5
Heat Exchangers
UNIT 11 HEAT EXCHANGERS
Structure
11.1 Introduction
Objectives
11.2 Classification of Heat Exchanger
11.2.1 Compact Heat Exchanger
11.2.2 Classification by Construction Type 11.2.3 Classification by Flow Arrangement 11.2.4 Classification by Heat Transfer Mechanism 11.2.5 Classification according to the Type of Fluids
11.3 Temperature Distribution in Heat Exchangers 11.4 The Overall Heat Transfer Coefficient 11.5 Heat Exchanger Analysis
11.5.1 Log Mean Temperature Difference 11.5.2 The Effectiveness – NTU Method
11.6 Summary 11.7 Key Words 11.8 Answers to SAQs
11.1 INTRODUCTION
Heat exchangers are devices that facilitate heat transfer between two or more fluids at different temperatures. Many types of heat exchangers are developed to meet the demand of processes. Applications of heat exchangers are wide, such as steam power plants, chemical processes, building heating, air conditioning, house hold refrigerators, car radiators, radiators for space vehicles, etc.
Heat transfer, pressure drop analysis, sizing and performance testing, and economic aspects play important roles in the design of heat exchangers.
Objectives
After studying this unit, you should be able to
classify different heat exchangers and applications,
determine the overall heat transfer coefficient,
find the logarithmic mean temperature difference, and
apply method of rating and sizing to heat exchangers.
11.2 CLASSIFICATION OF HEAT EXCHANGER
Heat exchangers are classified according to : (a) compactness,
(b) construction,
(c) flow arrangement, and (d) heat transfer mechanism.
Heat and Mass Transfer
Applications 11.2.1 Compact Heat Exchanger
A heat exchanger having surface to volume ratio S V
more than 700 m2/m3 is known as compact heat exchanger. High value of compactness reduces the volume for a specific heat exchanger performance. Compactness becomes importance when one thinks about the criticality of the process such as aircraft, aerospace vehicles, automobile radiators, heating, ventilation and air conditioning, etc. Table 11.1 presents some surface densities of different applications.
Table 11.1 : Compactness of Some Heat Exchangers
Sl. No. Applications Compactness m2/m3
1. Automobile radiator 1100
2. Human lungs 20,000
3. Plane tubular heat exchanger/shell and tube heat
exchanger 70-500
4. Rotary heat exchangers 6500
11.2.2 Classification by Construction Type
Heat exchangers are classified according to their construction features.
Recuperator
In most of the heat exchangers, the fluids are separated by a heat transfer surface and ideally they do not mix. Such heat exchangers are called direct transfer heat exchanger or recuperator.
Tabular Heat Exchangers
Tubular exchangers are widely used and they are manufactured in many sizes, flow arrangements and types. They can accommodate a wide range of operating pressures and temperatures. The ease of manufacturing and their relatively low cost have been the principal reason for their wide spread use in engineering applications. The most common tubular heat exchanger is the shell and tube type exchanger. 85% of the heat exchangers in the world are the shell and tube type exchangers. Figure 11.1 illustrates the main features of a shell and tube type heat exchanger having one fluid flowing inside the tubes and the other flowing outside the tubes.
Figure 11.1 : Shell and Tube Heat Exchanger
The principal components of this type of heat exchanger are : (a) tube bundles,
(b) shell, (c) front header,
Tube-side outlet
Shell-side
outlet Baffle Header
Tube-side Fluid inlet Shell-side
Fluid inlet Shell
Tubes Header
7
Heat Exchangers
(d) rear header, and (e) baffles.
The baffles are used to support the tubes, to direct the fluid flow approximately normal to the tubes and to increase the turbulence of the shell fluid. There are various types of baffles and the choice of baffle type, spacing and geometry depends on the flow rate, allowable shell side pressure drop, tube support requirement and the flow induced vibration.
Figures 11.2(a) to (c) presents 3 (three) different type of shell and tube type heat exchangers. Figure 11.2(a) is a fixed head type of shell and tube heat exchanger (same as shown in Figure 11.1).
(a)
(b)
(c) U-type
Figure 11.2 : Different Types of Shell and Tube Heat Exchangers
If the tubes are fixed, during heat transfer operation the tubes gets expanded as both ends of the tubes are fixed. The tubes may bend due to expansion. To prevent the bending of the tubes, the floating head arrangements are done (Figure 11.2(b)).
Another improvement in the shell and tube type is the incorporation of U-bend tubes which will facilitate more turbulence and secondary flow, thus increasing heat transfer rate (Figure 11.2(c)). Feed water heaters in thermal power plants uses U-bend type exchangers.
Plate Heat Exchanger
Plate heat exchangers as shown in Figure 11.3 are extensively used in liquid-to- liquid heat exchange processes. This type of heat exchanger is very popular in process industries where mixing, evaporation, reaction, distillation, separation processes are involved. It is one of the compact counter flow heat exchangers.
Effectiveness act
max
Q
Q is as high as 0.95. Temperature and pressure are the main
Floating Head Type Tube-side
outlet
Shell-side
outlet Baffle Header
Tube-side Fluid inlet Shell-side
Fluid inlet Shell
Tubes Header
Heat and Mass Transfer
Applications drawbacks in case of gasketed units. But with advance technology, better gaskets are available and can withstand high temperature and pressure.
