Heat Exchanger: Rating & Sizing Heat Exchangers: Rating & Sizing - I Dr. Md. Zahurul Haq Professor Department of Mechanical Engineering Bangladesh University of Engineering & Technology (BUET) Dhaka-000, Bangladesh zahurul@me.buet.ac.bd http://teacher.buet.ac.bd/zahurul/ HE 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. HE Sizing is concerned with the determination of the matrix dimensions to meet the specified heat transfer and pressure drop requirements. ME 307: Heat Transfer Equipment Design http://teacher.buet.ac.bd/zahurul/me307/ c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 2 / 32 Heat Exchanger: Energy Balance Equation 0 3456 6758947 9754 5745 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 ) T78 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) Heat Exchangers: Rating & Sizing - I ME 307 (207) 3 / 32 q = UA T m i is the fluid enthalpy, subscripts h and c refer to hot and cold fluids, whereas the subscripts i and o designate fluid inlet and outlet conditions. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 4 / 32
Special Heat Exchanger Conditions Heat Exchanger: Fouling 7 893 6 892 6 0234 564234 T67 T672 (a) (b) (a): C h C c or a condensing vapour. (b): An evaporating liquid or C h C c. 0 3 T670 (c): A counterflow heat exchanger with C h = C c. 9 9 5 0 0 5 0 3 7 0 2 7 89 (c) 0 2 During operation, heat exchangers become fouled with an accumulation of deposits of one kind or another on the heat transfer surface areas. Major categories of fouling: scaling or precipitation fouling 2 particulate fouling 3 chemical reaction fouling 4 corrosion fouling 5 biological fouling 6 solidification fouling c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 5 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 6 / 32 q = U o A o T LM Cengel Ex. -2 Effect of fouling on overall heat transfer coefficient. Double-pipe (shell-and-tube) heat exchanger made of steel, k = 5. W/m-K, inner-diameter of outside shell is 3.2 cm. U oa o = R = h i A i + R d,i A i + ÐÒ(Do/D i) 2πkL + R d,o A o + h oa o T79 T704 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 7 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 8 / 32
LMTD: Parallel-Flow Heat Exchanger LMTD: Counter-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 0 0 2 3 3 2 5 63 2 6 3 5 63 67 89 9 9 9 3 2 T702 ] q = UA[ T2 T ÐÒ( T 2/ T ) = UA T LM d q = U(T h T c )da 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 ) T 2 = (T h,o T c,o ) 3 T667 3 3 2 3 63 2 6 3 0 6 3 63 3 2 0 2 3 3 3 2 ] q = UA[ T2 T ÐÒ( T 2/ T ) = UA T LM q = UA T LM T = (T h,i T c,o ) T 2 = (T h,o T c,i ) c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 9 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 0 / 32 Correction for LMDT: Cross-Flow & Multipass HE 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. If a heat exchanger other than the double-pile 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 T707 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) / 32 T shell-side temperatures t tube-side temperatures F =.0 for boiling and condensation. F-values are presented in figures, using two dimensionless parameters: P = t2 t T t 2 R = T T2 : 0 P.0: thermal efficiencies of tube-side flow. = (mcp)tube side (mc p) shell side : 0 R : t 2 t R 0: vapour condensation on the shell side R : evaporation on the tube side. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 2 / 32
T74 T75 Correction-factor plot for exchanger with one shell pass and two, four, or any multiple of tube passes. Correction-factor plot for exchanger with two shell passes and four, eight, or any multiple of tube passes. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 3 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 4 / 32 T76 Correction-factor plot for single-pass cross-flow exchanger, both fluids unmixed. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 5 / 32 T77 Correction-factor plot for single-pass cross-flow exchanger, one fluid mixed, the other unmixed. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 6 / 32
Holman Ex. 0-4 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.9 kj/kg o C. Oil enters the exchanger at 0 o C and leaves at 75 o C. Given that, U o = 320 W/m 2o C. Estimate heat transfer area, A. 5.82 m 2. 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 320 W/m 2o C. 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 30 o C and leaves at 0 o C. U o = 275 W/m 2 o C. Calculate A. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 7 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 8 / 32 Cengel Ex. -3 Steam condenser with surface area of the tubes is 45 m 2, and the overall heat transfer coefficient is 200 W/m 2 K. 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. T706 T709 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 9 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 20 / 32
Ozisik Ex. -2 A heat exchanger is to be designed to cool 8.7 kg/s an ethyl alcohol solution [c p,h = 3840 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 85.7 m 2 2 counter flow, shell and tube 57.3 m 2 3 one shell pass and two tube pass 65.9 m 2 4 cross-flow, both fluids unmixed 6.2 m 2 5 cross-flow, one fluid unmixed 63.7 m 2 If the inlet and outlet temperatures of the hot and 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. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 2 / 32 Maximum Heat Transfer Rate, q max 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 ) c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 22 / 32 (Parallel-Flow Heat Exchanger) Number of Transfer Unit, NTU UA C min Capacity ratio, C r C min C max d( T) T = U [ C h + C c ]da ÐÒ( T 2 / T ) = UA = T2 T = Th,o Tc,o T h,i T c,i = ÜÔ( NTU(+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 ) = 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+ C r ǫ ǫ = ÜÔ( NTU(+Cr)) +C r Same result is obtained, if C min = C c ǫ = ÜÔ( NTU(+Cr)) +C r : Parallel-Flow HTX [ C h + C c ] c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 23 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 24 / 32
T70 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 25 / 32 T7 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 26 / 32 T72 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 27 / 32 T73 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 28 / 32
The value of capacity ratio, C r ranges between 0 and.0 For a given NTU, the effectiveness becomes maximum for C r = 0, and a minimum for C r =.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 = ÜÔ( NTU) C r 0 is applicable where heat exchanger is in contact with the ambient environment as C max is a very large number. Effectiveness is lowest for C r = C min /C max =, when heat rates of two fluids are the same. Example, HVAC applications. 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 30 o C and leaves at 0 o C. U o = 275 W/m 2 o C. Calculate A. Holman Ex. 0-9 Investigate the heat-transfer performance of the exchanger in Ex. 0-7 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. c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 29 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 30 / 32 Holman Ex. 0-4 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.9 kj/kg o C. Oil enters the exchanger at 0 o C and leaves at 75 o C. Given that, U o = 320 W/m 2o C. Estimate heat transfer area, A. 5.82 m 2. Cengel Ex. -8 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. Holman Ex. 0-0 The heat exchanger of Ex. 0-4 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. T707 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 3 / 32 c Dr. Md. Zahurul Haq (BUET) Heat Exchangers: Rating & Sizing - I ME 307 (207) 32 / 32