Magnetohydrodynamic natural convection flow with temperature dependent physical properties along a vertical wavy surface

Abstract

A steady two-dimensional laminar magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid with temperature dependent viscosity and thermal conductivity along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations with associated boundary conditions are converted to non-dimensional form using a suitable transformation. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as the Keller-box scheme. Depending on different flow conditions the abstract of the work are as follows: Firstly, the effect of magnetohydrodynamic natural convection boundary layer flow along a vertical wavy surface with a temperature dependent viscosity (linear function and inversely proportional to linear function of temperature) has been analyzed. The results of the numerical solution are shown graphically in the form of skin friction coefficient, the rate of heat transfer, the velocity and temperature profiles, the streamlines and the isotherms over the whole boundary layer for different values of temperature dependent viscosity, magnetic parameter, the amplitude-to-length ratio of the wavy surface and Prandtl number. The skin friction coefficient and the rate of heat transfer are also displayed in tables showing the effects of viscosity, Prandtl number and the intensity of magnetic field. Secondly, the effect of temperature dependent thermal conductivity on magnetohydrodynamic natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been studied numerically. The effects of temperature dependent thermal conductivity, magnetic field, Prandtl number and the amplitude-to-length ratio of the wavy surface on the surface shear stress in terms of the skin friction coefficient Cfx, the rate of heat transfer in terms of Nusselt number Nux, the velocity and temperature profiles, the streamlines and the isotherms over the whole boundary layer are displayed graphically. Numerical results of the local skin friction coefficient and the rate of heat transfer for different values of thermal conductivity, Prandtl number and magnetic parameter have also been presented in tabular forms. Thirdly, steady two-dimensional viscous incompressible fluid on magnetohydrodynamic free convection laminar flow with combined effects of temperature dependent viscosity and thermal conductivity of the fluid are taken to be proportional to a linear function of temperature along a uniformly heated vertical wavy surface have been considered. The numerical results of the surface shear stress in terms of skin friction coefficient Cfx and the rate of heat transfer in terms of local Nusselt number Nux, the stream lines and the isotherms have been presented graphically for a selection of parameters set consisting of temperature dependent viscosity, temperature dependent thermal conductivity, magnetic field, the amplitude-to-length ratio of the wavy surface and Prandtl number. Finally, the effect of Joule heating on MHD natural convection flow with viscosity and thermal conductivity variation owing to temperature along a uniformly heated vertical wavy surface has been studied. Here, the attention are focused on the surface shear stress in terms of the skin friction coefficient, the rate of heat transfer in terms of Nusselt number, the velocity, the temperature profiles, the streamlines and the isotherms for the effects of Joule heating, temperature dependent viscosity, temperature dependent thermal conductivity, the intensity of magnetic field, the amplitude-to-length ratio of the wavy surface and Prandtl number. In tabular form the numerical results of the local skin friction coefficient Cfx and the rate of heat transfer in terms of local Nusselt number Nux for different values of Joule heating parameter are also represented. Comparisons with previously reported investigations are performed and the results show excellent agreement.