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In this paper, the unsteady flow of two immiscible fluids with heat transfer is studied numerically\ud with a modified cubic B-spine Differential Quadrature Method. Generalized Couette flow of two\ud immiscible dusty (fluid-particle suspension) and pure (Newtonian) fluids are considered through\ud rigid horizontal channels for three separate scenarios: first for non-porous plates with heat\ud transfer, second for porous plates with uniform suction and injection and heat transfer, and third\ud for non-porous plates with interface evolution. The stable liquid-liquid interface is considered for\ud the two immiscible fluids in the first two cases. In the third case, it is assumed that the interface\ud travels from one position to another and may undergo serious deformation; hence the single\ud momentum equation based on the (volume of fluid) VOF method is combined with the continuum\ud surface approach model, and an interface tracking is proposed. The flow cases are considered to\ud be subjected to three different pressure gradients, of relevance to energy systems- namely, applied\ud constant, decaying, and periodic pressure gradients. For each case, the coupled partial differential\ud equations are formulated and solved numerically using MCB-DQM to compute the fluids\ud velocities, fluid temperatures, interface evolution. The effects of emerging thermo-fluid\ud parameters, i. e. Eckert (dissipation), Reynolds, Prandtl, and Froude numbers, particle\ud concentration parameter, volume fraction parameter, pressure gradient, time, and the ratio of viscosities, densities, thermal conductivities, and specific heats on velocity and temperature\ud characteristics are illustrated through graphs.