Viscoelastic dusty fluid Couette flow with heat and mass transfer across a porous oscillating plate in a rotating frame

Abstract

This research aims to enhance industrial processes and address environmental issues by studying the effects of suction and injection on the Couette flow of a viscoelastic dusty fluid over a porous oscillating plate in a rotating frame. We investigate how these factors influence fluid flow, heat, mass, and temperature transfer rates. Suction and blowing are common techniques for controlling fluid flow in conduits. The study considers the impact of the right plate's oscillation on fluid velocity along the x‐axis, as well as mass diffusion and thermal effects from the heating of the right plate. Due to the rotation, the velocities of both the fluid and dust particles exhibit complex primary and secondary behaviors. Also considered the dust particles are homogenously distributed in the base fluid. Furthermore, the variable temperature and concentration are associated with boundary conditions. We develop a mathematical model using partial differential equations (PDEs) to describe these phenomena. The governing equations are non‐dimensionalized and transformed into ordinary differential equations (ODEs) using periodic solutions and solved via the Poincare‐Lighthill perturbation method. Key engineering parameters such as the Sherwood number, Nusselt number, and skin friction are calculated. The study reveals the influence of uniform suction/injection on velocity and temperature distributions, showing that suction can significantly alter boundary layer development, even under resonance conditions. The radiation parameter, Grashof number, and second‐grade parameter cause a decrease in skin friction as their values increase. On the other hand, suction, rotation, magnetic, dusty fluid, and Reynold numbers cause a rise in skin friction.The objective of this research is to improve industrial processes and tackle environmental issues by examining the effects of suction and injection on the Couette flow of a viscoelastic dusty fluid over a porous oscillation plate in a rotating frame. The purpose of this study is to determine how suction/injection influences the Couette flow of a viscoelastic dusty fluid, as well as the heat, mass, and temperature transfer rates across a porous, oscillating plate in a rotating frame. It also takes heat transfer into account. When manipulating the flow of a fluid via a conduit, suction and blowing are common methods. As the right plate oscillates, the x‐axis becomes the primary consideration for fluid velocity. We also take into account the mass diffusion and thermal influence on the flow from the right plate's heating. As a consequence of the spin, the fluid, and dust particles have velocities that are both secondary and primary, making them complicated. Using PDEs, we may translate the aforementioned physical phenomena into a mathematical model of the relevant flow regime. The system of governing equations is non‐dimensionalized by the use of appropriate nondimensional variables. The system of PDEs is transformed into a system of ODEs with the help of assumed periodic solutions and then solved by the perturb solution with the help of Poincare‐Lighthill perturbation methods. We also calculate the Sherwood number, the Nusselt number, and the skin friction, all of which are of relevance to engineers. We also examine how changing these variables affects the velocity distributions of skin friction, viscoelastic fluid, and dust particles. We look at how uniform suction/injection affects the speed and temperature distributions. It is important to note that even in the resonance instance, suction/ injection directs the boundary layer to develop unexpectedly.