Figure 11.3 : Plate Heat Exchanger
Plate-fin Heat Exchanger
The compactness factor can be significantly improved (upto about 6000 m2/m3) by using the plate-fin type heat exchanger as shown in Figure 11.4. These types of heat exchangers are generally used for gas-to-gas applications, but they are used for low pressure applications not exceeding above 10 atm (1000 kPa). The maximum operating temperature is limited to about 800oC.
Figure 11.4 : Plate-fin Exchanger
Spiral Plate Heat Exchanger
It is a form of plate heat exchanger usually made of stainless steel. It is often used in cellulose industries where heat exchanger is subjected to severe fouling and corrosion. The plates of this type of heat exchanger are very long and thickness of passage between the plates must be rather small so that after the sheets forming the upper and lower surfaces are welded together, the unit can be wrapped into spiral form. That’s why it is called as spiral heat exchanger. The technical features of this type of heat exchanger are :
(a) Flow rates are relatively low (b) Pure counterflow heat exchanger (c) Highly compact (more than 700 m2/ m3) (d) Can withstand pressure upto 10 bar only
Header
Cold Fluid in
Hot Fluid Out Cold
Fluid Out Hot Fluid
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Heat Exchangers
Figure 11.5 : Spiral Heat Exchanger
Regenerator
Heat exchangers in which there is an intermittent flow of heat from hot to cold fluid via heat storage and heat rejection through the exchanger surface or matrix are referred to as indirect or storage type heat exchanger or regenerator. The regenerative type heat exchangers are either static or dynamic.
Static Type Regenerator (a) No moving parts.
(b) Consists of a porous medium (balls, pebbles, powders, etc.) through which hot and cold fluid pass alternatively.
(c) A flow switching device regulates the periodic flow of the two fluids.
(d) Compact for use in refrigeration and Stirling Engines.
(e) Non-compact in high temperature (900 – 1500oC) applications.
(f) Low cost and ruggedness are essential for the stationary type.
Storage Type or Regenerative Heat exchanger
Storage type or regenerative heat exchanger is shown in Figure 11.6. In this heat exchanger energy is stored periodically. Medium is heated or cooled alternatively.
Heating period and cooling period constitute 1 (one) cycle.
Features
(a) Periodic heat transfer-conduction.
(b) Heat transfer fluid can be a liquid, phase changing, non-phase changing.
(c) Solid storage medium is called matrix.
(d) Matrix may be stationary or rotating
Figure 11.6 : Storage Type/Regenerator Type Heat Exchanger Hot Out
Cold In
x
x
B
D A
C
In In
Heat and Mass Transfer
Applications Classical Applications
(a) Gas turbine regenerators : Heating the compressed air by the gas turbine exhaust before the air goes to the combustor.
(b) Reversed Stirling engine for liquefaction of air-Philips refrigeration machine.
Dynamic Type Regenerator
(a) Compact in nature, very high surface to volume ratio (more than 6500 m2/m3).
(b) Usually matrix rotates about an axis (i.e. Ljungstrom regenerative air preheater).
(c) Operating temperature is upto 870oC.
(d) Usually used as gas-to-gas heat exchanger.
Heat Wheels/Rotary Regenerator/Ljungstrom Air Preheater Features
(a) Annulus is divided into numbers of sectors.
(b) Matrix is filled up in these sectors.
(c) Out of these sectors, few are kept empty so that hot fluid/cold fluid cannot flow through the empty region.
(d) Matrix rotates at low RPM (3-4 RPM) driven by a motor through appropriate reduction gear in mesh.
(e) Heat capacity of matrixes are more than that of the gases
matrix gas
| |
p p
m c m c , hence it is useful for gas-to-gas recovery.
(f) For gas-to-liquid or liquid-to-liquid recovery, it is not useful as
matrix liquid
| < |
p p
m c m c .
Figure 11.7 : Heat Wheel Hot Fluid Cold Fluid
Heating Zone
Empty
Cooling Zone
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Heat Exchangers
Advantages (a) Cheap
(b) Compact (~ 6500 m2/ m3), large surface area, hence high heat transfer rate.
(c) Can operate upto 870oC with metal matrix Disadvantages
(a) Large pressure drop through the matrix.
(b) Fouling of surfaces with entrained solid particles causing reduction in flow passage area leading to increase in pressure drop.
(c) Leakage of one fluid in the duct to the duct where other fluid is flowing requires extra space to separate the flow passages.
(d) Energy required to rotate the wheel.
Applications
Heat wheels are widely used in thermal power plants to pre-heat air by the exhaust gases.
Rothemuhle Regenerator
This type of heat exchanger is extensively used in steel plants for heat recovery.
In this heat exchanger, the matrix is stationary and the hood rotates. One half of the hood is perforated. Air at ambient condition is passed through the central core of the heat exchanger. On one side of the central pipe also, perforation is provided to facilitate air movement to the matrix. Hot gas containing the waste heat enters from the top, passes through the perforated hood to the matrix thereby exchanges heat through the matrix and goes out at the bottom. Simultaneously, air passes through the other half of the previously hot matrix and get heated. Two different positions of this heat exchanger has been shown in Figure 11.8.
Figure 11.8 : Rothemuhle Heat Exchanger
Matrix Material.
(a) Usually knitted aluminium or stainless steel is used.
(b) For moisture removal from air, hygroscopic material like asbestose fibre impregnated with LiCl can be used.
Disadvantage
(a) Pressure drop is large.
