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We include in our analysis the thermal relaxation time of heat conduction, which insures that the termal waves propagate with a finite signal speed. One can investigate how the ansatz Thus, the complication of the mode conversion of P and SV waves can be removed. Integral transforms and their applications. On physical grounds, it is observed that the classical theory of heat conduction Fourier's law does not take into account the short time required to establish a steady-state heat conduction when a temperature gradient is suddenly produced in a solid; this neglected short time is called the thermal relaxation time.

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