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Academic Paper from the year 2019 in the subject Mathematics - Applied Mathematics, grade: A, Jawaharlal Nehru University (Madanapalle Institute of Science and Technology), course: Mathematics, language: English, abstract: In this thesis, MHD free convective heat and mass transfer flow of some Newtonian and non-Newtonian fluids through a porous medium has been investigated theoretically, to examine the various physical properties of the flow. The governing equations pertaining to the fluid flow are converted into a set of partial differential equations in non-dimensional form and then solved analytically and numerically, by applying various methods such as perturbation method, Laplace transform technique. The physical parameters namely magnetic parameter or Hartmann number, thermal radiation parameter, Grashof number or thermal buoyancy parameter, solutal Grashof number or mass buoyancy parameter, porosity parameter, time, Prandtl number, Hall parameter, radiation absorption parameter, Schmidt number, Soret number, chemical reaction parameter, heat source/sink parameter are considered for the study. The variations in velocity, temperature and concentration under the effect of these rheological parameters have been studied and discussed with the help of graphs and tables. Also, the influences of some important parameters on Nusselt number, Sherwood number and skin friction are analyzed. The basic concepts of MHD, heat and mass transfer along with governing equations associated with energy, conservation of momentum, conservation of mass and molecular diffusion are presented in the chapter First. This chapter also explains fundamental concepts and their importance such as viscosity, pressure, density, heat absorption/generation, Hall current effect, porous medium, boundary layer theory, etc. The parameters like magnetic parameter, Grashof number, Prandtl number, Schmidt number, Nusselt number and Sherwood number are also elucidated. The second chapter presents the literature survey which consists of the contributions of several researchers in this area and also the studies related to MHD, free convection, visco-elastic boundary layer, heat and mass transfer flows, the literature survey on the study of non-Newtonian fluids such as Second grade fluid and Micro polar fluid is performed. In the chapter Three, a systematic study has been conducted on the unsteady MHD natural convective rotating flow of an electrically conducting, viscous, incompressible and optically thick radiating second grade fluid past an impulsively moving vertical plate entrenched in a fluid inundated the porous medium, while temperature of the plate has a temporarily ramped profile.