Cool Air in
Cooled Out gas Stationary Heat Exchanger Matrix
Rotating Hood Hot Air Out
Hot Gas in
Cool Air in
Cooled Out Gas Stationary Heat Exchanger Matrix
Rotating Hood Hot Air Out
Hot Gas in
Heat and Mass Transfer
Applications (b) Subjected to fouling.
11.2.3 Classification by Flow Arrangement
Numerous possibilities exist for flow arrangement in heat exchangers. Some of the flow arrangements are as follows :
Parallel Flow
The hot and the cold fluid enter at the same end of the heat exchanger, flow through in the same direction, and leave at the other end, as illustrated in Figure 11.9.
Figure 11.9 : Parallel Flow Heat Exchanger
Counter Flow
The hot and cold fluids enter in the opposite ends of the heat exchanger and flow in opposite directions, as illustrated in Figure 11.10.
Figure 11.10 : Counter Flow Heat Exchanger
Cross Flow
In the cross flow exchanger, the two fluids usually flow at right angles to each other, as illustrated in Figure 11.11. In the cross flow arrangement, the flow may be called mixed or unmixed, depending on the design.
Figure 11.11 : Cross Flow Heat Exchanger
Figure 11.12(a) shows an arrangement in which both the cold and hot fluids flow through the individual channels formed by corrugation, therefore the fluids are not free to move in the transverse direction. Then each fluid stream is said to be unmixed. Figure 11.12(b) illustrates a typical temperature profile for the outlet temperatures when both fluids are unmixed (Figure 11.12(a)). The inlet
Cold Out
Hot In
Hot Out
Cold In
Hot In
Hot Out Cold In
Cold I Out
Cold In
Cold Out Hot
In Hot
Out
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Heat Exchangers
temperatures for both fluids are assumed to be uniform, but the outlet temperatures exhibit variation transverse to the flow.
(a)
(b)
(c)
Figure 11.12 : Cross Flow Arrangements (a) Both Fluids Unmixed, (b) Temperature Profile when Both Fluids are Unmixed, and (c) Cold Fluid Unmixed but Hot Fluid Mixed
In the flow arrangements shown in Figure 11.12(c), the cold fluid flows inside the tubes and is not free to move in the transverse direction. Therefore, the cold fluid is said to be unmixed. However, the hot fluid stream flows over the tubes and is free to move in the transverse direction. Therefore, the hot fluid stream is said to be mixed. The mixing tends to make the fluid temperature uniform in the transverse direction. Therefore, the exit temperature of a mixed stream exhibits negligible variation in the crosswise direction.
In general, in a cross flow exchanger, three idealised flow arrangements are possible :
(a) both fluids are unmixed,
(b) one fluid is mixed and the other fluid is unmixed, and (c) both fluids are mixed.
T c, out T h, out
Hot Fluid, T h, In
T c, In, Cold Fluid
T c, out
T c, in
T h, out
T h, in
y
x
Hot Fluid
Cold Fluid inside Tubes
Heat and Mass Transfer
Applications The last arrangement is not commonly used.
In a shell and tube exchanger, the presence of large number of baffles serves to mix the shell side fluid. Hence, temperature of the shell side fluid tends to be uniform at any cross-section.
Multipass Flow
The multipass flow arrangements are frequently used in heat exchanger design, because multipassing increases the overall effectiveness over the individual effectiveness. A wide variety of multipass arrangements are possible.
Figure 11.13 illustrates typical arrangements. The heat exchanger in
Figure 11.13(a) is a “one shell pass, two tube pass” arrangement. This is also called a one-two heat exchanger. Figure 11.13(b) presents a “two shell pass, four tube pass” arrangement and in Figure 11.13(c) shows a “three shell pass, six tube pass” arrangement.
(a)
(b)
(c)
Figure 11. 13 : Multipass Flow Arrangements (a) One Shell Pass, Two Tube Pass, (b) Two Shell Pass, Four Tube Pass, (c) Three Shell Pass, Six Tube Pass
11.2.4 Classification by Heat Transfer Mechanism
Heat exchangers can be classified based on the heat transfer mechanism, such as : (a) Single phase forced or free convection (sensible heat transfer).
(b) Phase change (boiling and condensation).
(c) Radiation or combined convection and radiation.
Tube-side Fluid Shell-side Fluid
Shell-side Fluid
Tube-side Fluid
Tube-side Fluid Shell-side Fluid
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Heat Exchangers
Single phase heat exchangers are already described in the preceeding subsections. In this type of heat exchangers, heat transfer between fluid streams occur due to exchange of sensible heat only. Phase change mechanisms and applications to boiler and condenser are described in Unit 12.
Metallic Radiative Recuperator Features
(a) Height upto 50 m (b) Diameter 0.25-3 m
(c) Natural draught, no need for a fan or blower (d) Heat transfer is chiefly by radiation
Examples : Metallic recuperators are used in (a) Steel plants
(b) Glass Melting Furnaces
Figure 11.14 : Metallic Recuperator
11.2.5 Classification according to the Type of Fluids
Heat exchangers may be further classified according to the type of fluids, such as gas-to-gas, gas to liquid and liquid to liquid heat exchanger.
