طراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS

Transcription

1 طراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS ١

2 TEMPERATURE DIFFERENCE For any transfer the driving force is needed General heat transfer equation : Q = U.A. T What T should be used? 3 LOG MEAN TEMPERATURE DIFFERENCE (LMTD) If there is a DPHE Q = m (H - H ) Q = m (H - H ) For for constant c (e.g. incompressible liquids, ideal gases) Q = m c (T - T ) Q = m c (T - T ) If no loss Q = Q If there is loss? dq = m c dt = m c dt dt = (1) dt = (2) 4 ٢

3 LOG MEAN TEMPERATURE DIFFERENCE (LMTD) (1) (2) dt dt = d(t T )= -dq( + ) The below equation is also available: dq = U(T T )da From above equation: d(t T ) = U T T 1 = T T m c Q 1 = T T m c Q m c m c da 5 LOG MEAN TEMPERATURE DIFFERENCE (LMTD) d(t T ) T T Integrating from both side = U T T Q + T T Q da ln T T T T = U Q T T ) (T T A Q = UA T T ) (T T ln T T T T = UA T T = LMTD = T T ) (T T 6 ln T T T T ٣

4 LOG MEAN TEMPERATURE DIFFERENCE (LMTD) LMTD is not complicated to calculate T 1 and T 2 shall have the same sign In LMTD formula LMTD = For the same inlet and exit temperatures of two fluids, the LMTD for counter flow is always greater than LMTD for parallel flow For both side phase change at constant temperature the LMTD is undefined. The simple T is used. 7 EXAMPLE In an exchanger: T h,i =100, T h,o =60, T c,i =20, T c,o =45 Calculate the LMTD for co-current and counter-current flow Counter-current: LMTD = T T ln T T = ln = 47.1 Co-current: LMTD = T T ln T T = ln = ۴

5 CORRECTED LMTD (CMTD) Because some time the is non-ideal countercurrent flow, the LMTD should be corrected CMTD = F LMTD F: temperature efficiency factor CMTD: Corrected effective mean temperature difference N: number of heat exchangers in series 9 CORRECTED LMTD (CMTD) P: Ratio of heat actually transferred to cold fluid to heat which would be transferred if the same fluid were to be heated to hot fluid inlet temperature = temperature effectiveness of HE on cold fluid side. R: Ratio of mcp value of cold fluid to mcp values of hot fluid = heat capacity rate ratio. The assumptions involved are: The shell fluid temperature is uniform over the cross-section in a pass. Equal heat transfer area in each pass. Overall heat transfer coefficient (U) is constant throughout the exchanger. Heat capacities of the two fluids are constant over the temperature range involved. No change in phase of either fluid. Heat losses from the unit are negligible. 10 ۵

6 CORRECTED LMTD (CMTD) For maximum heat recovery from the hot fluid, t 2 should be as high as possible. The difference (T 2 t 2 ) If t 2 > T 2 : temperature cross (F decreases very rapidly when there is only 1 shell-side pass) in parts of HE, heat is transferred in the wrong direction. 11 F 12 ۶

7 F 13 EXAMPLE Previous example: T 1 =100, T 2 =60, t 1 =20, t 2 =45 LMTD = T T ln T T = ln = 47.1 P = = = (P always < 1) R = = =1.6 from previous graph F: for 1&2: 0.89 F: for 2&4: ٧

8 OVERALL HEAT TRANSFER COEFFICIENT 15 OVERALL HEAT TRANSFER COEFFICIENT The General term for heat transfer resistance is For Cylinder 16 For Plate ٨

9 OVERALL HEAT TRANSFER COEFFICIENT (COULSON & RICHARDSON S VOL 6) 17 OVERALL HEAT TRANSFER COEFFICIENT (COULSON & RICHARDSON S VOL 6) 18 ٩

10 FOULING FACTOR (COULSON & RICHARDSON S VOL 6) 19 TUBE SIDE HEAT TRANSFER COEFFICIENT Heat-transfer coefficient for turbulent flow inside tube are usually correlated by an equation of the form: Nu: Nusselt number: Re: Reynolds number: Pr: Prandtl number: h i : inside coefficient d e : equivalent (or hydraulic mean) diameter, m 20 ١٠

11 TUBE SIDE HEAT TRANSFER COEFFICIENT Different coefficients were defined for C, a, b and c, but the common coefficients are a = 0.8 b = 0.4 for heating the liquid inside the tube = 0.3 for cooling the liquid inside the tube c = 0.14 C = for gases, = for non-viscous liquids, = for viscous liquids. 21 TUBE SIDE HEAT TRANSFER COEFFICIENT Heat-transfer coefficient for Laminar flow inside tube is usually correlated by below equation: If Nu < 3.5 then Nu assumed to be 3.5 The heat transfer coefficient can not be predicted in transition region Transition region: 2000 (2300) < Re < 2600 (4000) The transition region should be avoided in exchanger design. If this is not practicable the coefficient should be evaluated using both Laminar and Turbulent flow equations and select the smaller value 22 ١١

12 TUBE SIDE HEAT TRANSFER COEFFICIENT Viscosity correction factor Normally is significant for viscous liquids The wall temperature is needed The heat coefficient can be calculated without the correction Use the below relationship to estimate the wall temperature: t: tube-side bulk temperature (mean) t w : estimated wall temperature T: shell-side bulk temperature (mean) 23 TUBE SIDE HEAT TRANSFER COEFFICIENT Heat-transfer factor, j h correlate heat-transfer data in terms of a heat transfer j factor, which is similar to the friction factor St: Stanton number The above equation can be rearranged to a more convenient form 24 ١٢

13 TUBE SIDE HEAT TRANSFER COEFFICIENT (Coulson & richardson s vol 6) 25 ١٣