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A study on unsteady MHD natural convection flow of an optically thin, heat radiating, incompressible, viscous, chemically reactive, temperature dependent heat absorbing and electrically conducting fluid past an exponentially accelerated infinite vertical plate having ramped temperature, embedded in a porous medium is carried out, considering the effects of Hall current and rotation. Governing equations are non-dimensionalized and Laplace Transform Technique is used to find the exact solutions for non-dimensional velocity, temperature and concentration fields. The quantities of physical interest i.e. shear stress at the plate, rate of heat and mass transfers at the plate are also derived. Numerical results for the velocity, temperature and species concentration of the fluid are demonstrated with the help of graphs whereas those of shear stress at the plate, rate of heat and mass transfers at the plate are displayed in tables for various flow parameters. It is observed that fluid velocities as well as fluid temperature profiles are slower in case of ramped temperature plate than those of isothermal plate.

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The present study tends to investigate unsteady MHD flow of a Casson fluid near a vertical oscillating plate through a non-Darcy porous medium. The impact of Joule heating, viscous dissipation, thermo-diffusion and Newtonian heating are taken into consideration. Incorporating dimensionless variables and parameters, governing non-dimensional equations are solved by implicit finite difference technique of Crank-Nicolson type. Numerical simulation for the fluid velocity, fluid temperature and species concentration are carried out for a range of values of regulatory flow parameters that characterize the physics of the flow graphically whereas skin friction coefficient, Nusselt number and Sherwood number for the several values of the emerging flow parameters at the plate are presented in tabular form. One of the significant findings of this analysis include that an intensification in the Newtonian heating effect causes a downfall in the rate of heat transfer at the plate whereas another important outcome of the present study is that the concentration of species will gradually increase when we consider higher order chemical reactions, but the incremental effect will almost extinguish after a certain level. The present investigation may have bearings on several engineering processes such as glass blowing, paper production, extrusion of plastic sheet, annealing and tinning of copper wire, spinning of fibers and continuous casting of metals.

An investigation of unsteady MHD natural convection flow with Hall effects of an electrically conducting, viscous, incompressible and heat absorbing fluid past an exponentially accelerated vertical plate with ramped temperature through a porous medium in the presence of thermal diffusion is carried out. Exact solution for fluid velocity and fluid temperature is obtained in closed form by Laplace transform technique. The expressions for shear stress and rate of heat transfer at the plate are also derived. The numerical values of fluid velocity and fluid temperature are displayed graphically whereas those of shear stress and rate of heat transfer at the plate are presented in tabular form for various values of pertinent flow parameters.