The problem of unsteady unidirectional hydromagnetic flow due to stress applied at the free surface is studied here. The applied magnetic field is normal to the horizontal boundary. The dynamics of fluid and electric currents are investigated as functions of magnetic Prandtl number Pm (= σµ0ν), which measures the ratio of viscous diffusion to magnetic diffusion. In contrast to hydrodynamic Rayleigh problem, the transient dynamics consists of two diffusively growing layers as in the conventional MHD Rayleigh problem (see Dix [5]).The viscous Hartmann layer becomes steady soon, while the magnetic diffusion layer diffuses to infinity with Alfven speed. The electric currents generated in the Hartmann layer find a return path in the magnetic diffusion layer. It may also be seen that the free surface Hartmann layer is weak compared to rigid surface Hartmann layer.
In this paper, we have explored the pulsating flow of a magnetohydrodynamic (MHD) micropolar nanofluid in a vertical channel by applying Buongiorno’s nanofluid model with entropy analysis. The effects of Brownian motion, thermophoresis, Joule heating (Ohmic heating), and thermal radiation are taken into account. The specified concept is significant in the fields of polymer engineering, cancer therapy, and nano-drug delivery. The perturbation approach is applied to convert the governing partial differential equations (PDEs) into ordinary differential equations (ODEs) and cracked numerically by utilizing the shooting process via Runge-Kutta fourth-order method. The flow influences of velocity, microrotation, temperature, nanoparticle concentration, entropy generation, and Bejan number are deliberated by plotting graphs and analyzed in detail for the various values of emerging physical parameters. The heat and mass transfer rates are given in a table.
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