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
none of the listed here
the heat capacity is not constant and there is a phase change.

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Heat Transfer
Heat transfer by conduction results due to the transfer of free electrons, kinetic energy & vibrational energy from one molecule to another. Conduction heat transfer can not take place

Between two bodies in physical contact with each other
Both B & C
Between two bodies not in physical contact with each other
From one part of a body to the another part of the same body

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