Gas-to-Gas Heat Exchanger
(a) Plate-fin coupled prime surface exchanger (b) Heat Pipe
(c) Rotary regenerator (d) Convection recuperator (e) Liquid heat
Gas-to-Liquid Heat Exchanger (a) Boiler
(i) Fire tube
Hot Air to Process
Cold Air Intake
Flue Gas Waste Gas
Heat and Mass Transfer
Applications (ii) Water tube
(b) Economizer
(c) Fluidized bed heat exchanger (d) Heat pipe heat exchanger Liquid-to-Liquid Heat Exchanger
(a) Shell and tube (b) Plate
Gas-to-Gas Heat Exchanger
These types of heat exchangers require special arrangement to have high heat transfer rate. Gases are having low heat transfer coefficient. Usually heat transfer coefficients on opposite sides of the heat transfer surface are usually within a factor of 3 to 4 of each other. The absolute values are generally lower than liquid to liquid heat exchangers. Hence heat transfer enhancement is essential in such heat exchangers. Application of fin, surface roughening, inserts are usually employed. But pressure drop is also high. Leakage of either fluid may be tolerated upto 4%. Constructions are lighter and less rugged. Various types of gas-to-gas heat exchangers are :
(a) Plate-fin
(b) primary surface exchanger (c) rotary regenerator
(d) run around coil
(e) radiation and convective recuperator (f) heat pipe
Temperature Limitations
The minimum temperature to which the waste gas are cooled is an important consideration in the design of gas-to-gas waste heat recovery devices, i.e. air preheater. It is considered good practice to design so that temperature of
combustion gas (waste gas) leaving the heat exchanger does not drop below 300oF (148.88oC), because if this is not done, corrosion may result as a result of
condensation of sulphurous or sulphuric acid. These substances are formed from the sulphur present in most fuels reacting with the water vapour from combustion.
Oxidation of carbon steel becomes a serious problem for gas temperature in excess of 1000 F (537.78oC). Hence, ceramic material is to be used. For example, the air preheater for steel and blast furnace are ordinarily made of ceramic.
Applications of Gas-to-Gas Recovery Units (a) Air preheater for steam power plant (b) Gas fired heater for industrial processes
(c) Gas turbines – overall thermal efficiency may be doubled with gas-to-gas regenerative type heat exchanger. Used as intercooler between stages and compressor.
SAQ 1
(a) How do you classify the heat exchangers?
(b) What is a counterflow heat exchanger?
(c) Sketch the schematic diagram of a shell-and-tube heat exchanger and indicate its various parts.
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Heat Exchangers
(d) What is the major difference between a recuperator and a regenerator?
(e) How does a rotary heat exchanger work? Explain with diagram?
11.3 TEMPERATURE DISTRIBUTION IN HEAT EXCHANGERS
Figure 11.15 presents the variation of temperature for different arrangements along the flow path (along the length of the heat exchanger).
(a) Uniform Temperature Difference (b) Uniform Surface Temperature or Uniform Heat Flux (As in a Condensor)
(c) Uniform Surface Temperature (As in Boiling)
(d) Parallel Flow Heat Exchanger (e) Counter Flow Heat Exchanger Figure 11.15 : Axial Temperature Distribution in Typical Single-pass Heat Transfer Matrices
Figure 11.15(a) indicates a pure counterflow heat exchanger in which the temperature rise in the cold fluid is equal to the temperature drop in the hot fluid, thus the
temperature drop T between the hot fluid and the cold fluid is constant throughout.
However, in all other cases (Figures 11.15(b)-(e)), the temperature difference T between the hot and the cold fluids varies with position along the path of flow.
Figure 11.15(b) corresponds to a situation in which the hot fluid condenses and heat is transferred to the cold fluid causing its temperature to rise along the path of flow.
In Figure 11.15(c), cold liquid is evaporating and cooling the hot fluid along its path of flow.
Figure 11.15(d) shows a parallel flow arrangement in which both the fluids flow in the same direction, with cold fluid experiencing a temperature rise and the hot fluid a temperature drop. The outlet temperature of the cold fluid cannot exceed that of the hot fluid. Therefore, the temperature effectiveness of the parallel flow exchangers is limited.
Because of this limitation, generally they are not used for heat recovery.
Hot Fluid
Cold Fluid
T0
T1
Temperature
O Distance from Inlet L
T0
T1
Hot Fluid
Boiling
Temperature
O Distance from Inlet L
T0 T1
Hot Fluid
Cold Fluid
Temperature
O Distance from Inlet L
T0
T1
Hot Fluid
Cold Fluid
Temperature
O Distance from Inlet L
T0
T1
Condensing
Cold Fluid
Temperature
O Distance from Inlet L
Heat and Mass Transfer
Applications Figure 11.15(e) presents a counter flow arrangement in which fluids flow in opposite directions. The exit temperature of the cold fluid can be higher than that of the hot fluid.
Theoretically, the exit temperature of one fluid may approach the inlet temperature of the other. Therefore, thermal capacity of the counter flow exchanger can be twice that of the parallel flow heat exchangers. The high heat recovery and temperature effectiveness of this exchanger makes it preferable to the parallel flow exchanger whenever the design requirements permit such a choice.
Temperature distributions are more complicated in multi-pass and cross flow
arrangements. Figure 11.16 shows the temperature distribution in a one shell pass, two tube pass heat exchanger.
Figure 11.16 : Axial Temperature Distribution in One Shell Pass, Two Tube Pass Heat Exchanger
Figure 11.17 shows a typical temperature profile in a cross flow heat exchanger when both fluids are unmixed. It may be noted that inlet temperatures for both the streams are uniform but the out let temperatures are non-uniform for both the streams.
