# Magneto Hydrodynamics Case Study

The science of magneto hydrodynamics (MHD) deals with geophysical, astrophysical and engineering problems since many years. This subject has attracted attention of many researchers in the MHD flow on Newtonian fluids on plate, cones and disks. Hari R [30] investigated the chemical and radiation effects on MHD casson fluid flow past an oscillating vertical plate embedded in porous medium. Subbaiah Naidu [70] studied the effect of Hall current on free convective flow of stratified fluid over an infinite vertical porous plate. Venkateswarlu M et.al [74] studied the effects of chemical reaction and heat generation on MHD boundary layer flow of a moving vertical plate with suction and dissipation. Ibrahim and Makinde [32] have studied

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Reddy PS and Chamkha AJ [65] studied the Soret and Dufour effects on unsteady MHD heat and mass transfer from a permeable stretching sheet with thermophoresis and non–uniform heat generation/ absorption. Radiation effect on MHD flow past an impulsively started vertical plate with variable heat and mass transfer was studied by Rajput US and Kumar S [58]. Sharma PR et.al [68] studied the heat and mass transfer effects on unsteady MHD free convective flow along a vertical porous plate with internal heat generation and variable suction. Mohammed Ibrahim S et al.[49] discussed Radiation effect on unsteady MHD free mass transfer flow past vertical porous plate embedded in a porous medium with viscous dissipation. Aarti Manglesh and Gorla MG [1] Studied MHD free convective flow through porous medium in the presence of hall current, radiation and thermal diffusion. Sarada S and Shankar B [37] have investigated the effects of Soret and Dufour on an unsteady MHD free convective flow past a vertical porous plate in the presence of suction

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5.1: Physical configuration and coordinate system

The objective of the present chapter is to analyze the Soret and Dufour effects on unsteady MHD flow past an oscillating vertical plate by taking into account of viscous dissipation.

MATHEMATICAL FORMULATION

The plate is taken along upwards direction and is taken normal to the plate. Let be the velocity component of the fluid generated along axis due to the oscillating of the plate. It is assumed that initially the plate and the fluid are at the same temperature and concentration levels are , and time , the plate is oscillated with a velocity , where refers to the velocity and phase angle, in its own plate and the temperature of the plate is increased to as shown in figure 5.1. Then by Boussinesq’s approximation, the governing boundary layer equations are ... 5.1 ... 5.2 ... 5.3

The boundary conditions for the velocity, temperature and concentrations fields are ... 5.4

Invoking Rosseland approximation for radiative heat flux we get ...