Journal of Material Sciences & Engineering

Analytical and Numerical Analysis of Functionally Graded Heat Conduction Based on Dirichlet Boundary Conditions.

Abstract

Essa S

An analytical and numerical solution for the one dimensional of heat conduction in a slab exposed to different temperature at both ends is presented. The distribution of heat throughout the transient direction obeys to functionally graded (FG) temperature based on Dirichlet boundary conditions. The variation of functionally graded temperature can be described by any form of continuous function. In this case, where the external heat fluxes are not directly definite based on the Dirichlet or mixed boundary conditions, the fluxes that concluded over the slab faces are free to vary until the equilibrium condition is reached. By numerically solving the resulting heat-conduction equation, the distribution of temperature which vary with time through the slab is obtained. The obtained analytical results are presented graphically and the influence of the gradient variation of the temperature on shape formed with changed time is investigated.