Figure 11.17 : Temperature Distribution in a Cross Flow Heat Exchanger, Both Fluids are Unmixed
11.4 THE OVERALL HEAT TRANSFER COEFFICIENT
In the heat transfer analysis of heat exchangers, various thermal resistances in the path of heat flow from the hot to the cold fluid are combined into an overall heat transfer coefficient U.
Consider that the total thermal resistance R to heat flow across a tube, between the inside and the outside flow, is composed of the following thermal resistances
R = (thermal resistance of inside flow) + (thermal resistance of the tube material)
+ (thermal resistance of outside flow)
and various terms are given by
Hot Fluid In
Cold Fluid In Cold Fluid Out
Hot Fluid Out
Out Tube-Side
Fluid In Shell-Side
Fluid in
Shell-Side Fluid Out
Distance Hot Fluid – Shell side
Cold Fluid – Tube side
O L
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Heat Exchangers
1 1
i i m o o
R t
A h k A A h
. . . (11.1)
where Ao, Ai = outside and inside surface areas of tube respectively, m2
ln
o i
m
o i
A A
A A
A
logarithmic mean area, m2
ho, hi = Heat transfer coefficients for inside and outside flow respectively, W/(m2.oC), k = Thermal conductivity of tube material, W/(m.oC),
R = Total thermal resistance from inside to outside flow oC/W, and t = Thickness of tube, m.
The thermal resistance R given by Eq. (11.1) can be expressed as an overall heat transfer coefficient based on either the inside or the outside surface of the tube. It does not matter on which area it is based as long as it is specified in its definition. For example, the overall heat transfer coefficient Uo based on the outside surface of the tube is defined as
1 1
1 1
o
o o o
i i m o
U A R A A t
A h A k h
. . . (11.2)
or, 1
1 1 ln 1
2
o
o o
o
i i i o
U D D
D h k D D h
. . . (11.3)
Since ln
2
o o o
m i
A D D
A t D
o i 2 D D t
and Di and Do are the inside and out side diameter of the tube respectively.
Similarly, the overall heat transfer coefficient Ui based on the inside surface of the tube is defined as
1 1
1 1
i
i i i
i m o o
U A R A t A
h A k A h
. . . (11.4)
or 1
1 1 1
2 ln
i
o i
i
i i o o
U D D
h k D D D h
. . . (11.5)
When the wall thickness is small and its thermal conductivity is high, the tube resistance can be neglected and Eq. (11.4) reduces to
1
1 1
i
i o
U
h h
. . . (11.6)
In heat exchanger applications, the heat transfer surface is fouled with the accumulation of deposits which in turn introduces additional thermal resistance in the path of heat flow. The effect of fouling is generally introduced in the form of a fouling factor F (m2.oC/W).
Heat and Mass Transfer
Applications We now consider heat transfer across a tube, which is fouled by deposit formation on both the inside and outside surfaces. The thermal resistance R in the path of heat flow for this case is given by
1 i o 1
i i i m o o o
F t F
R A h A k A A A h . . . (11.7)
where Fi and Fo are the fouling factors at the inside and outer tube surface of the tube.
Then Eq. may be represented in terms of the overall heat transfer coefficient based on the outside surface of the tube as
1
1 1
2 ln
o
o o o
o
i i i o
U D D D
D h k D F h
. . . (11.8)
The values of overall heat transfer coefficients for different types of applications vary widely. Typical ranges of Uo are given in Table 11.2.
Table 11.2 : Typical Values of Overall Heat Transfer Coefficient Uo
for Different Types of Heat Exchangers
Type of Heat Exchangers Uo (W/m2.oC)
Water to oil exchangers 60-350
Gas-to-gas exchangers 60-600
Air conditioners 350-800
Ammonia condensers 800-1400
Steam condensers 1500-5000
11.4.1 Fouling Factor
Mechanism of fouling is very complicated. No reliable technique is available to predict the fouling factor. Some recommended values are given in Table 11.3.
Table 11.3 : Fouling Factors
Sl. No. Fluid Fouling Factor (m2.K/W)
1. Sea water 0.000088
2. Treated boiler water 0.000180
3. Fuel oil 0.009000
4. Diesel engine exhaust 0.001800
Category of Fouling
Scaling or Precipitating Fouling
Due to the crystallization from solutions of dissolved substance on to the heat transfer surface.
Particulate Fouling
Accumulation of finely divided solids suspended in the process fluids on to the heat transfer surface.
Chemical Reaction Fouling
The deposit formation on to the heat transfer surface by chemical reaction.
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Heat Exchangers
Corrosion Fouling
Accumulation of corrosion products on to the heat transfer surface.
Biological Fouling
Attachment of micro-organisms to a heat transfer surface.
Solidification Fouling
Crystallization of a pure liquid or one component from the liquid phase on a sub-cooled heat transfer surface.
SAQ 2
(a) What do you mean by fouling?
(b) How does fouling effect the overall heat transfer coefficient of a heat exchanger?
11.5 HEAT EXCHANGER ANALYSIS
11.5.1 Log Mean Temperature Difference
To design or to predict the performance of heat exchanger, it is essential to relate the total transfer rate to quantities such as the inlet and outlet fluid temperatures, the overall heat transfer coefficient, and the total surface area for heat transfer. Two such relations may readily be obtained by applying overall energy balances to the hot cold fluids. In particular, if q is the total rate of heat transfer between the hot and cold fluids and there is negligible potential and kinetic energy changes, application of the steady flow energy equation gives
, , 0
( )
h h i h
qm i i . . . (11.9)
and qm ic (c o, ic i, ) . . .
