Heat Exchangers: Rating & Performance Parameters. Maximum Heat Transfer Rate, q max

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1 Heat Exchangers: Rating & Performance Parameters Dr. Md. Zahurul Haq HTX Rating is concerned with the determination of the heat transfer rate, fluid outlet temperatures, and the pressure drop for an existing heat exchanger or the one which is already sized. Professor Department of Mechanical Engineering Bangladesh University of Engineering & Technology (BUET) Dhaka-1000, Bangladesh ME 307: Heat Transfer Equipment Design T791 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 1 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 2 / 35 Maximum Heat Transfer Rate, q max If the inlet & outlet temperatures of the hot & cold fluid, and the overall heat transfer coefficients are specified, the LMDT method can be used to solve rating and sizing problem (e.g. process, power and petrochemical industries). If only the inlet temperatures and fluid (hor & cold) flow rates are given LMDT estimation requires cumbersome iterations. ǫ-ntu method is generally performed for the design of compact heat exchangers for automotive, aircraft, air conditioning, and various industrial applications where the inlet temperatures of the hot and cold fluids are specified and the heat transfer rates are to be determined. Maximum HT could be achieved in counter-flow HE with x. If C c < C h : T c > T h, COLD fluid have T max. If x T c,o = T h,i q max = C c (T h,i T c,i ) If C c > C h : T c < T h, HOT fluid have T max. If x T h,o = T c,i q max = C h (T h,i T c,i ) = = q max = C min (T h,i T c,i ) = C min T max Effectiveness, ǫ q q max = C h(t h,i T h,o ) C min (T h,i T c,i ) or C c(t c,o T c,i ) C min (T h,i T c,i ) Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 3 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 4 / 35

2 (Parallel-Flow Heat Exchanger) Number of Transfer Unit, NTU UA C min Capacity ratio, C r C min C max d( T) T = U [ 1 C h + 1 C c ]da ln( T 2 / T 1 ) = UA = T2 T 1 = Th,o Tc,o T h,i T c,i = exp( NTU(1+C r )) If C min = C h :, C r = C h C c = m hc p,h m cc p,c = Tc,o T c,i T h,i T h,o ǫ = Cc(Tc,o T c,i) C min (T h,i T c,i ) = 1 C r T c,o T c,i T h,i T c,i = T h,i T h,o T h,i T c,i Th,o Tc,o T h,i T c,i = ǫ+1 C r ǫ ǫ = 1 exp( NTU(1+Cr)) 1+C r Same result is obtained, if C min = C c ǫ = 1 exp( NTU(1+Cr)) 1+C r : Parallel-Flow HTX [ 1 C h + 1 C c ] T710 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 5 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 6 / 35 T711 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 7 / 35 T712 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 8 / 35

3 The value of capacity ratio, C r ranges between 0 and 1.0. For a given NTU, ǫ max for C r = 0, and ǫ min for C r = 1.0. C r = C min /C max 0 corresponds to C max, which is realized during a phase-change process in a condenser or boiler. Hence, ǫ = ǫ max = 1 exp( NTU) T792 T713 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 9 / 35 Effectiveness is lowest for C r = C min /C max = 1, when heat rates of two fluids are the same. Example, HVAC applications. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 10 / 35 Holman Ex A cross-flow heat exchanger, one fluid mixed and one unmixed, is used to heat an oil in the tubes (c = 1.9 kj/kg o C) from 15 o C to 85 o C. Steam (5.2 kg/s, c = 1.86 kj/kg o C) blows across the outside of the tube, enters at 130 o C and leaves at 110 o C. U o = 275 W/m 2 o C. Calculate A. Holman Ex In a counterflow double-pipe heat exchanger, water at the rate of 68 kg/min is heated from 35 to 75 o C by an oil having a specific heat of 1.9 kj/kg o C. Oil enters the exchanger at 110 o C and leaves at 75 o C. Given that, U o = 320 W/m 2o C. Estimate heat transfer area, A m 2. Holman Ex Investigate the heat-transfer performance of the exchanger in Ex if the oil flow rate is reduced in half while the steam flow remains the same. Assume U remains constant at 275 W/m 2o C. Holman Ex The heat exchanger of Ex is used for heating water. Using the same entering-fluid temperatures, calculate the exit water temperature when only 40 kg/min of water is heated but the same quantity of oil is used. Also calculate the total heat transfer under these new conditions. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 11 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 12 / 35

4 HTX: Behaviour as C r 0 Cengel Ex The overall heat transfer coefficient of the heat exchanger is 640 W/m 2 K. Using the effectiveness-ntu method determine the length of the heat exchanger required to achieve the desired heating. T707 The effect of the heat exchanger configuration on its performance is related to the interaction between the temperature changes of the two fluid streams. The limit of C r 0 is approached in many practical heat exchangers; e.g., the interaction of a flowing fluid with a constant temperature solid (as in a cold-plate) or a well-mixed tank of fluid or the situation that occurs when one of the two streams is undergoing constant pressure evaporation or condensation. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 13 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 14 / 35 If C r 0, no such interaction. For all configurations, lim ǫ = 1 exp( NTU) C r 0 HTX: Behaviour as NTU 0 If NTU is small, heat exchanger is under-sized & rate of heat transfer is not sufficient to change the temperature of either fluid substantially. Hence, T = (T h,in T c,out ) NTU 0: q = UA(T H,in T C,in ), ǫ q C min (T H,in T C,in ) lim ǫ = NTU NTU 0 T779 Temperature distribution within a (a) counter-flow and (b) parallel-flow heat exchanger as the capacity ratio approaches zero because C c >> C h. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 15 / 35 T780 Temperature distribution within a (a) counter-flow and (b) parallel-flow heat exchanger as NTU approaches zero. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 16 / 35

