The function of a heat exchanger is to transfer the heat transfer current per unit length q′ to an ideal gas stream (ṁ , R, c P ) flowing through a stack of n parallel-plate channels. The total...

The function of a heat exchanger is to transfer the heat transfer current per unit length q′ to an ideal gas stream (ṁ , R, c_P) flowing through a stack of n parallel-plate channels. The total thickness of the stack, D, is fixed. The plate-to-plate spacing of each channel is D/n, the mass flow rate through each channel is ṁ ∕n, and the heat current transmitted to the ṁ ∕n stream is q′ ∕n. Assuming that the flow regime is laminar, determine the optimal number of channels (nopt) so that the overall entropy generation rate of the stack (S′
_gen) is minimized.