It is well known that the model was built on the classical Fourier's law
, implying an infinite thermal propagation velocity and an instantaneous thermal effect [8, 9].
is based purely on empirical observation and is not derived from other physical principles.
satisfies the heat conduction induced by a small temperature gradient in steady state.
In classical thermoelasticity, the heat conduction is governed by the Fourier's law
, which means that the heat flux is proportional to the gradient of temperature.
In Pennes bio-heat equation, the heat conduction in biological tissue is modeled by using Fourier'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.
is quite accurate for most common engineering problems.
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.
The relation between the heat flux and temperature gradient is given by Fourier's law