An improved lumped model for transient heat conduction in different geometries

Abstract

This paper deals with the analysis of transient heat conduction in various geometries, namely, large plate, long cylinder, and sphere by employing the polynomial approximation method. A wide variety of guess profiles have been tried to obtain the temporal variation of temperature in the solid and the best profile is identified for different geometry. The effect of convection has been expressed by a unique parameter termed as the modified Biot number, the exact value of which depends on the geometry and process parameters. This parameter enables us to provide a generalized three-parameter relationship for transient conduction and eliminates the development of different models for different geometry. Compared to other analytical models the present prediction exhibits excellent agreement with the exact solution (0.67% error in large plate, 3.84% error in long cylinder, and 1.47% in sphere). © 2012 by Begell House, Inc.