Computation of unsteady generalized Couette flow and heat transfer in immiscible dusty and non‐dusty fluids with viscous heating and wall suction effects using a modified cubic B‐spine differential quadrature method

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