ABSTRACT

An exact analytical solution in closed form is obtained for a two-dimensional initial-boundary-value problem of heat wave propagation in a thick slab of an anisotropic rigid thermal conductor within the dual-phase-lag model. One-sided Fourier transform technique is used to obtain a formal solution. The method requires an essential change of the dependent variable in order to guarantee a suitable asymptotic time behavior of the unknown function. The solution satisfies prescribed boundary temperatures and zero initial conditions. Numerical results are presented to put in evidence the effect of the two thermal relaxation times on the behavior of the heat conduction process. In particular, it is shown that the governing equation for temperature includes both characters of wave propagation and diffusion due to the interplay between relaxation times. The influence of anisotropy is investigated. The present results confirm previous findings about heat propagation within dual-phase-lag. The proposed method can treat other geometries, viz. the half-space, quarter-space and the rectangular domain with arbitrary boundary and initial conditions. The obtained exact solution can be used to check approximate solutions arising from other techniques.

摘要

对于双相滞后模型中各向异性刚性热导体的厚板中热波传播的二维初始边界值问题，获得了封闭形式的精确解析解。单面傅立叶变换技术用于获得形式解。该方法需要对因变量进行必要的更改，以确保未知函数具有合适的渐近时间行为。该溶液满足规定的边界温度和零初始条件。数值结果表明，这两个热弛豫时间对导热过程的行为有影响。特别地，示出了由于松弛时间之间的相互作用，温度的控制方程包括波传播和扩散的特征。研究了各向异性的影响。目前的结果证实了先前关于双相滞后内热传播的发现。所提出的方法可以处理其他几何形状，即。具有任意边界和初始条件的半空间，四分之一空间和矩形域。所获得的精确解可用于检查其他技术产生的近似解。