## THERMAL SCIENCE

International Scientific Journal

### COMPUTATIONAL ANALYSIS OF MHD FLOW, HEAT AND MASS TRANSFER IN TRAPEZOIDAL POROUS CAVITY

**ABSTRACT**

Numerical simulations are conducted for two-dimensional steady-state double diffusive flow in a trapezoidal porous cavity, submitted to axial magnetic field. The Darcy equation, including Brinkmamn and Forchheimer terms account for viscous and inertia effects, respectively is used for the momentum equation, and a SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: 103 ≤ Ra ≤ 106,1 ≤ Ha ≤ 102, Da =10-5, N = 1, and Le = 10. It is shown that the application of a transverse magnetic field normal to the flow direction decreases the Nusselt number and Sherwood number. Illustrative graphs are presented.

**KEYWORDS**

PAPER SUBMITTED: 2007-06-28

PAPER REVISED: 2008-06-18

PAPER ACCEPTED: 2008-12-28

**THERMAL SCIENCE** YEAR

**2009**, VOLUME

**13**, ISSUE

**1**, PAGES [13 - 22]

- Trevisan, O., Bejan, A., Natural Convection with Combined Heat and Mass Transfer Effects in a Porous Medium, Int. J. Heat and Mass Transfer, 28 (1985), 8, pp. 1597-1611
- Lage, J. L., Effect of the Convective Inertia Term on Bénard Convection in a Porous Medium, Numerical Heat Transfer, 22 (1992), 4, pp. 469-485
- Agrawal, A. K., Samria, N. K., Gupta, S. N., Combined Buoyancy Effects of Thermal and Mass Diffusion on Hydromagnetic Viscoelastic Natural Convection Flow Past an Accelerated Infinite Plate, J. En. Heat Mass Tran., 20 (1998), 2, pp. 35-42
- Helmy, K. A., MHD Unsteady Free Convection Flow Past a Vertical Porous Plate, ZAMM, 78 (1998), 4, pp. 255-270
- Shanker, B., Kishan, N., The Effects of Mass Transfer on the MHD Flow Past an Impulsively Started Infinite Vertical Plate with Variable Temperature or Constant Heat Flux, J. En. Heat Mass Tran, 19 (1987), 1, pp. 273-278
- Ram, P. C., Takhar, H. S., MHD Free Convection from an Infinite Vertical Plate in a Rotating Fluid with Hall and Ion Slip Currents, Fluid Dyn Res, 11 (1993), 3, pp. 99-105
- Ezzat, M. A., State Space Approach to Unsteady Two-Dimensional Free Convection Flow Through a Porous Medium, Can. J. Phys, 1 (1994), 5-6, pp. 311-317
- Ezzat, M. A., et al., State Space Formulation to Viscoelastic Magnetohydrodynamic Unsteady Free Convection through a Porous Medium, Acta Mech., 119 (1996), 5-6, pp. 147-164
- Ezzat, M. A., Abd-Elaal, M., Free Convection Effects on a Viscoelastic Boundary Layer Flow with One Relaxation Time through a Porous Medium. J. Franklin Inst., 334 (1997), 4, pp. 685-709
- Bian, W., Vasseur, P., Bilgen, E., Meng, F., Effect of Electromagnetic Field on Natural Convection in Inclined Porous Layer, J. Heat Transfer and Fluid Flow, 17 (1996), 1, pp-36-44
- Boussaid, M., Djerrada, A., Bouhadef, M., Thermosolutal Transfer within Trapezoidal Cavity, Numerical Heat Transfer, A 43 (2003), 4, pp. 431-448
- Natarajan, E., Basak, T., Roy, S., Natural Convection Flows in a Trapezoidal Enclosure with Uniform and Non-Uniform Heating of Bottom Wall, International Journal of Heat and Mass Transfer, 51 (2008), 3-4, pp. 747-756
- Baytas, A. C., Pop, I., Natural Convection in a Trapezoidal Enclosure Filled with a Porous Medium, International Journal of Engineering Science, 39 (2001), 2, pp. 125-134
- Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Comp., McGrawHill, New York, USA, 1980
- Lauriat, G., Prasad, V., Non-Darcian Effects on Natural Convection in a Vertical Porous Enclosure, Int. J. Heat and Mass Transfer, 32 (1989), 11, pp. 2135-2148
- Nithiarasu, P., Seetharamu, K. N., Sundararajan, T., Double-Diffusive Natural Convection in an Enclosure Filled with Fluid-Saturated Porous Medium: a Generalized Non-Darcy Approach, Numerical Heat Transfer, Part A, 30 (1996), 4, pp. 413-426
- Ergun, S., Fluid Flow through Packed Columns, Chem. Eng. Progr., 48 (1952), 2, pp. 89-94
- Kimura, S., Bejan, A., The Boundary Layer Natural Convection Regime in a Rectangular Cavity with Uniform Heat Flux From the Side, J. of Heat Transfer, 106 (1984), 1, pp. 98-103