Chapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

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1 Chapter 11: Heat Exchangers Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

2 Objectives When you finish studying this chapter, you should be able to: Recognize numerous types of heat exchangers, and classify them, Develop an awareness of fouling on surfaces, and determine the overall heat transfer coefficient for a heat exchanger, Perform a general energy analysis on heat exchangers, Obtain a relation for the logarithmic mean temperature difference 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 heat exchangers when outlet temperatures are not known using the effectiveness-ntu method, Know the primary considerations in the selection of heat exchangers.

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4 Types of Heat Exchangers Different heat transfer applications require different types of hardware and different configurations of heat transfer equipment. What should we choose?

5 (1) Double-Pipe Heat Exchangers The simplest type of heat exchanger is called the double-pipe heat exchanger. One fluid flows through the smaller pipe while the other fluid flows through the annular space between the two pipes. Two types of flow arrangement parallel flow, counter flow.

6 (2) Compact Heat Exchanger Large heat transfer surface area per unit volume. Area density β heat transfer surface area of a heat exchanger to its volume ratio. Compact heat exchanger β >700 m 2 /m 3. Examples: car radiators (β 1000 m 2 /m 3 ), glass-ceramic gas turbine heat exchangers (β 6000 m 2 /m 3 ), the regenerator of a Stirling engine (β 15,000 m 2 /m 3 ), and the human lung (β 20,000 m 2 /m 3 ).

7 Compact heat exchangers are commonly used in gas-to-gas and gas-to liquid (or liquid-to-gas) heat exchangers. Typically cross-flow configuration the two fluids move perpendicular to each other. The cross-flow is further classified as unmixed flow and mixed flow.

8 (3) Shell-and-Tube Heat Exchanger The most common type of heat exchanger in industrial applications. Large number of tubes are packed in a shell with their axes parallel to that of the shell. The other fluid flows outside the tubes through the shell. Baffles are commonly placed in the shell. Shell-and-tube heat exchangers are relatively large size and weight. Shell-and-tube heat exchangers are further classified according to the number of shell and tube passes involved.

9 (4) Plate and Frame Heat Exchanger Consists of a series of plates with corrugated flat flow passages. The hot and cold fluids flow in alternate passages Well suited for liquid-to-liquid heat exchange applications, provided that the hot and cold fluid streams are at about the same pressure.

10 The Overall Heat Transfer Coefficient A heat exchanger typically involves two flowing fluids separated by a solid wall. Heat is transferred from the hot fluid to the wall by convection, through the wall by conduction, and from the wall to the cold fluid by convection. The thermal resistance network two convection and one conduction resistances.

11 For a double-pipe heat exchanger, the thermal resistance of the tube wall is ln ( D ) 0 Di Rwall = (11-1) 2π kl The total thermal resistance 1 ln ( D ) 0 Di 1 R = total R + i R + wall R = o ha + 2π kl + h A (11-2) i i o o When one fluid flows inside a circular tube and the other outside of it, we have A = π DL ; A = π D L i i o o

12 It is convenient to combine all the thermal resistances in the path of heat flow from the hot fluid to the cold one into a single resistance R T Q Δ = = UAΔ T = UiAiΔ T = UoAoΔT R U is the overall heat transfer coefficient, whose unit is W/m 2 ºC. Canceling T, Eq reduces to (11-3) = = = R= + Rwall + (11-4) UA U A U A h A h A s i i o o i i o o

13 When the wall thickness of the tube is small and the thermal conductivity of the tube material is high (R wall =0) and the inner and outer surfaces of the tube are almost identical (A i A o A s ), Eq simplifies to When h i >>h o When h i <<h o (11-5) U h h i o 1 1 U h o 1 1 U h i

14 The overall heat transfer coefficient U in Eq is dominated by the smaller convection coefficient { h water >>h oil >>h gas } EXAMPLE: If (h i << h o ), we have 1/h i >> 1/h o, and thus U h i. Therefore, the smaller heat transfer coefficient creates a bottleneck on the path of heat transfer and seriously impedes heat transfer. 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 Usually gases have very low thermal conductivities When the tube is finned on one side to enhance heat transfer, the total heat transfer surface area on the finned side becomes

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16 Fouling Factor The 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 and causes the rate of heat transfer in a heat exchanger to decrease. The fouling factor R f The net effect of these accumulations on heat transfer. Two common type of fouling: precipitation of solid deposits in a fluid on the heat transfer surfaces. corrosion and other chemical fouling.

