%0 Journal Article
%T Modeling granular materials as compressible nonlinear fluids: Heat transfer boundary value problems
%A Mehrdad Massoudi
%A Tran X. Phuoc
%J Mathematical Problems in Engineering
%D 2006
%I Hindawi Publishing Corporation
%R 10.1155/mpe/2006/56046
%X 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.
%U http://www.hindawi.com/journals/mpe/2006/056046/abs/