Thermal radiation effects on unsteady MHD dusty viscoelastic Couette flow through an inclined porous channel

This paper describes an analytical study of unsteady magnetohydrodynamic (MHD) Couette flow of a dusty second-grade viscoelastic fluid between two infinite inclined porous plates. The problem involves the combined influences of porous medium permeability, uniform suction/injection, rotation of the system, thermal radiation, and coupled heat and mass transfer. The fluid is electrically conducting with a transverse magnetic field, and the dust particles are coupled to the base fluid by Stokes drag forces. The porous channel is inclined, which causes a buoyancy force in the flow direction, thus affecting the momentum and heat transfer characteristics. The equations of motion for the fluid and dust particles are developed with suitable assumptions and scaled to obtain dimensionless equations. Periodic solutions for velocity, temperature, and concentration are derived using the Poincaré-Lighthill perturbation method. The results are presented to illustrate the effects of various dimensionless parameters such as the magnetic parameter, Darcy number, rotation parameter, viscoelastic parameter, radiation parameter, Peclet number, thermal Grashof number, mass Grashof number, and dust concentration parameter. The results show that the magnetic field intensity, rotation, dust concentration, and porous resistance reduce fluid and dust particle velocities. Buoyancy forces and permeability increase fluid velocity. Thermal radiation increases temperature profiles, and higher Peclet numbers decrease thermal diffusion. The skin friction, Nusselt number, and Sherwood number results illustrate the effects of porous resistance, electromagnetic damping, and convective transport. The results of this study will help in understanding the control of multiphase viscoelastic fluid transport in inclined porous media, which are applicable to thermal management systems, rotating machinery cooling, porous reactors, and particle-laden energy transport devices. For the parameter ranges considered, the Nusselt number varies by about 5% with the radiation parameter and the Sherwood number by about 1% with the Schmidt number.

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