Solution of a Heat Equation of Hyperbolic Type with Mixed Boundary Conditions on the Surface of an Isotropic Half-Space

Abstract

INTRODUCTION The phenomenological theory of heat conduction assumes that the heat propagation velocity is infinitely large, which is justified by computations of temperature fields in bodies under ordinary conditions observed in practice. However, for rarefied media and nonstationary processes of high intensity, one should take account of the fact that heat propagates at a finite velocity. Lykov [1, p. 21] suggested a theory of finite heat and particle propagation velocities in capillary-porous bodies, which implies that wr = √ λ/ (cγτr), where wr is the heat propagation velocity, τr is the time constant of the thermal flow, λ is the thermal conductivity, c is the specific heat, and γ is the material density. As a rule, wr ∼= 150− 300 m/sec and τr ∼= 10−9 − 10−15 sec for gases, and the effect of the finite heat propagation velocity on the heat transfer becomes observable in the case of a supersonic flow. Then the heat equation has the form [1, p. 21]