MHD natural convection inside an inclined trapezoidal porous enclosure with internal heat generation or absorption subjected to isoflux heating

Abstract

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

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

“…Convergence criteria (10 −6 ) is chosen for all dependable variables and the value of (0.1) is used for the relaxation parameters the approach similar to Ref. [2]. It is found that a grid size (48 × 192) ensured a grid independent solution for the present study as shown in Table 1.…”

“…Governing equations were solved in a generalized orthogonal coordinate system using high-order compact finite difference method. Effects of geometrical parameters such as eccentricity, ratio axis length of elliptic enclosure as well as cylinder were investigated on heat transfer rate at a constant Ra = 100 and hydraulic-radius ratio (2). They concluded that the rate of heat transfer losses could be minimized by a proper choice of the elliptic shape of a concentric annulus which could be further enhanced if the geometry was made eccentric.…”

“…One of the most important phenomenon in a thermal system is free or natural convection, this is due to its wide applications in nature and engineering such as oceanic current, sea-wind, fluid flows around shrouded heat dissipation fins, free air cooling without the aid of fans, electronic cooling, heat exchanger between the soil and atmosphere, high performance insulation for buildings, chemical catalytic reactors, food processing, electrochemistry, metallurgy, grain storage, cooling of radioactive waste containers, solar collector energy, and compacted bed for the chemical industry to mention a few [1,2] So far, many studies in the field of natural convection inside simple enclosures have been performed so that it is a classic problem now. However, the natural convection heat transfer problem inside an enclosure with a nonsimple shape and with different geometry is a topic that has recently received more attention.…”

“…One of the most important phenomenon in a thermal system is free or natural convection, this is due to its wide applications in nature and engineering such as oceanic current, sea‐wind, fluid flows around shrouded heat dissipation fins, free air cooling without the aid of fans, electronic cooling, heat exchanger between the soil and atmosphere, high performance insulation for buildings, chemical catalytic reactors, food processing, electrochemistry, metallurgy, grain storage, cooling of radioactive waste containers, solar collector energy, and compacted bed for the chemical industry to mention a few …”

Numerical analysis of natural convection and entropy generation in a 3D partitioned cavity

“…Oztop et al [6] considered an open porous tilted square and concluded that the inclination angle is the most important control parameter for the evolution of the flow and the convection. Kherief et al [7] considered an inclined rectangular cavity filled with mercury in the presence of a magnetic field which reduce significantly the average Nusselt number, as well as Hussein et al [8] who's considered a range of angles between 0° and 90° to study the magnetohydrodynamic natural convection in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium. Some authors have chosen to add partitions in different position on the cavities; for example, Mamou et al [9] studied the heat transfer for different inclinations and partition's number and thickness.…”