An analysis is made of incompressible laminar forced convection heat transfer between two parallel plates that have a specified heat production to be dissipated at their surfaces. The heat production can vary in an arbitrary manner with time and position along the channel, starting from an initially isothermal condition. The fluid velocity is assumed constant over the channel cross section, but can vary with time. The variation of fluid temperature over the channel cross section is accounted for. General relations are presented in closed form and their application is illustrated by carrying out some typical examples. The results are compared with previous analyses that have assumed constant temperatures over the channel cross section and a constant heat-transfer coefficient.

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