A mathematical model for unsteady heat transfer and flow of an electrically conducting, viscous, incompressible dusty fluid in a channel formed between two concentric cylinders is developed. In the model, the fluid is driven along the channel by a constant pressure gradient, and an external magnetic field is applied in the direction perpendicular to the channel flow. The two cylinders are considered electrically insulated, and the surfaces maintained at constant but different temperatures with the outer cylinder being at a higher temperature. The viscosity and electrical conductivity of the fluid are considered varying with temperature. The equations governing flow and temperature distribution of both the fluid and the dust particles are a set of coupled momentum and energy equations. The derived system of non-linear partial differential equations is solved numerically on a two-dimensional computation grid using the Galerkin finite element method. The paper ends with discussions of the effect of the applied magnetic field and the variations in viscosity and electrical conductivity with temperature on the time development of the velocity and temperature distributions for both the fluid and dust particles.

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