Temperature waves analysis in a cylinder subject to heat flow inertia

The phenomenological Fourier hypothesis by which heat propagates in space at infinite velocity underlies classical theory of heat conduction. In fact heat propagation velocity is high, but finite. It can be left out of account in the majority of heat-conduction problems, but has a significant influence on the result of solution in certain cases. In such instances it is appropriate to use Maxwell-Cattaneo-Lykov theory taking into account heat flow inertia that results in hyperbolic thermal conductivity equation. There are a limited number of solutions of this equation for certain problems. In the work, the temperature field of an unbounded cylinder under transient periodical conditions of heat exchange with surroundings has been studied. The approximate analytical quasi-stationary solution of the hyperbolic thermal conductivity equation in the form of the partial sum of the trigonometric Fourier series is obtained. The temperature fields are computed and the heat flow relaxation time influence on the temperature peak-to-peak value of the cylinder is investigated.

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