Abstract

We study, via hydrodynamic equations, the granular temperature profile of a granular fluid under gravity and subjected to energy injection from a base. It is found that there exists a turn-up in the granular temperature and that, far from the base, it increases linearly with height. We show that this phenomenon, observed previously in experiments and computer simulations, is a direct consequence of the heat flux law, different form Fourier's, in granular fluids. The positive granular temperature gradient is proportional to gravity and a transport coefficient ?0, relating the heat flux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value ?0 for different restitution coefficients. The theoretical predictions are verified by means of molecular dynamics simulations, and the value of ?0 is computed for the two-dimensional inelastic hard sphere model. We provide, also, a boundary condition for the temperature field that is consistent with the modified Fourier's law. © 2003 Published by Elsevier Science B.V.