Abstract
The numerical solution of natural convection in unsteady hydromagneticCouette flow of a viscous incompressible electrically conducting fluid between two vertical parallel plates in the presence of thermal radiation is obtained here. The fluid is considered to be a gray, absorbing – emitting but non – scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing coupled, non – linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank – Nicolson method. Computations are performed for a wide range of the governing flow parameters, viz., the thermal Grashof number, SolutalGrashof number, Magnetic field parameter (Hartmann number), Prandtl number, Thermal radiation parameter and Schmidt number. The effects of these flow parameters on the velocity and temperatureare shown graphically. Finally, the effects of various parameters on the on the skin – friction coefficient and Rate of heat and mass transferat the wall are prepared with various values of the parameters.These findings are in quantitative agreement with earlier reported studies.
Highlights
Natural convection flow induced by thermal and solutal buoyancy forces acting over bodies with different geometries in a fluid saturated porous medium is prevalent in many natural phenomena and has varied and wide range of industrial applications
In atmospheric flows, the presence of pure air or water is impossible because some foreign mass may be present either naturally or mixed with air or water due to industrial emissions. Natural processes such as attenuation of toxic waste in water bodies, vaporization of mist and fog, photosynthesis, drying of porous solids, transpiration, sea – wind formation, and formation of ocean currents [1] occur due to thermal and solutal buoyancy forces developed as a result of difference in temperature or concentration or a combination of these two
Comprehensive reviews of natural convection boundary layer flow over various geometrical bodies with heat and mass transfer in porous and nonporous media are well documented by Eckert and Drake [11], Gebhartet al. [12], Nield and Bejan [13], Pop and Ingham [14] and Incroperaet al. [15]
Summary
Natural convection flow induced by thermal and solutal buoyancy forces acting over bodies with different geometries in a fluid saturated porous medium is prevalent in many natural phenomena and has varied and wide range of industrial applications. Analytical solutions are obtainedfor the governing coupled dimensionless partial differential equations ofvelocity and temperature.An unsteady, two – dimensional, hydromagnetic, laminar free convective boundary – layer flow of an incompressible, Newtonian, electrically conducting and radiating fluid past an infinite heated verticalporous plate with heat and mass transfer is analyzed by Ramachandra Prasad and Bhaskar Reddy [27], by takinginto account the effect of viscous dissipation. The objective of the present chapter is to study the radiation, heat and mass transfer effects on an unsteady two – dimensional natural convective Couetteflow of a viscous, incompressible, electrically conducting fluid between two parallel plates with suction, embedded in a porous medium, under the influence of a uniform transverse magnetic field.The problemis described by a system of coupled nonlinear partial differential equations, whose exact solutions are difficult to obtain,whenever possible.
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