17 The overall heat transfer coefficient needs to be modified to account for the effects of fouling on both the inner and the outer surfaces of the tube. For an unfinned shell-and-tube heat exchanger, it can be expressed as 1 R ( ) f, i ln D0 Di Rf, o 1 R = (11-8) ha A 2 kl A h A i i i π o o o R f,i and R f,o are the fouling factors at those surfaces. R f,i and R f,o Table 11-2

18 EXAMPLE: Water at an average temperature of 107 C and an average velocity of 3.5 m/s flows through a 5-m-long stainless steel tube (k = 14.2 W/m C) in a boiler. The inner and outer diameters of the tube are D i = 1.0 cm and D o = 1.4 cm, respectively. If the convection heat transfer coefficient at the outer surface of the tube where boiling is taking place is h o =8400 W/m2 C, determine the overall heat transfer coefficient U i of this boiler based on the inner surface area of the tube. Outer surface D 0, A 0, h 0, U 0, R f0 Inner surface D i, A i, h i, U i, R fi

19 Properties The properties water at 107 C 110 C are (Table A-9) Analysis: υ = μ / ρ = k = Pr = W/m K 6 m 2 /s Re = V m D h υ = (3.5 m/s)(0.01 m) m 2 / s = 130,600 which is greater than 10,000. Therefore, the flow is turbulent. Assuming fully developed flow, Nu hd = k h = 0.023Re 0.8 Pr 0.4 = 0.023(130,600) 0.8 (1.58) 0.4 = 342 h k = Nu D h = W/m. C (342) = 23,324 W/m 2. C 0.01m

20 R 1 ln( Do / Di ) 1 = Rtotal = Ri + Rwall + Ro = + + hi Ai 2πkL ho Ao 1 ln(1.4 /1) = + 2 (23,324 W/m. C)[ π (0.01 m)(5 m)] [2π (14.2 W/m. C)(5 m)] + (8400 W/m = C/W 2 1. C)[ π (0.014 m)(5 m)] R = U 1 i A i U i = 1 RA i = 1 ( C/W)[ π (0.01m)(5 m)] = 4055 W/m 2. C

21 Analysis of Heat Exchangers Two different design tasks: 1) Specified: - the temperature change in a fluid stream, and - the mass flow rate. Required: - the designer needs to select a heat exchanger. 2) Specified: - the heat exchanger type and size, - fluid mass flow rate, - inlet temperatures. Required: - the designer needs to predict the outlet temperatures and heat transfer rate. Two methods used in the analysis of heat exchangers: the log mean temperature difference (or LMTD) best suited for the #1, the effectiveness NTU method NTU: Number of Transfer Units best suited for task #2.

22 The analysis of heat exchangers can be greatly simplify by making the following assumptions, which are closely approximated in practice: steady-flow, kinetic and potential energy changes are negligible, the specific heat of a fluid is constant, axial heat conduction along the tube is negligible, the outer surface of the heat exchanger is perfectly insulated. The first law of thermodynamics requires that the rate of heat transfer from the hot fluid be equal to the rate of heat transfer to the cold one.

23 The transfer rate to the cold fluid: Q = m c T T = C T T C = m c ( ) ( ) c pc c, out c, in c c, out c, in ; c c pc (11-9) (11-12) The transfer rate to the hot fluid: Q = m c T T = C T T C = m c ( ) ( ) h ph h, in h, out h h, in h, out ; h h ph (11-10) (11-13) Heat Capacity Rate {C c, C h } (11-11) (11-11) Two special types of heat exchangers commonly used in practice are condensers and boilers. One of the fluids in a condenser or a boiler undergoes a phase-change process, and the rate of heat transfer is expressed as Q = mh fg (11-14)

24 The Log Mean Temperature Difference Method The temperature difference between the hot and cold fluids varies along the heat exchanger. it is convenient to have a mean temperature difference T m for use in the relation Consider the parallel-flow double-pipe heat exchanger. (11-15) Q= UAΔT s m

