Non-linear heat conduction in dense fluids

Abstract

In a dense fluid with very large heat flow J. the thermal conductivity lambda = lambda 0+ lambda 2J2. An estimate of lambda 2/ lambda 0 is made for hard spheres with mass and diameter appropriate to Ar and density just below the gas-solid transition. This estimate indicates that Fourier's law will hold in the form appropriate to low J if J<or approximately=109 W m-2 and that the J dependence of pressure and internal energy is of the same order as that of lambda . The calculation utilises an earlier derivation from the classical Liouville equation which expresses lambda at high density in terms of the thermodynamic pressure. The latter can be calculated with the aid of reciprocity and integrability conditions of extended non-equilibrium thermodynamics which treats J as a state variable.