Magneto hydrodynamic flow with viscous dissipation effects in the presence of suction and injection

Abstract

Gyarmati's variational principle developed on the thermodynamic theory of irreversible pro- cesses is employed to study the viscous dissipation effects with uniform suction and injection on the infinite flat plate. The velocity and temperature fields inside the boundary layer are approximated as simple polynomial functions, and the functional of the variational principle is constructed. The Euler Lagrange equations are reduced to simple polynomial equations in terms of velocity and thermal boundary layer thicknesses. The velocity, temperature pro- files, skin friction and heat transfer with the viscous dissipation effects are analyzed and are compared with known numerical solutions. The comparison of the present solution with the existing solutions establishes the fact that the accuracy is remarkable. The prime objective of this investigation is to study the effects of viscous dissipation on the magneto hydrodynamic flow over a semi infinite flat plate with uniform suction and injection by using some recent developments in the field of thermodynamics of irreversible processes and to obtain numerical solution to the boundary layer flow and heat transfer with the help of a variational technique based on the governing principle of dissipative processes. According to the boundary layer theory, the irreversible processes of momentum and heat transfer in flows around bodies occur mainly inside a very thin layer adjacent to the surface of the body. Hence, it is quite appropriate to study these non equilibrium processes by a variational technique developed in the field of irreversible thermodynamics. The boundary layer flow of an incompressible electrically conducting fluid past a semi infinite flat plate in the presence of a transverse magnetic field has been studied recently by many rese- archers. The boundary layer solution for the magneto hydrodynamic flow over a semi infinite flat plate in the presence of transverse magnetic field was studied by Watanabe (1978, 1986) and Wa- tanabe and Pop (1994) by means of a difference-differential method. The analysis on stagnation point flow and asymmetric flow was investigated by Sparrow et al. (1963), Ariel (1994), Raptis (1991) and Chamkha (1998). Watanabe (1986) analyzed the magneto hydrodynamic boundary layer flow over a wedge and did not considered the energy equation. Hossain (1992) treated the viscous and Joule heating effects on magneto hydrodynamic free convection boundary layer flow with variable temperature on the plate. Watanabe and Pop (1993) solved the problem of ma- gneto hydrodynamic free convection flow over a wedge in the presence of a transverse magnetic field. Soundalgekar and Takhar (1977) considered the boundary layer equations for the aligned flow and temperature of an electrically conducting fluid past a semi infinite heated flat plate in the presence of a transverse magnetic field.