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A steady laminar two‐dimensional magneto‐hydrodynamic natural convection flow in an inclined trapezoidal enclosure filled with a fluid‐saturated porous medium is investigated numerically using a finite difference method. The left and right vertical sidewalls of the trapezoidal enclosure are maintained at a cold temperature. The horizontal top wall is considered adiabatic while the bottom wall is subjected to isoflux heating. A volumetric internal heat generation or absorption is embedded inside the trapezoidal enclosure while an external magnetic field is applied on the left sidewall of the enclosure. In the current work, the following parametric ranges of the non‐dimensional groups are used: Hartmann number is varied as $0 \le Ha \le 50$, Darcy number is taken as $Da = 10^{-3}$, 10−4, and 8 × 10−5, Rayleigh number is varied as $10^3 \le Ra \le 10^5$, Prandtl number is considered constant at Pr = 0.7, the dimensionless internal heat generation or absorption parameter is varied as Δ = −0.2, 0, 1, and 2.0, while the trapezoidal enclosure inclination angle is varied as $0^\circ \le \psi \le 90^\circ$. The results indicated a strong flow circulation occurs when the Darcy and the Rayleigh numbers are high. In addition, it is found that the Hartmann number, internal heat generation or absorption parameter and inclination angle have an important role on the flow and thermal characteristics. It is also found that when the enclosure inclination angle and Hartmann number increase the average Nusselt number along the hot bottom wall decreases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21013

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Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross-section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss-Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (10 4 , 10 5 , and 10 6 ), and Darcy number (10 −3 , 10 −4 , and 10 −5 ). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58°a nd 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure. C⃝ -Finite difference method adopting Gauss-Seidel iteration techniques is used to solve this problem.-Average Nusselt Number (Nu a ) for the parametric range 0.6 ≤ e < 1 is mixed convection conduction.-Local Nusselt number (Nu) increased for the parametric range 0.4 ≤ e < 1, that is, 0.4 to 0.8.-Inclination angle increases significantly for the range 58°≤ ∅ ≤ 90°, that is, 58°and 90°i nclination.-Hartmann number effect increasing with decreasing flow circulation (i.e., velocity distribution). Grashof and Darcy numbers effect increasing strongly with increasing flow circulation (velocity distribution) for Grashof number = 10 6 and 10 −4 .

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