Heat Chap13-032

Heat Chap13-032 - Chap 15 Heat Exchangers The Log Mean...

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Unformatted text preview: Chap 15 Heat Exchangers The Log Mean Temperature Difference Method 13-32C ∆ 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 parallel-flow heat exchangers and ∆ ∆ T T T T T T h in c out h out c in =- =- , , , , 2 for counter-flow heat exchangers 13-33C 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. 13-34C ∆ 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 . 13-35C 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. 13-36C In the parallel-flow 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 counter-flow 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. 13-37C The ∆ T lm will be greatest for double-pipe counter-flow heat exchangers. 13-38C 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 counter-flow heat exchanger in terms of its logarithmic mean temperature difference. F cannot be greater than unity. 13-19 Chap 15 Heat Exchangers 13-39C In this case it is not practical to use the LMTD method because it requires tedious iterations. Instead, the effectiveness-NTU method should be used. 13-40C 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 = 13-41 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.

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Heat Chap13-032 - Chap 15 Heat Exchangers The Log Mean...

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