm

Tt

TTR

tT

ttP

mC

.

.

12

21

11

12 1 – inlet2 – outlet

T – Shellsidet = Tubeside

Determination of F requires the inlet and outlet temperatures of both the hot and cold fluids.

0 < P < 1 0 < R < infinity

Phase change Tube sidePhase change shell side

(boiling/condensation)

F = 1

For condensers or boilers F = 1 regardless of the configuration of the heat exchanger 40

41

1. Water at the rate of 68.0 kg/min is heated from 35 oC to 75.0 oC by an oil having a specific heat capacity of 1.9 kJ/kg oC. The fluids are used in a counter current flow double pipe heat exchanger and the oil enters at 110.0 oC and leaves at 75.0 oC. Using 320.0 W/m2 oC for the overall heat transfer coefficient calculate the heat exchanger area.

2. If instead of a double pipe heat exchanger we use a shell and tube heat exchanger with water making one shell pass and the oil making two tube passes what would be the required area using the same U value?

42