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Unformatted text preview: Chap 15 Heat Exchangers The Log Mean Temperature Difference Method 1332C ∆ T lm is called the log mean temperature difference, and is expressed as ∆ ∆ ∆ ∆ ∆ T T T T T lm = 1 2 1 2 ln( / ) where ∆ ∆ T T T T T T h in c in h out c out 1 2 = = , , , , for parallelflow heat exchangers and ∆ ∆ T T T T T T h in c out h out c in = = , , , , 2 for counterflow heat exchangers 1333C The temperature difference between the two fluids decreases from ∆ T 1 at the inlet to ∆ T 2 at the outlet, and arithmetic mean temperature difference is defined as ∆ ∆ ∆ T T T m = + 2 1 2 . The logarithmic mean temperature difference ∆ T lm is obtained by tracing the actual temperature profile of the fluids along the heat exchanger, and is an exact representation of the average temperature difference between the hot and cold fluids. It truly reflects the exponential decay of the local temperature difference. The logarithmic mean temperature difference is always less than the arithmetic mean temperature. 1334C ∆ T lm cannot be greater than both ∆ T 1 and ∆ T 2 because ∆ T ln is always less than or equal to ∆ T m (arithmetic mean) which can not be greater than both ∆ T 1 and ∆ T 2 . 1335C No, it cannot. When ∆ T 1 is less than ∆ T 2 the ratio of them must be less than one and the natural logarithms of the numbers which are less than 1 are negative. But the numerator is also negative in this case. When ∆ T 1 is greater than ∆ T 2 , we obtain positive numbers at the both numerator and denominator. 1336C In the parallelflow heat exchangers the hot and cold fluids enter the heat exchanger at the same end, and the temperature of the hot fluid decreases and the temperature of the cold fluid increases along the heat exchanger. But the temperature of the cold fluid can never exceed that of the hot fluid. In case of the counterflow heat exchangers the hot and cold fluids enter the heat exchanger from the opposite ends and the outlet temperature of the cold fluid may exceed the outlet temperature of the hot fluid. 1337C The ∆ T lm will be greatest for doublepipe counterflow heat exchangers. 1338C The factor F is called as correction factor which depends on the geometry of the heat exchanger and the inlet and the outlet temperatures of the hot and cold fluid streams. It represents how closely a heat exchanger approximates a counterflow heat exchanger in terms of its logarithmic mean temperature difference. F cannot be greater than unity. 1319 Chap 15 Heat Exchangers 1339C In this case it is not practical to use the LMTD method because it requires tedious iterations. Instead, the effectivenessNTU method should be used. 1340C First heat transfer rate is determined from Q mC T T p in out = [ ] , ∆ T ln from ∆ ∆ ∆ ∆ ∆ T T T T T lm = 1 2 1 2 ln( / ) , correction factor from the figures, and finally the surface area of the heat exchanger from , Q UAFDT lm cf = 1341 Steam is condensed by cooling water in the condenser of a power plant. The mass flow rate of the Steam is condensed by cooling water in the condenser of a power plant....
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This note was uploaded on 08/25/2009 for the course AET AET432 taught by Professor Rajadas during the Spring '06 term at ASU.
 Spring '06
 Rajadas

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