Couette flow of viscoelastic dusty fluid through a porous oscillating plate in a rotating frame along with heat transfer

Usually, suction/blowing is used to control the channel's fluid flow, which is why this worth-noting effect is considered. The fluid velocity is considered along the x-axis due to the oscillations of the right plate. The thermal effect on the flow due to the heated right plate is also considered. The fluid and dust particles have complex velocities due to the rotation, which are the sum of primary and secondary velocities. To convert the aforementioned physical phenomenon into mathematical form, partial differential equations are used for modeling the subject flow regime. Appropriate nondimensional variables are employed to nondimensionalize the system of governing equations. With the assistance of assumed periodic solutions, the system of partial differential equations is reduced to a system of ordinary differential equations which is then solved by the perturb solution utilizing Poincare-Lighthill perturbation techniques. The engineering interest quantities, the Nusselt number, and skin friction are also determined. The impact of various parameters on skin friction, viscoelastic fluid, and dust particle velocity profiles is also investigated. It is worth mentioning that suction controls the boundary layer to grow unexpectedly, even in the resonance case. The obtained solution is also valid in the case of injection. The radiation parameter, Grashof number, and second-grade parameter cause a decrease in skin friction as their values increase. On the other hand, the suction, rotation, magnetic, dusty fluid, and Reynolds numbers cause a rise in skin friction.