T718. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 307 (2018) 2/ 21 T793

Transcription

1 HX: Energy Balance and LMTD Dr. Md. Zahurul Haq Professor Department of Mechanical Engineering Bangladesh University of Engineering & Technology (BUET) Dhaka-000, Bangladesh T78 ME 07: Heat Transfer Equipment Design c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) / 2 Application of and contrast between (a) a thermodynamic and (b) a heat transfer model for a typical shell-and-tube heat exchanger used in chemical processing. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 2/ 2 Heat Exchanger: Energy Balance Equation Special Heat Exchanger Conditions T666 q = m h (i h,i i h,o ) = m h c p,h (T h,i T h,o ) = C h (T h,i T h,o ) q = m c (i c,o i c,i ) = m c c p,c (T c,o T c,i ) = C c (T c,o T c,i ) q = UA T m i is fluid enthalpy, subscripts h & c refer to hot & cold fluids, whereas the subscripts i & o designate fluid inlet & outlet conditions. C mc p heat capacity rate [W/K]. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) / 2 T79 (a) C h >> C c or a condensing vapour. (b) An evaporating liquid or C h << C c. (c) A counterflow heat exchanger with equivalent fluid heat capacities (C h = C c ). A condenser or a boiler can be considered to be either a parallel or counterflow HTX since both approaches give the same result. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 4/ 2

2 LMTD: Parallel-Flow Heat Exchanger q = UA T LM d q = m h c p,h dt h = C h dt h d q = m c c p,c dt c = C c dt c T029 d q = U(T h T c )da Typical temperature profiles inside boilers, evaporators, and condensers. d( T) = dt h dt c d T = [ C h + C c ]d q d( T) T = U [ C h + C c ]da T = (T h,i T c,i ) T00 Temperature cross in a counterflow heat exchanger. T702 ] q = UA[ T2 T ÐÒ( T 2/ T ) = UA T LM T 2 = (T h,o T c,o ) c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 5/ 2 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 6/ 2 LMTD: Counter-Flow Heat Exchanger q = UA T LM T = (T h,i T c,o ) T 2 = (T h,o T c,i ) Cengel Ex. -4 Heating Water in a Counter-Flow Heat Exchanger: If U o = 640 W/m 2 K, determine the length of the heat exchanger required to achieve the desired heating. Re-estimate the length for Parallel-Flow configuration T667 ] q = UA[ T2 T ÐÒ( T 2/ T ) = UA T LM T707 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 7/ 2 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 8/ 2

3 Holman Ex. 0-4 In a counterflow double-pipe heat exchanger, water at the rate of 68 kg/min is heated from 5 to 75 o C by an oil having a specific heat of.9 kj/kg o C. Oil enters the exchanger at 0 o C and leaves at 75 o C. Given that, U o = 20 W/m 2o C. Estimate heat transfer area, A. Condenser Sizing: Saturated water at 20 o C with a quality of x i = 0.2 and a mass flow rate, m h = 0 kg/s is to be cooled to 60 o C with a water flow of m c = 40 kg/s at 20 o C. If for liquid water, h w = 8000 W/m 2 K, and for condensing vapour, h v = W/m 2 K, and C p = 4200 J/KgK for liquid water, and h fg = 2200 kj/kg at 20 o C, estimate the heat transfer surface area. Subcooling Condensation 20 o C 60 o C 20 o C T769 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 9/ 2 Condenser, Evaporator (Boiler) c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 0 / 2 with Corrections Correction for LMDT: Cross-Flow & Multipass HTX T778 T777 Condenser: Q = m h (h i h o ) = m h x i h fg Q = ( mc p ) c (T co T ci ) = UA T LM T LM = (Tsat T ci) (T sat T co) ÐÒ( Tsat T ci T sat Tco ) = Tco T ci Tsat T ÐÒ( ci ) T sat Tco A = Cc Tsat T ci U T sat T co Tsat T ci ÜÔ T sat T co = ÐÒ Boiler: Q = m c (h o h i ) = m c x i h fg Q = ( mc p ) h (T hi T ho ) = UA T LM T LM = (T hi T sat) (T ho T sat) ÐÒ( Thi T sat T ho T sat ) = T hi T ho ) Thi T ÐÒ( sat T ho T sat A = C h Thi T sat U T ho T sat T hi T sat ÜÔ T ho T sat = ÐÒ UA C c UA C h If a heat exchanger other than the double-pipe type is used, q is calculated by using a correction factor, F applied to LMDT for counter-flow arrangement with same hot and cold fluid temperatures. q = FUA T LM F =.0 for boiling and condensation. F-values are presented in figures, using two dimensionless parameters: P = t2 t T t : 0 P.0: thermal efficiencies of tube-side flow. 2 R = T T2 t 2 t = (mcp)tube side (mc p) shell side : 0 R : R 0: vapour condensation on the shell side R : evaporation on the tube side. T shell-side temperatures t tube-side temperatures c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) / 2 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 2 / 2