5 HTX: Behavior as NTU Effectiveness as a function of NTU T781 Temperature distribution within a balanced (i.e., C r = 1) (a) counter-flow and (b) parallel-flow heat exchanger for a finite NTU. The temperature distribution within a balanced (c) counter-flow and (d) parallel-flow heat exchanger as NTU. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 17 / 35 T782 ǫ as a function of NTU for various configurations (C r = 1). Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 18 / 35 T783 ǫ as a function of NTU for various configurations (C r = 0.5). T784 ǫ as a function of NTU for various configurations (C r = 0.25). Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 19 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 20 / 35

6 DPHX: Double Pipe Heat Exchanger T787 T788 Hairpin heat exchanger. T789 T790 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 21 / 35 Multi-tube hairpin heat exchanger. Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 22 / 35 T734 T761 T759 Laminar: Nu = 1.86(Gz) 1/3 ( µb µ w ) 0.14; Gz = RePr Turbulent: Nu = 0.023Re 0.8 Pr n ; n = L/D { 0.4 : heating 0.3 : cooling Friction { factor ξcorr [64/Re] for laminar flow f = (1.82log 10 Re 1.64) 2 for turbulent flow Tube area: Equivalent diameter, De t = Dh t = ID t Pressure drop, P t = f t L ID t ( 1 2 ρ tv 2 t ), ξ corr = 1 Annular area: Dh a = ID a OD t, De a = ID2 a OD2 t OD t 1 ξ corr = 1+κ2 + 1+κ (1 κ) 2 (1 κ)ln(κ), κ = OD t/id a P a = (f a L Dh a + 1)( 1 2 ρ av 2 a ) Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 23 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 24 / 35

7 DPHX Rating Oil is to be heated from 30 o C using hot water at 100 o C. Oil flow rate is 0.06 kg/s in the annulus, while wate flow rate is 0.5 kg/s.the heat exchanger is made of 2 x 1 1/4 std type M cupper tubing that is 5.0 m long. Use appropriate fouling factors, rate the DPHX. DPHX Sizing Oil is to be heated to 45 o C from 30 o C using hot water at 100 o C. Oil flow rate is 0.05 kg/s in the annulus, while wate flow rate is 0.5 kg/s.the heat exchanger is made of 2 x 1 1/4 std type M cupper tubing. Use appropriate fouling factors, size the DPHX. T763 T764 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 25 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 26 / 35 T795 Shell-and-tube evaporator, flooded. T735 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 27 / 35 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 28 / 35

8 T758 T760 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 29 / 35 T794 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 30 / 35 Tube area: A t = N t π(idt 2)/4N p, N t = no. of tubes, N p = no. of pass For smooth { pipes, 0.316Re 0.25 : Re f t = 0.184Re 0.20 : Re 3 10 ) 5 Pressure L drop, P t = N p (f t ID t + 4 ( 1 2 ρ tvt 2) Shell area: Dh s = 4A P = [ ] 4 PT 2 πod2 t 4 = 4P2 T πod t OD t : square pitch [ πod t 3 4 A s = DsCB P T ] 4 P2 T πod2 t 8 πod t = 2 Nu = 0.36Re 0.55 s 3P 2 T πod t OD t : triangular pitch, D s = shell inside diam., B = baffle spacing Pr 1/3, Re s = V s Dh s /ν s f s = exp[ ln(Re s )] P a = f s (N b + 1) Ds D e ( 1 2 ρ sv 2 s ), N b = number of baffles Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 31 / 35 STHX Rating 20.0 kg/s water at 50 o C is to be cooled using 20.0 kg/s water available at 25 o C. N t = 200, N p = 2, L = 5.0, N b = 15, B = mm, D s = mm, ID t = mm, OD t = mm. Assume 25.4 mm triangular pitch. T762 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 32 / 35

9 T765 NTU = UoAoNs ( mc p) min, A o = bl Effective NTU = F corr NTU, Plate & Frame Heat Exchanger (PFHX) Plate & Frame Heat Exchanger (PFHX) T766 F corr = NTU Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 33 / 35 T767 Flow velocity, V = { b 2 m ρsb(n s+1) 2 m ρsbn s, Plate & Frame Heat Exchanger (PFHX) s : odd number of plates 2 m ρsb(n s+2) : even number of plates Heat transfer & pressure loss correlations are based on the hydraulic diameter, D h of the passage formed by the two plates. 4(cross sectional area) D h = wetted perimeter = 4sb 2s+2b 4sb 2b = 2s, Re = VD h ν Laminar flow: Nu = 1.86(Gz) 1/3 ( µb µ w ) 0.14; Gz = RePr L/D Re < 100 Turbulent flow: Nu = 0.374Re Pr 1/3 ; Re > Re : 1 < Re < Friction factor, f = Re : 10 < Re < : Re > 100 Re Pressure drop, P = fl D h ( 1 2 ρv 2 )+1.3( 1 2 ρv p) 2 fl D h ( 1 2 ρv 2 ) Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 34 / 35 Plate & Frame Heat Exchanger (PFHX) PFHX Rating kg/s water at 25 o C is to be cooled using 1.0 kg/s water available at 7 o C. If b = 457 mm, L = 914 mm, s = 5.08 mm, t = mm, k = 14.3 W/mK, Ns = 11, fouling coefficients for both fluids = 3.52 x 10 6, rate the heat-exchanger. T768 Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Performance Parameters ME 307 (2017) 35 / 35