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DR MAZLAN

SMJ 4463: HEAT TRANSFERSMJ 4463: HEAT TRANSFER

INSTRUCTOR: PM DR MAZLAN ABDUL WAHIDhttp://www.fkm.utm.my/~mazlan

TEXT: Introduction to Heat Transferby Incropera, DeWitt, Bergman, Lavine5th Edition, John Wiley and Sons

DR MAZLAN

Chapter 11Chapter 11

Heat ExchangersHeat Exchangers

Assoc Prof. Dr Mazlan Abdul WahidFaculty of Mechanical Engineering

Universiti Teknologi Malaysiawww.fkm.utm.my/~mazlan

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Objectives• Recognize numerous types of heat exchangers, and

classify them.

• Develop an awareness of fouling on surfaces, anddetermine the overall heat transfer coefficient for a heatexchanger.

• Perform a general energy analysis on heat exchangers.

• Obtain a relation for the logarithmic mean temperaturedifference for use in the LMTD method, and modify it for different types of heat exchangers using the correction factor.

• Develop relations for effectiveness, and analyze heatexchangers when outlet temperatures are not known using the effectiveness-NTU method.

• Know the primary considerations in the selection of heat exchangers.

TypesTypes

Heat Exchanger Types

Heat exchangers are ubiquitous in energy conversion and utilization. They involve heat exchange between two fluids separated by a solid and encompass a wide range of flow configurations.

• Concentric-Tube Heat Exchangers

Parallel Flow Counterflow

� Simplest configuration.

� Superior performance associated with counter flow.

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Types (cont.)Types (cont.)

• Cross-flow Heat Exchangers

Finned-Both FluidsUnmixed

Unfinned-One Fluid Mixedthe Other Unmixed

� For cross-flow over the tubes, fluid motion, and hence mixing, in the transversedirection (y) is prevented for the finned tubes, but occurs for the unfinned condition.

� Heat exchanger performance is influenced by mixing.

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Compact heat exchanger: It has a large heat transfer surface area per unit volume (e.g., car radiator, human lung). A heat exchanger with the area density β > 700 m2/m3 is classified as being compact.

Cross-flow: In compact heat exchangers, the two fluids usually move perpendicular to each other. The cross-flow is further classified as unmixed and mixed flow.

Types (cont.)Types (cont.)

• Compact Heat Exchangers

� Widely used to achieve large heat rates per unit volume, particularly when

one or both fluids is a gas.� Characterized by large heat transfer surface areas per unit volume, small

flow passages, and laminar flow.

(a) Fin-tube (flat tubes, continuous plate fins)(b) Fin-tube (circular tubes, continuous plate fins)(c) Fin-tube (circular tubes, circular fins)(d) Plate-fin (single pass)(e) Plate-fin (multipass)

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Shell-and-tube heat exchanger: The most common type of heat exchanger in industrial applications.

They contain a large number of tubes (sometimes several hundred) packed in a shell with their axes parallel to that of the shell. Heattransfer takes place as one fluid flows inside the tubes while the other fluid flows outside the tubes through the shell.

Shell-and-tube heat exchangers are further classified according to thenumber of shell and tube passes involved.

Types (cont.)Types (cont.)

• Shell-and-Tube Heat Exchangers

One Shell Pass and One Tube Pass

� Baffles are used to establish a cross-flow and to induce turbulent mixing of theshell-side fluid, both of which enhance convection.

� The number of tube and shell passes may be varied, e.g.:

One Shell Pass,Two Tube Passes

Two Shell Passes,Four Tube Passes

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Regenerative heat exchanger:Involves the alternate passage of thehot and cold fluid streams through the same flow area.

Dynamic-type regenerator: Involves a rotating drum and continuous flow of the hot and cold fluid through different portions of the drum so that any portion of the drum passes periodically through the hot stream, storing heat, and then through the cold stream, rejecting this stored heat.