4 with Corrections with Corrections T74 Correction-factor, F for exchanger with one shell pass and two, four, or any multiple of tube passes. T75 Correction-factor, F for exchanger with two shell passes and four, eight, or any multiple of tube passes. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) / 2 with Corrections c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 4 / 2 with Corrections T76 Correction-factor, F for single-pass cross-flow exchanger, both fluids unmixed. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 5 / 2 T77 Correction-factor, F for single-pass cross-flow exchanger, one fluid mixed, the other unmixed. c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 6 / 2

5 with Corrections with Corrections Cengel Ex. - Steam condenser with surface area of the tubes is 45 m 2, and the overall heat transfer coefficient is 200 W/m 2 K. Holman Ex. 0-4 In a counterflow double-pipe heat exchanger, water at the rate of 68 kg/min is heated from 5 to 75 o C by an oil having a specific heat of.9 kj/kg o C. Oil enters the exchanger at 0 o C and leaves at 75 o C. Given that, U o = 20 W/m 2o C. Estimate heat transfer area, A. Holman Ex. 0-5 Instead of the double-pipe heat exchanger of Ex. 0-4, it is desired to use a shell-and-tube exchanger with the water making one shell pass and the oil making two tube passes. Calculate the area, A, assuming that the overall heat-transfer coefficient remains at 20 W/m 2o C. T706 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 7 / 2 with Corrections c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 8 / 2 with Corrections Holman Ex. 0-7 A cross-flow heat exchanger, one fluid mixed and one unmixed, is used to heat an oil in the tubes (c =.9 kj/kg o C) from 5 o C to 85 o C. Steam (5.2 kg/s, c =.86 kj/kg o C) blows across the outside of the tube, enters at 0 o C and leaves at 0 o C. U o = 275 W/m 2 o C. Calculate A. Cengel Ex. -6 Cooling of Water in an Automotive Radiator: The radiator has 40 tubes of internal diameter 0.5 cm and length 65 cm in a closely spaced plate-finned matrix. Hot water enters the tubes at a rate of 0.6 kg/s. Determine the overall heat transfer coefficient U i of this radiator based on the inner surface area of the tubes. T709 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 9 / 2 c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 20 / 2

6 with Corrections Ozisik Ex. -2 A heat exchanger is to be designed to cool 8.7 kg/s an ethyl alcohol solution [c p,h = 840 J/kg o C] from 75 o C to 45 o C with cooling water [c p,c = 480 J/kg o C entering the tube side at 5 o C at a rate of 9.6 kg/s. Given, U o = 500 W/m 2o C. Estimate heat transfer area, for: parallel flow, shell and tube 2 counter flow, shell and tube one shell pass and two tube pass 4 cross-flow, both fluids unmixed. 5 cross-flow, one fluid unmixed, c Dr. Md. Zahurul Haq (BUET) HX: Energy Balance and LMTD ME 07 (208) 2 / 2