(11.10)
where i is the fluid enthalpy. The subscripts h and c refer to the hot and cold fluids, where i and o designate the fluid inlet and outlet conditions. If the fluids are not undergoing a phase change and constant specific heats are assumed, these expressions reduce to
, ( , , 0)
h p h h i h
qm c T T . . . (11.11)
and qm cc p c, (Tc o, Tc i, ) . . . (11.12) where the temperature appearing in the expression refer to the mean fluid temperatures at the designated locations. Another useful expression may be obtained by relating the total heat transfer rate q to the temperature difference T between the hot and cold fluids, where
h c
T T T
. . . (11.13)
Such an expression would be an extension of Newton's law of cooling, with the overall heat transfer coefficient Uo used in place of the single convection coefficient h.
However, since T varies with position in the heat exchanger, it is necessary to work with a rate equation of the form
o m
q U A T . . . (11.14)
where Tm is an appropriate mean temperature difference.
The Parallel Flow Heat Exchanger
Heat and Mass Transfer
Applications The hot and cold fluid temperature distributions associated with a parallel-flow heat exchanger are shown in Figure 11.7. The temperature difference T is initially large but decays rapidly with increasing x, approaching zero asymptotically. It is important to note that, for such an exchanger, the outlet temperature of the cold fluid never exceeds that of the hot fluid. In Figure 11.7 the subscripts 1 and 2 designate opposite ends of the heat exchanger. This convection is used for all types of heat exchangers considered. For parallel flow, it follows that
1,i, h o, 1,2, c,1
T T T T . . . (11.15)
, , 2
c o c
T T . . . (11.16)
The form of Tm may be determined by applying an energy balance to differential elements in the hot and cold fluids (Figure 11.18). Each element is of length dx and heat transfer surface area dA.
Figure 11.18 : Parallel Flow
The energy balance and the subsequent analysis are subjected to the following assumptions :
(a) The heat exchanger is insulated from its surroundings, in which case the only heat exchange is between the hot and cold fluids.
(b) Axial conduction along the tubes is negligible.
(c) Potential and kinetic energy changes are negligible.
(d) The fluid specific heats are constant.
(e) The overall heat transfer coefficient is constant.
The specific heats may of course change as a result of temperature variations, and the overall heat transfer may change because of variations in fluid properties and flow condition. However, in many applications such variations are not significant, and it is reasonable to work with average values of cp, c, cp, h and U for the heat exchanger.
Applying an energy balance to each of the elements of Figure 11.18, it follows that
, ,
h p h h h h
dq m c dT C dT . . . (11.17)
Ch
CC
dx dq
dA
Th + dTh
TC + dTC
Heat Transfer Surface Area
T1 T
Th,i
Tc,i
dq
dTh
dTc
1 2
T2 Th,
Tc, Th, Ch
Tc, Cc
T
x Th
Tc
23
Heat Exchangers
and dq m Cc p c, ,dTc C dTc c . . . (11.18) where Ch and Cc are the hot and cold fluid heat capacity rates, respectively. These expressions may be integrated across the heat exchanger to obtain the overall energy balances given by Eqs. (11.11) and (11.12). The heat transfer across the surface area dA may also be expressed as
dq U TdA . . . (11.19)
where T = Th – Tc is the local temperature difference between the hot and cold fluids.
To determine the integrated form of Eq. (11.19), we begin by substituting Eqs. (11.17) and (11.18) into differential form of Eq. (11.13)
( ) h c
d T dT dT . . . (11.20)
to obtain 1 1
( )
h c
d T dq
C C
. . . (11.21)
Substituting for dq from Eq. (11.19) and integrating across the heat exchanger, We obtain
2 2
1 1
( ) 1 1
h c
d T
U dA
T C C
. . . (11.22)or, 2
1
1 1
ln
h c
T UA
T C C
. . . (11.23)
Substituting for and Ch and Cc from Eqs. (11.11) and (11.12), respectively, it follows that
, , , ,
2 1
ln T Th i Th o Tc o Tc i
T UA q q
UA ( c o, c i, ) ( h i, h o, )
T T T T
q
. . . (11.24)
Recognizing that for the parallel-flow heat exchanger of Figure 11.18,
1 ( h i, c i, )
T T T
. . . (11.25)
and T2(Th o, Tc o, ) . . . (11.26)
and we then obtain
2 1
2 1
( )
ln
T T
q UA T
T
. . . (11.27)
Comparing the above expression with Eq. (11.14), we conclude that the appropriate average temperature difference is a log mean temperature difference, Tm. Accordingly, we may write
q UA T m . . . (11.28)
where 2 1 1 2
2 1
1 2
( ) ( )
ln ln
m
T T T T
T T T
T T
Heat and Mass Transfer
Applications 1 ,1 ,1 , ,
2 , 2 , 2 , ,
h c h i c i
h c h o c o
T T T T T
T T T T T
. . . (11.29)
The Counter Flow Heat Exchanger
The hot and cold fluid temperature distributions associated with a counter flow heat exchanger are shown in Figure 11.19. In contrast to the parallel-flow exchanger, this counter flow Heat Exchanger, configuration provides for heat transfer between the hotter portions of the two fluids at one end, as between the colder portions at the other. For this reason, the change in the temperature
difference, T Th Tc, with respect to x is nowhere as large as it is for the inlet region of the parallel flow exchanger. Note that the outlet temperature of the cold fluid may now exceed the outlet temperature of the hot fluid.
