Spatial decay of transient end effects in functionally graded heat conducting materials

Abstract

The purpose of this research is to investigate the influence of material inhomogeneity on the spatial decay of end effects in transient heat conduction for isotropic inhomogeneous heat conducting solids. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The spatial decay of solutions to an initial-boundary value problem with variable coefficients on a semi-infinite strip is investigated. It is shown that the spatial decay of end effects in the transient problem is faster that that for the steady-state case. Qualitative methods involving second-order partial differential inequalities for quadratic functionals are first employed. Explicit decay estimates are then obtained by using comparison principle arguments involving solutions of the one-dimensional heat equation with constant coefficients. The results may be interpreted in terms of a Saint-Venant principle for transient heat conduction in inhomogeneous solids.