Heat Transfer
Log mean temperature difference (LMTD) cannot be used, if

there exists an unsteady state
heat transfer co-efficient over the entire heat exchanger is not constant
the heat capacity is not constant and there is a phase change.
none of the listed here

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Heat Transfer
In the equation Q = UAΔt; Δt is

Geometric mean temperature difference
Logarithmic mean temperature difference
Arithmetic mean temperature difference
The difference of average bulk temperatures of hot and cold fluids

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