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Magnetohydrodynamic natural convection flow of a nanofluid due to sinusoidal surface temperature variations

We examine the natural convection flow that arises in an electrically conducting nanofluid due to the sinusoidal surface temperature variations along a vertical surface. The effect of thermal radiation is also incorporated. The reduced system of governing equations is solved using an efficient implicit finite difference method which is also known as the Keller box method. The results are presented in terms of the shear stress and the rate of heat transfer as well as the velocity and temperature profiles. In general, the amplitude of the undulation of the shear stress gradually decreases and that of the rate of heat transfer increases along the streamwise direction. The significant finding is that, with an increase in the volume fraction of nanoparticles, the shear stress diminishes, whereas the rate of heat transfer considerably increases. Due to the increase in the amplitude of oscillation of the surface temperature, conduction–radiation parameter, and surface temperature, a substantial increase is observed in both the shear stress and the rate of heat transfer. Contrary to this, the shear stress and the rate of heat transfer decrease with the increase in the magnetic field parameter. For any value of the relevant parameters, the use of nanoparticles in a pure fluid reduces the shear stress and enhances the rate of heat transfer. Moreover, when a nanofluid is used instead of pure fluid, the thicknesses of momentum and thermal boundary layers are found to increase, irrespective of the physical parameters.