Journal of Power System Engineering (동력기계공학회지)
- Volume 3 Issue 3
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- Pages.14-21
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- 1999
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- 2713-8429(pISSN)
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- 2713-8437(eISSN)
Comparative Analysis of the Parabolic and Hyperbolic Heat Conduction and the Damped Wave in a Finite Medium
유한한 평판에서 포물선형 및 쌍곡선형 열전도 방정식과 파동 방정식의 비교 해석
Abstract
The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(