E-Jurnal Matematika Vol. 9(4), November 2020, pp. 219-228 ISSN: 2303-1751 DOI: https://doi.org/10.24843/MTK.2020.v09.i04.p302 219 EFFECT OF NON-UNIFORM HEAT SOURCE AND RADIATION ON UNSTEADY MHD FREE CONVECTION FLOW PAST AN INFINITE HEATED VERTICAL PLATE IN POROUS MEDIUM Pratibha Mishra 1§ , Sweta Tripathi 2 1 Department of Mathematics, Applied Sciences &Humanities, Kanpur Institute of Technology, Kanpur- 208002, U.P, India [E-mail: pratibha.mishra@kit.ac.in, pratibha.mishra003@gmail.com] 2 Department of Electronics & Communication Engineering, Kanpur Institute of Technology, Kanpur- 208002, U.P, India [E-mail: swetatripathi16@gmail.com] § Corresponding Author ABSTRACT Influence of radiation and non-uniform heat source on unsteady, magneto-hydrodynamic free convection flow of viscous incompressible fluid past an infinite vertical heated plate embedded in porous medium of an optically thin environment with time dependent suction and viscous dissipation is investigated in this paper. Analytical solutions of the coupled non-linear equations are obtained for the velocity field and temperature distribution using oscillating time-dependent perturbation technique. Expressions for skin-friction and heat transfer rate are also derived. The effects of the material parameters on velocity, temperature, skin-friction, and rate of heat transfer are discussed quantitatively. Keywords: Non-Uniform heat source, time dependent suction, viscous dissipation 1. INTRODUCTION The study of magneto hydrodynamic natural convection flow and heat transfer of an electrically conducting fluid past a heated semi- infinite vertical porous plate finds useful applications in many engineering problems such as MHD generators, nuclear reactors, geothermal extractions, heat exchanger devices and boundary layer control in the field of aeronautics and aerodynamics. Because of numerous applications in several engineering and industrial manufacturing processes, such flows have got renewed interest among researchers. The effects of radiation are of vital importance. Recent development in hypersonic flights, rocket combustion chambers, power plants for interplanetary flights and gas cooled nuclear reactors have focused attention on thermal radiations as a mode of energy transfer, and emphasized the need for an improved understanding of radiative transfer in these processes (Cowling, 1957; Ferraro & Plumpton, 1961). Cess (1966) investigated the interaction of radiation with laminar free convection heat transfer from a vertical plate for an absorbing emitting liquid in the optically thick region and used the singular perturbation technique. Arpaci (1968) considered a similar problem in both, the optically thin and optically thick regions using the appropriate integral technique. Cheng and Ozisik (1972) investigated an absorbing, emitting and isotropically scattering fluid. Ali et. al. (1984) considered the effects of radiation on natural convective flow of a viscous fluid over a horizontal surface, while Bestman (1985) considered the same problem for the flow of non-Newtonian fluid along a vertical plate under uniform transverse magnetic field. Bestman & Adjepong (1988) also investigated free convection unsteady flow considering radiative heat transfer in a rotating fluid under the influence of uniform magnetic field. Ibrahim (1990) studied mixed convection and radiation interaction for flow of a viscous fluid considering horizontal and vertical surfaces, respectively. Hossain & Takhar (1996) studied the radiation effects on mixed convection along a vertical plate with uniform surface temperature and employed Keller Box finite