Mechanical Engineering Faculty Research


Analysis of Heat Transfer in Slabs With Variable Properties Subjected to Radiation and Convection

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Transient heat transfer in a plane slab with temperature dependent properties subject to thermal radiation and internal generation is studied. The temperature distribution inside the solid is obtained based on three approximate analytical techniques. They are Biot's variational method, Goodman's integral method and the modified integral method, due to Volkov and Li-Orlov. To test the accuracy of the above techniques, the same nonlinear problem is solved directly using a finite difference scheme. Comparisons show that all the approximate solutions agree very well with the numerical solutions. However, at the insulated surface, the modified integral method yields more accurate results than that of others when the radiation parameter is large; at the beat transfer surface, the Biot's variational method appears to be the best among three. Under certain limiting conditions, the present solutions are found to reduce to the results of some earlier analyses.

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American Society of Mechanical Engineers