25 An energy balance on each fluid in a differential section of the heat exchanger δq = m hcphdt (11-16) h δq = m ccpcdtc (11-17) δq dth = (11-18) mc h ph δq dtc = mc (11-19) c pc Taking their difference, we get 1 1 = = δ + h ph c pc dt ( ) h dtc d Th Tc Q mc mc (11-20)

26 The rate of heat transfer in the differential section of the heat exchanger can also be expressed as (11-21) δ Q= U T T da ( ) h c s Substituting this equation into Eq and rearranging give d( T ) h T c 1 1 = UdAs + Th T c mhcph mcc pc (11-22) Integrating from the inlet of the heat exchanger to its outlet, we obtain T T 1 1 = UA +,, ln h out c out s Thin, T cin, m h cph m c cpc (11-23)

27 Solving Eqs and for m c c pc and m h c ph and substituting into Eq give (11-24) Q= UAΔT Δ T = lm s lm ΔT1 ΔT2 ln ΔT ΔT ( ) 1 2 (11-25) Applicable for: 1- parallel and counter-flow double pipe 2- Condenser 3- Boiler ΔT lm is the log mean temperature difference. ΔT 1 and ΔT 2 are the temperature difference between the two fluids at the two ends (inlet and outlet). It makes no difference which end of the heat exchanger is designated as the inlet or the outlet.

28 Counter-Flow Heat Exchangers The relation already given for the log mean temperature difference for parallel-flow heat exchanger can be used for a counter-flow heat exchanger. ΔT 1 and ΔT 2 are expressed as shown in the Fig ΔT lm, CF > ΔT lm, PF A smaller surface area (a smaller heat exchanger) is needed to achieve a specified heat transfer rate in a counter-flow heat exchanger.

29 Multipass and Cross-Flow Heat Exchangers: Use of a Correction Factor Shell & Tube H.E Compact H.E The log mean temperature difference relation developed earlier is limited to parallel-flow and counter-flow heat exchangers only. To simplify the analysis of cross-flow and multipass shell-and-tube heat exchangers, it is convenient to express the log mean temperature difference relation as Δ T = FΔ T (11-26) Q = UA ΔT lm lm, CF F is the correction factor, and ΔT lm, CF is the log mean temperature for counter-flow case. s lm

30 F Charts for Common Shell-and-Tube and Cross-Flow Heat Exchangers. Shell and Tube Heat Exchanger Cross Flow Heat Exchanger Tubes

31 EXAMPLE: A double-pipe counter-flow heat exchanger is to cool ethylene glycol (C p = 2560 J/kg C) flowing at a rate of 3.5 kg/s from 80 C to 40 C by water (C p = 4180 J/kg C) that enters at 20 C and leaves at 55 C. The overall heat transfer coefficient based on the inner surface area of the tube is 250 W/m2 C. Determine (a) the rate of heat transfer, (b) the mass flow rate of water, and (c) the heat transfer surface area on the inner side of the tube.

32 Analysis (a) The rate of heat transfer is Q = [ mc p ( Tin Tout )] glycol = (3.5 kg/s)(2.56 kj/kg. C)(80 C = kw 40 C) Hot Glycol 80 C 3.5 kg/s 55 C Cold Water 20 C 40 C (b) The rate of heat transfer from water must be equal to the rate of heat transfer to the glycol. Then, Q = [ mc ( T T )] water m water p out in = = C p ( T Q out T in kj/s (4.18 kj/kg. C)(55 C 20 C) ) = 2.45 kg/s

33 (c) The temperature differences at the two ends of the heat exchanger are ΔT = T T = 80 C 55 C=25 C 1 hin, cout, ΔT = T T = 40 C 20 C=20 C 2 h, out c, in ΔT lm = ΔT1 ΔT = ln( ΔT / ΔT ) ln( 25 / 20) 1 2 = C Q = U i A ΔT i lm A i = U i Q ΔT lm = (0.25 kw/m kw 2. C)(22.4 C) 2 = 64.0 m

34 The Heat Exchanger Design Procedure using the LMTD 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 ΔT lm and the correction factor F, if necessary. 4. Obtain (select or calculate) the value of the overall heat transfer co-efficient U. 5. Calculate the heat transfer surface area A s needed to meet requirements.

