Abstract
In the literature, one can find numerous heat conduction models with different backgrounds. In general, a heat equation beyond Fourier consists of additional time and spatial derivatives, which makes it more challenging to solve the mathematical model correctly. In the present paper, we revisit the famous Guyer-Krumhansl heat equation for which it has been reported earlier that can lead to negative temperatures by violating the maximum principle. We show that for proper initial and boundary conditions with thermodynamic compatibility, the maximum principle is fulfilled. Our work further emphasizes the importance of the thermodynamic origin of heat equations and their compatibility with the second law. Furthermore, we use two different approaches how to determine the initial state in a thermodynamically compatible way. Computational simulations support our results.
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