Common Misperceptions of the Hyperbolic Heat Equation

The Cattaneo equation has been proposed as a more general form of Fourier's law and, to date, many believe that Cattaneo's equation extends the validation regime of Fourier's law to time scales shorter than the relaxation time of a material. Cattaneo's equation leads to a form of the heat equation known as the hyperbolic heat equation, which is a damped-wave equation and predicts that heat will propagate in waves with a finite speed. Because of lack of experimental evidence and no sound derivation of hyperbolic heat equation, there is simply no justification for accepting Cattaneo's equation. Experiments claiming results corresponding to hyperbolic heat equation near room temperature in nonhomogenous media are misleading and more than likely due to improper specification of the problem or other phenomena associated with the porous materials used in the experiment. Accepting hyperbolic heat equation simply because it predicts a finite speed of propagation is fundamentally misleading with regard to conduction heat transfer at short time scales. This paper provides a point-to-point clarification, including statistical theories, equilibrium and irreversible thermodynamics, and the experimental aspect, as regards to the common misunderstandings of hyperbolic heat equation by many past and contemporary heat transfer researchers.

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