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MATHEMATICAL MODELLING OF BUOYANCY-DRIVEN MAGNETO-CONVECTIVE HEAT AND MASS TRANSFER FROM AN ISOTHERMAL SPHERE IN A NON-DARCY PERMEABLE REGIME WITH THERMOPHYSICAL EFFECTS

Research Authors
V. R. Prasad1, A.Y. Bakier2, O. A. Bég3, and Q. Li4
Research Abstract

The natural convection magneothydrodynamic (MHD) heat and mass transfer in laminar, steady, boundary-layer flow from a permeable isothermal sphere embedded in a non-Darcy porous medium including Soret and Dufour effects is theoretically and numerically studied. The resulting governing equations are non-dimensionalized and transformed into non-similar form and then solved numerically using the extensively validated, robust Sparrow-Quack-Boerner local nonsimilarity method (LNM). Dimensionless velocity (f /), temperature () and concentration () are all increased with distance along the sphere surface from the lower stagnation point ( ~0) but decrease continuously with distance into the boundary layer (i.e. with  coordinate). An increase in Darcy number (Da) increases velocity (f /) but causes a reduction in temperature () and concentration () values throughout the regime normal to the sphere surface i.e. with  coordinate. An increase in Prandtl number (Pr) substantially decreases temperature (). Negative transpiration (injection) i.e. fw < 0 causes an increase in velocity (f /) whereas positive transpiration (suction) i.e. fw > 0, at the sphere surface decelerates the flow i.e. reduces velocity (f/). Increasing Schmidt number (Sc) decreases the concentration () values for all . An increase in the concentration to thermal buoyancy ratio parameter, N, causes a reduction in velocity (f /), temperature () and concentration (). Increasing magnetic parameter (M) strongly decelerates the flow throughout the boundary layer. Increasing Dufour number (Du) and simultaneously decreasing Soret number (Sr) significantly increases temperature (), although no temperature overshoot is identified. An increase in Soret number (Sr) and simultaneous decrease in Dufour number (Du) induces a strong rise in concentration value (); for Sr > 1 a significant concentration overshoot occurs near the sphere surface. Increasing Forchheimer inertial drag parameter () reduces flow velocity (f /) but increases temperature () throughout the regime. Applications of the study include magnetic materials processing and electromagnetic control of waste migration.

Research Department
Research Journal
Int. J. of Appl. Math and Mech.
Research Rank
1
Research Vol
6 (5):
Research Year
2010
Research Pages
80-98,