Temperature inversion in granular fluids under gravity

✍ Scribed by Rosa Ramı́rez; Rodrigo Soto

• Book ID: 104340753
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 371 KB
• Volume: 322
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00028-1

✦ Synopsis

We study, via hydrodynamic equations, the granular temperature proÿle of a granular uid 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 ux law, di erent form Fourier's, in granular uids. The positive granular temperature gradient is proportional to gravity and a transport coe cient 0, relating the heat ux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value 0 for di erent restitution coe cients. The theoretical predictions are veriÿed 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 ÿeld that is consistent with the modiÿed Fourier's law.