Thermal and stability characteristics of viscoelastic dusty fluid flow in rotating Couette systems with entropy considerations

This research aims 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 fluid velocity is measured along the x-axis due to the oscillation of the right plate. The heated right plate's thermal effect on the flow is also considered. The movement of fluid and dust particles in a rotating system can be complicated, with both primary and secondary velocities adding to their overall movement. To represent this phenomenon mathematically, we use partial differential equations to model the flow. Also make use of appropriate non-dimensional variables to simplify the system of governing equations. The Navier-Stokes equations are used to explain fluid motion in this research, while the energy equation is used to account for heat transmission inside the system. 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 mathematical techniques. The impact of various parameters on viscoelastic fluid, and dust particle velocity profiles is also investigated. As the suction/injection parameter increases, both velocity profiles are reduced. 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. This research emphasizes the significance of using suction and injection to optimize Couette flow when dealing with viscoelastic dusty fluids. The benefits of this approach include enhanced industrial operations and improved environmental management in dusty environments. Also, Parameters such as skin friction, entropy generation, and the Bejan number were meticulously analyzed, showing a 15% increase in entropy generation with rising dust particle parameters. These findings contribute to designing advanced microfluidic devices and enhancing nanotechnology-based thermal management systems. The results demonstrate that nanoparticle inclusion enhances heat transfer, while viscoelasticity significantly influences velocity distribution, with validated findings offering potential applications in industrial and biomedical systems.