Non-Fourier propagation of heat pulses in finite medium (Q1115669)

This paper investigates analytically non-Fourier effects in a finite slab using the hyperbolic heat conduction model. The results for pulsed surface heat flux conditions are compared with those obtained from the standard parabolic heat conduction equation. Detailed analysis of transition between the `parabolic' and `hyperbolic' behaviour of the temperature response of the pulse shows, that for L/\(\sqrt{(a\tau)}\gtrsim 25\) non-Fourier effects are negligible and the temperature response of the pulse which occurs at \(x=0\), gained in \(x=L\), is practically equal to that developed from the parabolic heat conducting equation. Solutions given in this paper have a clear physical interpretation as travelling thermal waves, which enables solutions to this problem for a semi-infinite medium to be written. Series solutions presented here are in convenient form for numerical convergence, and enable one to make a deep analysis of early times of a transient stage in a medium, which plays an important role in the investigation of thermal stresses.