:5 ) Geometric means, logarithmic means, etc ., are useful when data varies in those specific ways.
2.
In mathematics, the "'logarithmic mean "'is a difference divided by the logarithm of their quotient.
3.
When compact heat exchangers are calculated, the logarithmic mean air temperature is used . \ dot { m } is the air mass flow rate in kg / s.
4.
The logarithmic mean of two numbers is smaller than the arithmetic mean but larger than the geometric mean ( unless the numbers are the same, in which case all three means are equal to the numbers ):
5.
We assume that a generic heat exchanger has two ends ( which we call " A " and " B " ) at which the hot and cold streams enter or exit on either side; then, the LMTD is defined by the logarithmic mean as follows:
6.
More generally, Vartia's expertise is axiomatic index numbers, where he is known for his " consistency in aggregation " test and his discovery, along with Kazuo Sato of the " ideal log-change index ", which utilised logarithms and logarithmic mean to define the Sato-Vartia or " Vartia II " index ( both 1976 ).
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