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In thermal engineering, the logarithmic mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger.
The number of transfer units (NTU) method is used to calculate the rate of heat transfer in heat exchangers (especially parallel flow, counter current, and cross-flow exchangers) when there is insufficient information to calculate the log mean temperature difference (LMTD). Alternatively, this method is useful for determining the expected heat ...
Three-dimensional plot showing the values of the logarithmic mean. In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineering problems involving heat and mass transfer.
The driving temperature across the heat transfer surface varies with position, but an appropriate mean temperature can be defined. In most simple systems this is the "log mean temperature difference" (LMTD). Sometimes direct knowledge of the LMTD is not available and the NTU method is used.
Where A is the surface area available for heat transfer and ∆T is the log mean temperature difference. [2] From these results, the NTU method can be performed to calculate the heat exchanger’s effectiveness. [1] (,,) where
LMTD is just the mean temperature difference (ie, just an arithmetic mean), it just turns out the arithmetic mean using infinitesimal steps has a log in it (see the derivation section)! Calling it a logarithmic mean just confuses the issue and makes it appear more abstract than it actually is. 'F' is a 'correction factor'.
It is commonly applied to the calculation of heat transfer in heat exchangers, but can be applied equally well to other problems. For the case of a heat exchanger, U {\displaystyle U} can be used to determine the total heat transfer between the two streams in the heat exchanger by the following relationship:
Countercurrent heat exchangers are most efficient because they allow the highest log mean temperature difference between the hot and cold streams. Many companies however do not use two pass heat exchangers with a u-tube because they can break easily in addition to being more expensive to build.