Three-dimensional Couette flow of a dusty fluid with heat transfer

This work is focused on the mathematical modeling of three-dimensional Couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively, subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phases are obtained by solving the governing partial differential equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem.