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The LMTD is a steady-state concept, and cannot be used in dynamic analyses. In particular, if the LMTD were to be applied on a transient in which, for a brief time, the temperature difference had different signs on the two sides of the exchanger, the argument to the logarithm function would be negative, which is not allowable.
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 ...
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'.
The CLTD/CLF/SCL (cooling load temperature difference/cooling load factor/solar cooling load factor) cooling load calculation method was first introduced in the 1979 ASHRAE Cooling and Heating Load Manual (GRP-158) [1] The CLTD/CLF/SCL Method is regarded as a reasonably accurate approximation of the total heat gains through a building envelope ...
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.
The heat transfer coefficient has SI units in watts per square meter per kelvin (W/(m 2 K)). The overall heat transfer rate for combined modes is usually expressed in terms of an overall conductance or heat transfer coefficient, U. In that case, the heat transfer rate is: ˙ = where (in SI units):
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...