A numerical study of the flow of granular materials between two vertical flat plates which are at different temperatures

The present study considers an assembly of spherical particles, densely pac ked, between two vertical flat plates which are at different temperatures. A continuum model is used and the now due to such a temperature difference is investigated. For a fully developed flow of these materials, the governi ng equations reduce to a system of coupled, non-linear ordinary differentia l equations. The equations are integrated numerically. In so doing, the equ ations are discretized using the conventional central finite difference app roximation technique and the unknown conditions are assumed to reduce the p roblem to an initial value problem. After the trial solutions the known bou ndary conditions at the edge of the integration interval are compared with the correspondent values provided by the trial solutions. If the solutions at this point do not agree with the known boundary conditions the Newton-Ra phson method is used to correct the initial guesses and the iteration is re peated. This procedure continues until the solutions converge to the given values. The technique is found to be powerful for this type of application.