Shear-induced heat transport and the relevance of generalized Fourier's law in granular Poiseuille flow

It is shown that both normal and tangential heat-flux profiles in acceleration-driven Poiseuille flow of a granular gas can be qualitatively different from those in a molecular gas. Comparisons with a generalized Fourier's law confirm that the cross-thermal conductivity is responsible for the double-well-shaped profile of the tangential heat flux, and the net heat-flow rate can be directed along or against the external acceleration, depending on the value of the restitution coefficient and the Knudsen number (Kn). Collectively, the tensorial thermal conductivity and the inelasticity-induced clustering of particles can explain the anomalous behavior of shear-induced heat fluxes in a nonrarefied (Kn -> 0) granular gas. The importance of the heat-flux terms driven by the density gradient and the kinetic-stress gradient is discussed in the context of both molecular and granular gases.