Fourier experimental observations served to formulate quantitative relationship later known as "The First Fourier's law of heat conduction
" (Ficker 2008).
The third equation of system (1.1) represents Cattaneo's law of heat conduction
modeling thermal disturbances as wave-like pulses traveling at finite speed.
(i) Heat conduction follows non-Fourier law of heat conduction
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 1822 French mathematician Jean Baptiste Joseph Fourier (1768-1830) postulated that the rate of heat transfer is proportional to the temperature gradient present in a solid.
Under such conditions, Fourier's law of heat conduction
, which is based on the continuum assumption, becomes invalid (39).
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.
Lord and Shulman  generalized the classical thermoelastic model of Biot , by incorporating a flux rate term into the Fourier's law of heat conduction
which results into a hyperbolic heat transport equation admitting finite speed of thermal signals.
Fourier's law of heat conduction
is used to determine the thermal conductivity of the test specimens from the measured heat flux and the known specimen dimensions.
The authors state that this book evolved from a series of courses given at Cornell University and UCLA to students with a wide range of backgrounds (geology, geophysics, physics, mathematics, chemistry and engineering), and that the book is designed to encourage a thorough understanding of some of the fundamental physical laws, e.g., Hooke's law of elasticity, Fourier's law of heat conduction
, and Darcy's Law for fluid flow in porous media.
From Fourier's law of heat conduction
the conduction process can be quantified as a heat flux rate equation.