Figure 11.19 : Counter Flow Heat Exchanger
Eqs. (11.11) and (11.12) apply to any heat exchanger and hence may be used for the counter flow arrangement. Moreover, from an analysis like that performed in Section 11.5, it may be shown that Eqs. (11.28) and (11.29) also apply. However, for the counter flow exchanger the endpoint temperature differences must now be defined as
1 h,1 c,1 h i, c o,
T T T T T
2 h, 2 c, 2 h o, c i,
T T T T T
. . . (11.30)
Note that, for the same inlet and outlet temperature, the log mean temperature difference for counter flow exceeds that for parallel flow, Tlm CF, Tlm PF, . Hence the surface area required to effect a prescribed heat transfer rate q is smaller for the counter flow than for the parallel-flow arrangement, assuming the same value of U. Also note that Tc, o, can be exceed Th, o for counter flow but not for parallel flow.
Multi Pass and Cross-flow Heat Exchangers
Although flow conditions are more complicated in multi pass cross-flow heat exchangers, Eqs. (11.9)-(11.12) and (11.28) may still be used if the following modification is made to the log mean temperature difference
Ch
CC
dx dq
dA
Th + dTh
TC + dC
Heat Transfer Surface Area
T1 T
Th,i
Tc,o
dq
dTh
dTc
1 2
T2 Th,o
Tc,i Th, Ch
Tc, Cc
T
x Th
Tc + DTc
25
Heat Exchangers ,
lm lm CF
T F T
. . . (11.31)
That is the appropriate form of Tlm is obtained by applying a correlation factor to the value of Tlm that would be computed under the assumption of counter flow conditions. Hence,
1 h,1 c o, and 2 h o, c i,
T T T T T T
. . . (11.32)
Algebraic expressions for the correlation factor F have been developed for various shell-and tube and cross flow heat exchanger configurations and the results may be represented graphically. Selected results are shown in Figures 11.20(a)-(d) for common heat exchanger configurations.
(a) (b)
b
(c) (d)
Figure 11.20 : Correction Factors for a Shell and Tube Heat Exchanger
The notation (T, t) is used to specify the fluid temperature, with the variable t always assigned to the tube-side fluid. With this convention it does not matter whether the hot fluid or the cold fluid flows through the shell or the tubes. An important implication of Figures 11.20(a)-(d) is that if temperature change of one fluid is negligible, either P or R is zero and F is 1. Hence heat exchanger
behaviour is independent of the specific configuration. Such would be the case if one of the fluids underwent a phase change.
6.0 4.0 3.0 2.0 1.0 1.0 0.8 0.6 0.2 Ti
Tc 1.0
0.9 0.8 0.7 0.6
0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 to
ti
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0
0.9 0.8 0.7
0.6 0.5
6.0 4.0 3.0 2.0 1.5 1.0 0.8 0.6 0.2 Ti
To
ro t1
0.4 T - Toi
R = t - to i
t - ti i P =
T - Toi
To
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0
0.9 0.8 0.7 0.6 0.5
4.0 3.0 2.0 1.5 1.0 0.8 0.6 0.4 0.2
ti t0
P R
Ti
To
ti t0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0
0.9 0.8
0.7 0.6 0.5
4.0 3.0 2.0 1.6 1.0 0.8 0.6 0.4 0.2 R=
P=
Ti
Heat and Mass Transfer
Applications SAQ 3
(a) How do you estimate the heat transfer rate for a parallel flow heat exchanger?
(b) Why counter flow heat exchanger is preferred to a parallel flow exchanger?
(c) What is LMTD? When do you use LMTD method?
11.5.2 The Effectiveness-NTU Method
It is a simple matter to use the log mean temperature difference (LMTD) method of heat exchanger analysis when the fluid inlet temperatures are known and the outlet
temperature are specified or readily determined from the hanger may then be determined.
However, if only the inlet temperatures are known, use of the LMTD method requires to iterative procedure. In such cases it is preferable to use an alternative approach, termed the effectiveness-NTU method.
Definitions
To define the effectiveness of a heat exchanger, we must first determine the maximum possible heat transfer rate, qmax, for the exchanger. This heat transfer rate could, in principle, in a counter flow heat exchanger of finite length. In such an exchanger, one of the fluids would experience the maximum possible
temperature difference, Th i, Tc i, .
To illustrate this point, consider a situation for which Cc < Ch, in which case, from Eqs. (11.17) and (11.18), dTc dTh . The cold fluid would then be heated to the inlet temperature of the hot fluid (Tc o, Th i, ), Accordingly, from Eq. (11.12), if Cc < Ch.
max c ( h,1 c i, )
q C T T . . . (11.33)
Similarly, if Ch < Cc
max h( h,1 c i, )
q C T T . . . (11.34)
From the foregoing results we are then prompted to write the general expression
max min ( h,1 c i, )
q C T T . . . (11.35)
where cmin is equal to Cc and Ch, whichever is smaller. For prescribed hot and cold fluid inlet temperature, Eq. (11.35) provides the maximum heat transfer rate that could possibly be delivered by the exchange. A quick mental exercise should convince the reader that the maximum possible heat transfer rate is not equal to Cmax (Th,1Tc i, ). If the fluid having the larger heat capacity rate were to experience the maximum possible temperature change, conservation of energy in the form Cc(Tc o, Tc i, )Ch(Th i, Th o, )
would require that the other fluid experience yet a larger temperature change.