Condenser: One of the fluids is cooled and condenses as it flows through the heat exchanger.

Boiler: One of the fluids absorbs heat and vaporizes.

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Plate and frame (or just plate) heat exchanger: Consists of a series of plates with corrugated flat flow passages. The hot and cold fluids flow in alternate passages, and thus each cold fluid stream is surrounded by two hot fluid streams, resulting in very effective heat transfer. Plate heat exchangers are well suited for liquid-to-liquid applications.

A plate-and-frame liquid-to-liquid heat exchanger.

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Overall CoefficientOverall Coefficient

Overall Heat Transfer Coefficient• An essential requirement for heat exchanger design or performance calculations.

• Contributing factors include convection and conduction associated with thetwo fluids and the intermediate solid, as well as the potential use of fins on bothsides and the effects of time-dependent surface fouling.

• With subscripts c and h used to designate the cold and hot fluids, respectively,the most general expression for the overall coefficient is:

( ) ( )

( ) ( ) ( ) ( ), ,

1 1 1

1 1

c h

f c f hw

o o o oc c h h

UA UA UA

R RR

hA A A hAη η η η

= =

′′ ′′= + + + +

Overall Coefficient (cont.)Overall Coefficient (cont.)

�

( )o,

Overall surface efficiency of fin array (Section 3.6.5)

1 1

o

fc or h f

c or h

A

A

η

η η

→ = − −

total surface area (fins and exposed base) surface area of fins only

t

f

A AA

= →→

Assuming an adiabatic tip, the fin efficiency is

( ), or

or

tanhf c h

c h

mL

mLη =

( )or or2 /c h p w c h

m U k t=

, or

or

partial overall coefficient1p c h

f c h

hUhR

= → ′′+

�2 for a unit surFouling fa face area (ctor m K/W)fR′′ → ⋅

Table 11.1→

conduction resistan Wall (K/Wce ) wR →�

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THE OVERALL HEAT TRANSFER COEFFICIENT• A heat exchanger typically involves two

flowing fluids separated by a solid wall.

• Heat is first transferred from the hot fluid to the wall by convection, through the wall byconduction, and from the wall to the cold fluid again by convection.

• Any radiation effects are usually included in the convection heat transfer coefficients.

Thermal resistance networkassociated with heat transfer in a double-pipe heat exchanger.

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U is the overall heat transfercoefficient, W/m2⋅°C.

When

The overall heat transfer coefficient U is dominated by the smaller convection coefficient. When one of the convection coefficients is much smaller than the other (say, hi << ho), we have 1/hi >> 1/ho, and thus U ≈ hi. This situation arises frequently when one of the fluids is a gas and the other is a liquid. In such cases, fins are commonly used on the gas side to enhance the product UA and thus the heat transfer on that side.

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The overall heat transfer coefficient ranges from about 10 W/m2⋅°C for gas-to-gas heat exchangers to about 10,000 W/m2⋅°C for heat exchangers that involve phase changes.

For short fins of high thermal conductivity, we can use this total area in the convectionresistance relation Rconv = 1/hAs, or

to account for fin efficiency.

When the tube is finned on one side to enhance heat transfer, the total heat transfer surface area on

the finned side is

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Fouling FactorThe performance of heat exchangers usually deteriorates with time as a result of accumulation of deposits on heat transfer surfaces. The layer of deposits represents additional resistance to heat transfer. This is represented by a fouling factor Rf.

The fouling factor increases with the operating temperature and the length of service and decreases with the velocity of the fluids.

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ANALYSIS OF HEAT EXCHANGERSAn engineer often finds himself or herself in a posi tion1. to select a heat exchanger that will achieve a specified temperature

change in a fluid stream of known mass flow rate – the log mean temperature difference (or LMTD) method .

2. to predict the outlet temperatures of the hot and cold fluid streams in a specified heat exchanger – the effectiveness-NTU method .

