Abstract

The natural convection and entropy generation during double-diffusive MHD natural convection in a tilted sinusoidal corrugated porous enclosure is investigated numerically in this work by using heatline visualization technique. The top and bottom horizontal walls are assumed as adiabatic and non-diffusive, while the left and right vertical corrugated sidewalls are maintained at a constant hot and cold temperatures and concentrations respectively. The flow in the enclosure is subjected to an inclined magnetic field. The enclosure is filled with an electrically conducting fluid [Pr = 0.024] saturated with a porous media. The numerical computations are presented for various values of Rayleigh number (Ra), Hartmann number (Ha), Lewis number (Le), Darcy number (Da), buoyancy ratio (N), magnetic field orientation angle (φ) and enclosure inclination angle (Φ). In addition, the entropy generation due to fluid friction, thermal gradients, diffusion, and magnetic field beside the total entropy generation are studied and discussed. It is found that the flow circulation decreases strongly when the magnetic field applied horizontally and the enclosure is considered vertical. Heatline visualization concept is successfully applied to the considered problem. The average Nusselt number decreases when the Lewis number increases, while the average Sherwood number increases when the Lewis number increases. Also, both average Nusselt and Sherwood numbers increase when the Darcy number and buoyancy ratio increase. Moreover, the results show that the entropy generations due to magnetic field when the enclosure is subjected to the horizontal magnetic field are higher than the corresponding values when it subjected to the vertical magnetic field.

Abstract

This paper presents unsteady numerical results of double diffusive mixed convection flow in a trapezoidal enclosure with the uniform magnetic field effect applied in negative horizontal direction. At the bottom wall, the uniform and non-uniform heat and mass are applied while the heat and mass absorbed uniformly at the top wall. Other side walls are impermeable and adiabatic. The top wall moves along x-axis direction with a constant velocity. The transport phenomenon of this problem can be expressed by the coupled governing equation derived from the conservation of mass and momentum along with the energy equation for temperature and concentration. The finite element method (FEM) based on Galerkin weighted residual technique is used to compute the numerical result from these governing equations. The numerical computation is carried out for Lewis number (Le = 0.1–50) and Richardson’s number (Ri = 0.1–100). Computed numerical results of mass, temperature and velocity distribution are expressed graphically as iso-concentration lines, isotherm lines and streamlines respectively. Average Sherwood and Nusselt number values are used to show the mass and heat transfer rate from the heated and concentrated surface of the enclosure. It is found from the analysis that mass transfer strongly depends on Lewis number. Heat and mass transfer for uniformly heated and concentrated bottom wall is larger than the non-uniformly heated and concentrated bottom wall. Finally, a correlation has been done for average Nusselt and Sherwood numbers for both of the cases.

Abstract

A numerical work has been carried out to study the effects of magnetic field on double diffusive natural convection in a trapezoidal enclosure. Both inclined walls and bottom wall were kept at constant temperature and concentration where the bottom wall temperature and concentration are higher than those of the inclined walls. Top wall of the cavity is adiabatic and impermeable. The trapezoidal enclosure is subjected to a horizontal magnetic field. To investigate the effects, finite volume method is used to solve the governing equations for different parameters such as Grashof number, inclination angle of inclined wall of the enclosure, Hartmann number and buoyancy ratio. The numerical results are reported for the effect of studied parameters on the contours of streamline, temperature, and concentration. In addition, results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study is done for constant Prandtl number, Pr = 0.7, aspect ratio = 1 and Lewis number, Le = 2. The studied range of Grashof number is from Gr = 103 to 106, inclination angle from 0° to 75°, Hartmann number from 0 to 15 and buoyancy ratio from −2 to 2 which covers the double diffusive range in the cases of aiding and opposing flows. It is found that heat and mass transfer decreased as φ increases from 0° to 75°. Also heat and mass transfer decreased as Hartman number increased from 0 to 15. Finally, the predicted results for both average Nusselt and Sherwood numbers were correlated in terms of the studied parameters.