Mathematical Problems in Engineering 
Volume 2006 (2006), Article ID 56046, 31 pages
doi:10.1155/MPE/2006/56046

Modeling granular materials as compressible nonlinear fluids: Heat transfer boundary value problems

Mehrdad Massoudi and Tran X. Phuoc

 U.S. Department of Energy, National Energy Technology Laboratory, P.O. Box 10940, Pittsburgh 15236-0940, PA, USA
Received 28 August 2006; Accepted 13 September 2006

Abstract

We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.