One-Dimensional Temperature and Stress Distributions Associated with Hyperbolic Heat Conduction

Abstract

The classical Fourier heat conduction law gives sufficient accuracy for many practical engineering applications. However, it cannot exactly reflect the real physical mechanism of heat conduction by highly-varying thermal load, at very low temperatures, or at nanoscale. The hyperbolic heat conduction equation can better explain heat conduction in solids. However, such equation is very difficult to solve. This paper studies the temperature field for a 1-D plate and a 1-D cylinder. The associated thermal stress for a 1-D plate is also given. Only in these simple situations, closed form solutions are possible and are given. The results can be used in the future analysis of thermal shock cracking and reliability analysis of materials in modern science and technology.