Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles

The Casson model is a fascinating model, which is genuinely recommended for use with fluids of a non-Newtonian type. The conventional model is not capable to represent the Casson model with the suspension of foreign bodies (dust particles). Due to this, the two-phase model for the mixture of Casson model fluid and dust particles is formulated. This study examines the emerging role of dust particles in changing the behavior of Casson model. In particular, two-phase flow of dusty Casson model with modified magnetic field and buoyancy effect under Newtonian heating boundary condition along a vertically stretching sheet is considered. The equations that govern under Casson model, together with dust particles, are reduced to a system of nonlinear ordinary differential equations by employing the suitable similarity variables. These transformed equations are then solved numerically by implementing the Runge–Kutta–Fehlberg (RKF45) method. The numerical results of skin friction coefficient plus Nusselt number are displayed graphically. The results revealed the fluid’s velocity tends to deteriorate due to the existence of dust particles, whilst its temperature is increased. The two-phase flow is one of the mathematical modeling techniques for multiphase flow, where the relationship between the fluid and solid is examined more closely. It is expected that the present findings can contribute to the understanding of the theory of two-phase flow mathematically, which will continue to produce significant research in this field.