Analysis of Unsteady State Problems of Nonlinear Heat Conduction Materials : 1st. Report: One-dimensional Exponential Models of x = constant

Abstract

Development of the new engineering materials such as ceramics, amorphous semiconductors, synthetic polymers, extreme-low and high temperature resisting materials, etc. has made it more and more important to analyze the unsteady non-linear heat conduction problems concerning these materials. This paper deals with two cases of one-dimensional exponential models of x=constant: (1) λand cρ are functions of coordinate x (model A) and (2) λand cρare functions of temperature T (model B). The transient features of heat transfer for both models have been mathematically analyzed and numerically calculated according to exact solutions.