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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 ...
The maximum amount of heat or mass transfer that can be obtained is higher with countercurrent than co-current (parallel) exchange because countercurrent maintains a slowly declining difference or gradient (usually temperature or concentration difference). In cocurrent exchange the initial gradient is higher but falls off quickly, leading to ...
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.
Also I think calling the log mean temperature difference a 'logarithmic average' is a bit of a misnomer. 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 ...
Two fluids, of different starting temperatures, flow through the heat exchanger. One flows through all the tubes in parallel and the other flows outside the tubes, but inside the shell, typically in counterflow. Heat is transferred from one fluid to the other through the tube walls, either from tube side to shell side or vice versa.
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At the pinch point, where the hot and cold streams are the most constrained, large heat exchangers are required to transfer heat between the hot and cold streams. Large heat exchangers entail high investment costs. In order to reduce capital cost, in practice a minimum temperature difference (Δ T) at the pinch point is demanded, e.g., 10 °F.