Computational Techniques for The Evaluation of Inhomogeneity Parameters on Transient Conduction in Functionally Graded Layers

Abstract

Transient thermal response of a functionally graded material (FGM) layer is considered and individual effects of inhomogeneity parameters on temperature distribution are examined. Transient conduction equation has variable coefficients controlling conductivity, mass density and specific heat capacitance due to the material property variation along the thickness of the graded layer. In order to solve the time dependent conduction equation for the unknown interior temperatures, computational methods are employed based on finite difference and finite element methods. Governing partial differential equation is discretized in space and time grids and computer codes are developed to implement explicit and implicit schemes. Results of explicit and implicit schemes are compared with those found by finite element method. A very good agreement is achieved for the applied boundary and initial conditions. Parametric study reveals the individual influences of various inhomogeneity parameters of FGM upon time dependent temperature distribution of a functionally graded layer. The results of the direct comparison study indicate that inhomogeneity parameters for specific heat and mass density have greater influence on temperature distribution than that for thermal conductivity.