Viscoelastic thermal transport in magnetohydrodynamic oscillatory Couette–Poiseuille flow with periodic pressure forcing

This study investigates magnetohydrodynamic oscillatory Couette-Poiseuille transport of an Oldroyd-B viscoelastic fluid between two infinite parallel plates with velocity slip, thermal radiation, internal heat generation, and periodic pressure forcing. The lower plate oscillates harmonically while the upper plate remains mechanically stationary. For the thermal problem, the lower wall is maintained at the reference temperature and the upper wall is subjected to a small harmonic temperature excitation, which supplies the non-homogeneous thermal forcing required by the analytical solution. The continuity equation is corrected so that the Lorentz force appears only in the momentum balance. Exact harmonic solutions are obtained for velocity, stress, and temperature by the complex-amplitude method. The Rosseland radiation parameter is defined as a positive quantity, and the thermal boundary conditions are made fully consistent with the temperature solution. The results show that slip and fluid elasticity enhance the oscillatory velocity, whereas the magnetic field suppresses motion through Lorentz damping. Increasing the heat-source parameter strengthens the thermal field, while radiation and thermal diffusion modify the wall-temperature gradient and Nusselt number. Joule and viscous heating are not included; therefore, no direct conversion of magnetic damping into thermal energy is claimed. The analytical expressions satisfy the governing ordinary differential equations and boundary conditions identically, and comparison with Ma et al. confirms the limiting hydrodynamic solution.