An improved lumped analysis for transient heat conduction in different geometries with heat generation

This article deals with the analysis of transient one-dimensional heat conduction in both Cartesian and cylindrical geometry by employing the polynomial approximation method (PAM). Four different models such as specified heat flux for both slab and tube and heat generation in both slab and tube have been analyzed. The transient temperature is found to depend on various model parameters, namely, Biot number, heat source parameter and time. With the use of PAM, it has been possible to derive a unified relation for the transient thermal behavior of solid (slab and tube) with both internal generation and boundary heat flux. Present prediction is found to be in good agreement with other analytical results reported in the literature.