The rate of heat transfer in heat exchanger (HE is insulated): Two fluid

streams that have the samecapacity rates

experience the same

temperature change in a well-

insulated heat exchanger.

Heat capacity rate

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Variation of fluid temperatures in a heat exchanger when one of the fluidscondenses or boils.

is the rate of evaporation or condensation of the fluid, .hfg is the enthalpy of vaporization of the fluid at the specified temperature or pressure.The heat capacity rate of a fluid during a phase-change process must approach infinity since the temperature change is practically zero.

∆Tm is an appropriate mean (average)temperature difference between the two fluids.

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THE LOG MEAN TEMPERATURE DIFFERENCE (LMTD) METHOD

Variation of the fluid temperatures in aparallel-flow double-pipe heat exchanger.

log mean temperature difference

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Arithmetic mean temperature difference:

The logarithmic mean temperaturedifference ∆Tlm is an exact representation of the average temperature difference between the hot and cold fluids.

Note that ∆Tlm is always less than ∆Tam. Therefore, using ∆Tam in calculationsinstead of ∆Tlm will overestimate the rate of heat transfer in a heat exchanger between the two fluids.

When ∆T1 differs from ∆T2 by no more than 40 percent, the error in using the arithmetic mean temperature difference is less than 1 percent. But the error increases toundesirable levels when ∆T1 differs from ∆T2 by greater amounts.

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Counter-Flow Heat ExchangersIn the limiting case, the cold fluid will be heated to the inlet temperature of the hotfluid.

However, the outlet temperature of the cold fluid can never exceed the inlet temperature of the hot fluid.

For specified inlet and outlet temperatures, the ∆Tlm for a counter-flow heat exchanger is always greater than that for a parallel-flow heat exchanger.

That is, ∆∆∆∆Tlm, CF > ∆∆∆∆Tlm, PF, and thus a smaller surface area (and thus a smaller heat exchanger) is needed to achieve aspecified heat transfer rate in a counter-flow heat exchanger.

When the heat capacity rates of the two fluids are equal

LMTD MethodLMTD Method

• A form of Newton’s law of cooling may be applied to heat exchangers byusing a log-mean value of the temperature difference between the two fluids:

mq U A T= ∆l

( )1 2

1 21n /m

T TT

T T

∆ − ∆∆ =∆ ∆l

Evaluation of depends on the heat exchanger type.1 2 and T T∆ ∆

• Counter-Flow Heat Exchanger:

1 ,1 ,1

, ,

h c

h i c o

T T TT T

∆ ≡ −= −

2 ,2 ,2

, ,

h c

h o c i

T T TT T

∆ ≡ −= −

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LMTD Method (cont.)LMTD Method (cont.) • Parallel-Flow Heat Exchanger:

1 ,1 ,1

, ,

h c

h i c i

T T TT T

∆ ≡ −= −

2 ,2 ,2

, ,

h c

h o c o

T T TT T

∆ ≡ −= −

� Note that Tc,o cannot exceed Th,o for a PF HX, but can do so for a CF HX.

� For equivalent values of UA and inlet temperatures,

,CF ,PFm mT T∆ > ∆l l

• Shell-and-Tube and Cross-Flow Heat Exchangers:

,CFm mT F T∆ = ∆l l

Figures 11S.1 - 11S.4→F

Energy BalanceEnergy Balance

Overall Energy Balance

• Assume negligible heat transfer between the exchanger and its surroundingsand negligible potential and kinetic energy changes for each fluid.