For example, it follows that (Th i, Th o, ) ChCc (Th i, Tc i, )
, in which case
(Th i, Th o, )(Th i, Tc i, ) . . . (11.36) Such a condition is clearly impossible.
It is now logical to define the effectiveness, , as the ratio of the actual heat transfer rate for heat exchanger to the maximum possible heat transfer rate
q
q . . . (11.37)
27
Heat Exchangers
From Eqs. (11.11), and (11.35), it follows that
,1 ,
min ,1 ,
( )
( )
h h h o
h c i
C T T
C T T
. . . (11.38)
,1 ,
min ,1 ,
( )
( )
c h c i
h c i
C T T
C T T
. . . (11.39)
By definition the effectiveness, which is dimensionless, must be in the range 0 1. It is useful because, if , Th i, andTc i, are known, the actual heat transfer rate may readily be determined from the expression, .Cmin (Th i, Tc i, )
For any heat exchanger it can be shown that , min
max f NTU C
C
. . . (11.40)
where min or
max
C C
C c h
C Ch Cc
, depending on the relative magnitude of the hot and cold fluid heat capacity rates. The number of transfer units (NTU) is a dimensionless parameter that is widely used for heat exchanger analysis and is defined as,
min NTU UA
C . . . (11.41)
Effectiveness-NTU Relations
To determine a specific form of the effectiveness-NTU relation 11.40 consider a parallel-flow heat exchanger for which Cmin = Ch. From Eq. (11.38) we obtain
( , , )
( , , )
Th i Th o Th i Tc i
. . . (11.42)
and from Eqs. (11.11) and (11.12) it follows that
, ,
min
max , ,
, ,
c o c i h
c h i h o
T T
m Cp h C
C m Cp c T T
. . . (11.43)
Now consider Eq. (11.23), which may be expressed as
, , min
ln 1
, min
, max
Th o Tc o UA C
Th i Tc i C C
. . . (11.44) or from Eq. (11.41)
, , exp 1 min
, , max
Th o Tc o NTU C
Th i Tc i C
. . . (11.45)
Re-arranging the left-hand side of this expression as
,
, , , , , ,
, , , c i
Th o Tc o Th o Th i Th i Tc o Th i Tc i Th i T
. . . (11.46)
And substituting for Tc, o from Eq. (11.43), it follows that
Heat and Mass Transfer
Applications , , , , min , ,
, , max
, , , ,
( h o h i) ( h i c i) ( h i h o)
h o c o
h i c i h i c i
T T T T C T T
T T C
T T T T
. . . (11.47)
Substituting the above expression into Eq. (11.45) and solving for , we obtain for the parallel-flow heat exchanger
min max min max
1 exp 1
1 NTU C
C C C
. . . (11.48)
Since precisely the same result may be obtained for Cmin = Cc, Eq. (11.48) applies for any parallel-flow heat exchanger, irrespective of whether the minimum heat capacity rate is associated with the hot or cold fluid. Similar expressions have been developed for a variety of heat exchangers, and representative results are summarized in Table 11.4, where Cr is the
Table 11.4 : Heat Exchanger Effectiveness Relations
Flow Arrangement
Concentric Tube Relation
Parallel flow 1 exp { [(1 )]}
(1 )
r r
NTU C
C
Counter flow 1 exp { [(1 )]}
1 exp [ (1 r )] ( r 1)
r r
NTU C
C NTU C C
1 NTU ( r 1)
NTU C
Shell and Tube One shell pass (2, 4 tube passes)
1 1
1 2
2 2
1 2 2
1 exp { (1 ) }
2
1 exp { (1 ) }
(1 r) (1 r ) r
r
NTU C
NTU C
C C
n shell passes (2n, 4n tube passes)
1
1 1
1 1
1 1
1 1 1
n n
r r
r
C C
C
Cross Flow (single pass)
(Both fluids unmixed) exp 1 0.22 {1 exp [ )0.78] 1
( ) r ( }
r
C NTU C NTU
Cmin (mixed), Cmax
(unmixed)
1 exp [ Cr1(1 exp ( Cr NTU))]
All exchangers (Cr = 0) exp (NTU)
29
Heat Exchangers
heat capacity ratio min
max r
C C
C . It is more convenient to work with -NTU relations of the form
min max
NTU f C C
. . . (11.49)
Explicit relations for NTU as a function of and Cr are provided in Table 11.5.
Table 11.5 : Heat Exchanger NTU Relations Flow Arrangement
Concentric Tube Relation
Parallel flow ln [1 (1 )]
(1 )
NTU Cr
Cr
Counter flow 1 ( 1)
ln ( 1)
1 ( 1)
NTU Cr Cr Cr
( 1)
( 1)
NTU Cr
Shell and Tube One shell pass
(2, 4 tube passes)
1 1
2 2
(1 ) ln
1
NTU Cr EE
2 (1 )
1 1
2 2
(1 )
Cr E
Cr
Shell passes (2n, 4n tube passes)
1
1
r
F
F C
and
1
1 1
r n
F C
Cross flow (single pass)
ln 1 1 ln (1 )
r r
NTU C
C
C (mixed), C (unmixed) 1
ln [ ln (1 ) 1]
NTU Cr
Cr
All exchangers NTU ln (1 )
SAQ 4
(a) Define effectiveness of a heat exchanger.
(b) What is NTU?
(c) When do you use NTU method?
