satisfies the heat conduction induced by a small temperature gradient in steady state.
One of which, called thermoelasticity with second sound, suggests the replacement of Fourier's law
by so called Cattaneo's law.
Due to the above assumption, the energy equation becomes the only governing equation for the analysis of PCMs, and it reduces to Fourier's law
of conduction given as,
Lord and Shulman  formulated the generalized thermoelasticity theory introducing one relaxation time in Fourier's law
of heat conduction equation and thus transforming the heat conduction equation into a hyperbolic type.
The simulation was carried out based on the Fourier's law
of heat conduction and Newton Law of cooling.
The background and foundation for this study evolve around thermal dynamics and Fourier's law
of heat conduction.
In classical unsteady heat transfer problems, the basic equations are derived from Fourier's law
of heat conduction, which results in a parabolic equation for the temperature field and an infinite speed of heat propagation, thus violating the principle of causality.
Some authors estimate G in an analytical way, based on Fourier's law
and the assumption of a monotonous temperature profile in the ground (Liang et al.
They looked at and applied some sophisticated maths using Fourier's law
in order to calculate the temperature increases that would be involved with their system.
To overcome the deficiencies of Fourier's law
in describing high rate heating processes the concept of wave nature of heat convection had been introduced .
Therefore, the presence of the relaxation time is much more than a minor quantitative correction, as in the high-frequency regime it leads to a completely different behaviour than that predicted by the classical Fourier's law
Dufour conduction operates in harmony with Fourier's law
and enhances the flux of thermal energy toward the external surface of the catalyst when thermal diffusion coefficients are negative.