( ), ,h i h ohq m i i⋅= −

( ), ,c c o c iq m i i⋅= −

fluid enthalpyi →

• Assuming no l/v phase change and constant specific heats,

( ), , ,p h h i h ohq m c T T⋅= − ( ), ,h h i h oC T T= −

( ), , ,c p c c o c iq m c T T⋅

= − ( ), ,c c o c iC T T= −

Heat capacity r es , ath cC C →

• Application to the hot (h) and cold (c) fluids:

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Special ConditionsSpecial Conditions

Special Operating Conditions

� Case (a): Ch>>Cc or h is a condensing vapor ( ).hC → ∞

– Negligible or no change in ( ), , .h h o h iT T T=

� Case (b): Cc>>Ch or c is an evaporating liquid ( ).cC → ∞

– Negligible or no change in ( ), , .c c o c iT T T=

� Case (c): Ch=Cc.

1 2 mT T T∆ = ∆ = ∆l

–

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Multipass and Cross-Flow Heat Exchangers:Use of a Correction Factor

The correction factor F depends on the geometry of the heat exchanger and the inlet and outlet temperatures of the hot and cold fluid streams.

F for common cross-flow and shell-and-tube heat exchanger configurations is given in Fig. 11-18 versus two temperature ratios P and R defined as

1 and 2: inlet and outletT and t: shell- and tube-side temperatures

F = 1 for a condenser or boiler

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FIGURE 11-18

Correction factor F charts for common shell-and-tube heat exchangers.

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FIGURE 11-18

Correction factor F charts for common shell-and-tube heat exchangers.

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The LMTD method is very suitable for determining the size of a heat exchanger to realize prescribed outlet temperatures when the mass flow rates and the inlet and outlet temperature s of the hot and cold fluids are specified.

With the LMTD method, the task is to select a heat exchanger that will meet the prescribed heat transfer requirements. The procedure to be followed by the selection process is:

1.Select the type of heat exchanger suitable for the application.

2.Determine any unknown inlet or outlet temperature and the heat transfer rate using an energy balance.

3.Calculate the log mean temperature difference ∆Tlm and the correction factor F, if necessary.

4.Obtain (select or calculate) the value of the overall heat transfercoefficient U.

5.Calculate the heat transfer surface area As.

The task is completed by selecting a heat exchanger that has a heat transfer surface area equal to or larger than As.

General Considerations

General ConsiderationsGeneral Considerations

• Computational Features/Limitations of the LMTD Method:

� The LMTD method may be applied to design problems for which the fluid flow rates and inlet temperatures, as well as a desired outlet temperature, are prescribed.For a specifiedHX type, the required size (surface area), as well as the other outlet temperature, are readily determined.

� If the LMTD method is used in performance calculations for whichboth outlet temperatures must be determined from knowledge of theinlet temperatures, the solution procedure is iterative.

� For both design and performance calculations, the effectiveness-NTUmethod may be used without iteration.

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THE EFFECTIVENESS–NTU METHODA second kind of problem encountered in heat exchanger analysis is thedetermination of the heat transfer rate and the outlet temperatures of the hot and cold fluids for prescribed fluid mass flow rates and inlet temperatures when the type and size of the heat exchanger are specified.

Heat transfer effectiveness

The maximum possible heat transfer rate

Cmin is the smaller of Ch and Cc .

DefinitionsDefinitions

Definitions• Heat exchanger effectiveness, : ε

max

qq

ε =

0 1ε≤ ≤

• Maximum possible heat rate:

( )max min , ,h i c iq C T T= −

min

if or

h h cC C CC

<= if c c hC C C<

� Will the fluid characterized by Cmin or Cmax experience the largest possibletemperature change in transit through the HX?

� Why is Cmin and not Cmax used in the definition of qmax?

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Definitions (cont.)Definitions (cont.)

• Number of Transfer Units, NTU

min

NTU UAC

≡

� A dimensionless parameter whose magnitude influences HX performance:

with NTUq ↑ ↑

HX RelationsHX Relations

Heat Exchanger Relations

( )( )

, ,

, ,

h i h oh

h h i h o

q m i ior

q C T T

⋅ = − = −

•

•( )( )

, ,

, ,

c c o c i

c c o c i

q m i ior

q C T T

⋅ = − = −

• ( )min , ,h i c iq C T Tε= −

• Performance Calculations:

� ( )min maxNTU, /f C Cε =

Cr

� Relations Table 11.3 or Figs. 11.10 - 11.15→

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HX Relations (cont.)HX Relations (cont.)

