A gradient system for a higher-gradient generalization of Fourier’s law of heat conduction

We derive a generalized heat conduction problem for rarefied gas at slip regime from gradient system where the driving functional is entropy. Specifically, we construct an Onsager [Formula: see text] such that associated evolution of given by text], operator, contains higher-gradients absolute temperature text]. Moreover, through Legendre–Fenchel theory, write as classical with induced flow equation, demonstrate usefulness approach modeling scale-size thermal effects in periodic media have been recently observed experimentally.