Entropy Generation in Heat and Mass Transfer in Porous Cavity Subjected to a Magnetic Field

Numerical investigation is carried out to predict the entropy generation for combined natural convection heat and mass transfer in a two dimensional porous cavity subjected to a magnetic field. The Darcy model is used in the mathematical formulation of the flow in porous media. The mathematical model is derived in dimensionless form. The governing parameters arise in the mathematical model are the Rayleigh number, Lewis number, buoyancy ratio and Hartmann number. The entropy generation is obtained as a function of velocity, temperature, concentration gradients and the physical properties of the fluid. The results are presented as average Nusselt number, Sherwood numbers and dimensionless form of local entropy generation rate for different values of the governing parameters.The numerical results show that increasing the magnetic field parameter (Hartmann number) leads to reduce the flow circulation strength in the cavity and this leads to a decrease in the rate of entropy generation. INTRODUCTION The natural convection in porous media has been studied and analysed widely in recent years. This interest was estimated due to many applications in, for example, packed sphere beds, high performance insulation for buildings, chemical catalytic reactors, to name of a few. Representative studies in this area may be found in the books by Kaviany [1], Nield and Bejan [2] and Ingham and Pop [3]. Double-diffusive convection in porous media concerns the processes of combined (simultaneous) heat and mass transfer which are driven by buoyancy forces. The buoyancy force not only affected by the difference of temperature, but also affected by the difference of concentration in the fluid. A detailed review of double-diffusive natural convection in porous media can be found in Mojtabi and Mojtabi [4]. Natural convection in a cavity saturated with porous media in the presence of magnetic a field is relatively a new topic and needs more investigation. The heat, mass and fluid flow can be described by means of the hydrodynamics, the convective heat and mass transfer mechanism and the electromagnetic field as they are linked together. In such cases, the fluid experiences a Lorentz force, which tends to oppose the fluid flow and hence reduce the flow velocities [5-6]. The irreversibility phenomena which are expressed by entropy generation are of important interest during the design of any thermodynamic system. Many studies concerning entropy generation in natural convection in porous media have been carried out [6-8]. However, the entropy generation during the double diffusive convection in enclosed cavities submitted to a magnetic field has not received much attention. The aim of this paper is to study numerically the problem of entropy generation in heat and mass transfer in square porous cavity filled with electrically conducting fluid and subjected to a magnetic field. A schematic diagram of the porous cavity and coordinate system is shown in Figure 1. Horizontal temperature and concentration differences are specified between the vertical walls and zero mass and heat fluxes are imposed at the horizontal walls.