35 The Effectiveness NTU Method This method is based on a dimensionless parameter called the heat transfer effectiveness ε ε = Q Q = Actual heat transfer rate Maximum possible heat transfer rate max (11-29) The actual heat transfer rate in a heat exchanger Q = C T T = C T T ( ) ( ) c c, out c, in h h, in h, out The maximum temperature difference max hin, cin, (11-30) Δ T = T T (11-31)

36 The fluid with the smaller heat capacity rate will experience a larger temperature change, and thus it will be the first to experience the maximum temperature, at which point the heat transfer will come to a halt. Therefore, the maximum possible heat transfer rate in a heat exchanger is The maximum possible heat transfer rate in a heat exchanger Q = C Δ T = C T T ( ) max min max min hin, cin, (11-32) where C min: is the smaller of C h and C c

37 Once the effectiveness of the heat exchanger is known, the actual heat transfer rate can be determined from Q = εq = εc T T (11-33) ( ) max min hin, cin, The effectiveness of a heat exchanger depends on: the geometry of the heat exchanger, and the flow arrangement. It can be shown that the effectiveness of doublepipe parallel-flow heat exchanger is ε parallel flow UA s 1 exp 1+ Cmin = Cmin 1+ C max C C min max (11-38)

38 Effectiveness relations of the heat exchangers typically involve a dimensionless group called the number of transfer units NTU UAs UAs NTU= = C mc (11-39) ( ) p For specified values of U and C min, the value of NTU is a measure of the heat transfer surface area A s. The larger the NTU, the larger the heat exchanger. It is also convenient to define a capacity ratio c Cmin c= (11-40) C max The effectiveness of a heat exchanger is a function of the number of transfer units NTU and the capacity ratio c. min min

39 Effectiveness for Several Heat Exchangers

40 Effectiveness Heat Exchangers Plots {Fig }

41 EXAMPLE: A cross-flow heat exchanger consists of 80 thin walled tubes of 3-cm diameter located in a duct of 1 m x 1 m cross-section. There are no fins attached to the tubes. Cold water (C p = 4180 J/kg C) enters the tubes at 18 C with an average velocity of 3 m/s, while hot air (C p = 1010 J/kg C) enters the channel at 130 C and 105 kpa at an average velocity of 12 m/s. If the overall heat transfer coefficient is 130 W/m 2 C, determine the outlet temperatures of both fluids and the rate of heat transfer.

42 Assumptions: The thickness of the tube is negligible Analysis: The mass flow rates of the hot and the cold fluids are 3 2 m =ρ VA = (1000 kg/m )(3 m/s)[80 π (0.03 m) /4] = kg/s c c ρ air P = = RT kpa (0.287 kpa.m / kg.k) ( K) = kg / m 3 m h = ρ VA = (0.908 kg / m )(12 m / s)(1 m) = kg / s c 3 2 A = nπ DL = 80 π (0.03 m)(1 m) = 7.54 m s C = m C = (169.6 kg/s)(4.18 kj/kg. C) = kw/ C c c pc C = m C = (10.9 kg/s)(1.010 kj/kg. C) = kw/ C h h ph 2

43 C = C = kw/ C min h C C min c = = = max Q = C (T T ) = (11.01 kw/ C)(130 C 18 C) = 1233 kw max min h,in c,in 2 2 UA s (130 W/m. C) (7.54 m ) NTU = = = C min 11,010 W/ C C min Noting that this heat exchanger involves mixed cross-flow, the fluid with is mixed, C max unmixed, effectiveness of this heat exchanger corresponding to c = and NTU = is determined using the proper relation in Table 13-4 to be 1 c NTU ε= 1 exp (1 e ) = 1 exp (1 e ) = c Note: You may use Fig , but with large error in this particular example

44 Q =ε Q = ( )(1233 kw) = 105 kw max Q 105 kw Q = C c(tc,out T c,in ) Tc,out = Tc,in + = 18 C+ = C Cc kw / C Q 105 kw Q = C h (Th,in T h,out ) Th,out = Th,in = 130 C = C C kw/ C h

45 Selection of Heat Exchangers An engineer going through catalogs of heat exchanger manufacturers will be overwhelmed by the type and number of readily available off-the-shelf heat exchangers. The proper selection depends on several factors: heat transfer rate cost procurement, maintenance, and power. pumping power, size and weight, Type, Materials, miscellaneous (leak-tight, safety and reliability, Quietness).

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