The present study considers an assembly of spherical particles, densely packed, 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 governing equations reduce to a system of coupled, non-linear ordinary differential equations. The equations are integrated numerically. In so doing, the equations are discretized using the conventional central finite difference approximation technique and the unknown conditions are assumed to reduce the problem to an initial value problem. After the trial solutions the known boundary 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-Raphson method is used to correct the initial guesses and the iteration is repeated. This procedure continues until the solutions converge to the given values. The technique is found to be powerful for this type of application.