• Design Calculations:

� ( )min maxNTU , /f C Cε=

� Relations Table 11.4 or Figs. 11.10 - 11.15→

• For all heat exchangers,

with rCε ↑ ↓

( )1 exp NTUε = − −

( )

or

NTU 1n 1 ε= − −

• For Cr = 0, to all HX types. a single NTU relation appliesε −

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Actual heat transfer rate

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The effectiveness of a heat exchanger depends on the geometry of the heat exchanger as well as the flow arrangement.

Therefore, different types of heat exchangers have different effectiveness relations.

Here, we illustrate the development of the effectiveness ε relation for the double-pipe parallel-flow heat exchanger.

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Effectiveness relations of the heat exchangers typically involve thedimensionless group UAs /Cmin.

This quantity is called the number of transfer units NTU .

For specified values of U and Cmin, the value of NTU is a measure of the surface area As. Thus, the larger the NTU, the larger the heat exchanger.

Capacity ratio

The effectiveness of a heat exchanger is a function of the number of transfer units NTU and the capacity ratio c.

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Table 11.3

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Effectiveness for heat exchangers.

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When all the inlet and outlet temperatures are specified, the size of the heatexchanger can easily be determined using the LMTD method. Alternatively, it can be determined from the effectiveness–NTU method by first evaluating the effectiveness ε from its definition and then the NTU from the appropriate NTU relation.

Table 11.4

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(e.g., boiler, condenser)

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Observations from the effectiveness relations and c harts

• The value of the effectiveness ranges from 0 to 1. It increases rapidly with NTU for small values (up to about NTU = 1.5) but rather slowly for larger values. Therefore, the use of a heat exchanger with a large NTU (usually larger than 3) and thus a large size cannot be justified economically, since a large increase in NTU in this case corresponds to a small increase in effectiveness.

• For a given NTU and capacity ratio c = Cmin /Cmax, the counter-flow heat exchanger has the highest effectiveness, followed closely by the cross-flow heat exchangers with both fluids unmixed. The lowest effectiveness values are encoun tered in parallel-flow heat exchangers.

• The effectiveness of a heat exchanger is independen t of the capacity ratio c for NTU values of less than about 0.3.

• The value of the capacity ratio c ranges between 0 and 1. For a given NTU, the effectiveness becomes a maximum for c = 0(e.g., boiler, condenser) and a minimum for c = 1 (when the heat capacity rates of the two fluids are equal).

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SELECTION OF HEAT EXCHANGERSThe uncertainty in the predicted value of U can exceed 30 percent. Thus, it is natural to tend to overdesign the heat exchangers.

Heat transfer enhancement in heat exchangers is usually accompanied by increased pressure drop, and thus higher pumping power.

Therefore, any gain from the enhancement in heat transfer should be weighed against the cost of the accompanying pressure drop.

Usually, the more viscous fluid is more suitable for the shell side (larger passage area and thus lower pressure drop) and the fluid with the higher pressure for the tube side.

The proper selection of a heat exchanger depends on several factors:•Heat transfer rate•Cost•Pumping power•Size and weight•Type•Materials

Annual cost of electricity associated with the operation of the pumps and fans:

The rate of heat transfer in the prospective heat exchanger is

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Summary

• Types of Heat Exchangers

• The Overall Heat Transfer Coefficient� Fouling Factor

• Analysis of Heat Exchangers

• The Log Mean Temperature DifferenceMethod� Counter-Flow Heat Exchangers

� Multipass and Cross-Flow Heat Exchangers:Use of a Correction Factor

• The Effectiveness-NTU Method

• Selection of Heat Exchangers