An Analytical Solution of the Effect of Peripheral Wall Conduction on Laminar Forced Convection in Rectangular Channels

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Abstract
This study deals with fully developed laminar forced convection in rectangular channels that are heated on the broad sides. The analysis determines the effect of peripheral heat conduction within the heated walls on the wall temperature distributions. The unheated short side walls are assumed nonconducting. The heat conduction within the broad walls was formulated in terms of an integral equation and coupled with the convective energy equation within the fluid. Analytical solutions were obtained where the heating extends over the entire width of the broad side, is removed from the corner region, or extends beyond the corner into the side wall. Transverse wall conduction produced substantial decreases in the peak wall temperature and in the temperature gradients along the long side.

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