More precisely, Fourier law
is diffusive and cannot predict the finite temperature propagation speed in transient situations, in this context, the Cattaneo-Vernotte equation corrects the nonphysical property of infinite propagation of the Fourier and Fickian theory of the diffusion of heat, and this equation also known as the telegraph equation for the temperature is a generalization of the heat diffusion (Fourier's law) and particle diffusion (Fick's laws) equations.
Tzou [11, 12] had introduced another modification to Fourier law, by inventing two time lags, Dual Phase Lag (DPL), between the heat flux and the temperature gradient namely the heat flux time lag and the temperature gradient time lag.
T] = 0 one obtain the Maxwell-Cattaneo model, and Fourier law obtained if [[tau].
This leads for isotropic systems to the Fourier law
The time-nonlocal generalization of the Fourier law
with the "long-tail" power kernel [11, 13-15] can be interpreted in terms of fractional calculus (theory of integrals and derivatives of noninteger order) and results in the time-fractional heat conduction equation