Transient Heat Conduction With Finite Wave Speeds

Transient Thermal Waves in the General Theory of Heat Conduction With Finite Wave Speeds

“…In [6] temperature rate waves of arbitrary form were examined, and it was concluded that "these waves will always decay to zero if the material constants satisfy a particular inequality." In [7] it was necessary to assume an expansion for small time of the heat relaxation function a and the energy relaxation function /3 to obtain results in agreement with those of [6]. The investigations reported in [6,7] are limited to wave-front approximations and do not consider exact and long time solutions.…”

“…To extend the results of [7], one considers more general expansions for a and /3 than those used in [7]. This is done by assuming that 6 …”

“…From equation (12) one can deduce the solution given in [7] by using the sine transform pair [9] £(f. + X»)-i -veto obtain the contour integral…”

“…In two recent papers, Chen [6] and Amos and Chen [7] consider the growth and decay of temperature rate waves of arbitrary form satisfying the linearized theory derived by Gurtin and Pipkin. This was done, first, by the use of singular surface analysis [6], and then by the use of Laplace transforms [7J.…”

“…In this paper, the small time expansion used in [7] is analyzed, and the differentiability conditions on a and /3 are relaxed to obtain new wave-front expansions. It is shown that the long time approximation satisfies the heat equation.…”