<p>This study numerically investigates magnetohydrodynamic buoyancy-driven convection in a porous wavy-walled square cavity filled with air and subjected to a partially applied magnetic field. Such a configuration is of interest for thermal-flow regulation and heat-transfer control in engineering systems involving porous structures and selectively magnetically controlled enclosures. The novelty of the present work lies in examining buoyancy-driven convection in a porous wavy-walled square cavity under a partially applied magnetic field, with particular emphasis on the coupled roles of localized magnetic damping, porous-medium resistance, and wall waviness in governing the flow and heat-transfer characteristics. The flow in the porous medium is described by the Brinkman–Forchheimer extended Darcy model, and the governing equations are solved using a meshless radial basis function-generated finite difference (RBF-FD) method with backward Euler time discretization. Simulations are performed for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ra = 10^4\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10^5\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(10^6\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Ha = 0\)</EquationSource> </InlineEquation>, 50, and 100, magnetic-field lengths of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(H_B = 0.3\)</EquationSource> </InlineEquation>, 0.5, and 0.7, Darcy numbers of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(Da = 10^{-4}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(10^{-3}\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(10^{-2}\)</EquationSource> </InlineEquation>, wave numbers of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(N = 0\)</EquationSource> </InlineEquation>, 1, 2, and 3, and wave amplitudes of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(A = 0\)</EquationSource> </InlineEquation>, 0.1, 0.2, and 0.3. The effects of these parameters are analyzed through isotherms, streamlines, centerline velocity and temperature profiles, and the average Nusselt number along the heated wall. The results show that increasing the Rayleigh number significantly intensifies buoyancy-driven circulation and enhances heat transfer, leading to a <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(349.01\%\)</EquationSource> </InlineEquation> increase in the average Nusselt number as <i>Ra</i> rises from <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(10^4\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(10^6\)</EquationSource> </InlineEquation>. In contrast, increasing the Hartmann number from 0 to 100 suppresses convection and reduces the average Nusselt number by <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(34.37\%\)</EquationSource> </InlineEquation>, while extending the magnetic-field length from 0.3 to 0.7 causes a further decrease of <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(30.08\%\)</EquationSource> </InlineEquation>. Increasing the Darcy number markedly enhances thermal transport, yielding a <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(140.89\%\)</EquationSource> </InlineEquation> increase in the average Nusselt number, whereas stronger wall waviness weakens convection: increasing the wave number reduces the average Nusselt number by <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(25.66\%\)</EquationSource> </InlineEquation>, and increasing the wave amplitude from 0 to 0.3 results in a <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(61.24\%\)</EquationSource> </InlineEquation> decrease. These findings provide useful physical insight and practical guidance for the design and optimization of heat-transfer systems involving porous media and partially magnetically controlled flows.</p>

Numerical modeling of buoyancy-driven convection in a porous wavy-walled square cavity under a partially applied magnetic field using a meshless RBF-FD method

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发表日期：

2026年4月17日

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Youssef Es-Sabry,
Mouad Benaicha,
Nabil Ammari,
Elmiloud Chaabelasri

摘要

This study numerically investigates magnetohydrodynamic buoyancy-driven convection in a porous wavy-walled square cavity filled with air and subjected to a partially applied magnetic field. Such a configuration is of interest for thermal-flow regulation and heat-transfer control in engineering systems involving porous structures and selectively magnetically controlled enclosures. The novelty of the present work lies in examining buoyancy-driven convection in a porous wavy-walled square cavity under a partially applied magnetic field, with particular emphasis on the coupled roles of localized magnetic damping, porous-medium resistance, and wall waviness in governing the flow and heat-transfer characteristics. The flow in the porous medium is described by the Brinkman–Forchheimer extended Darcy model, and the governing equations are solved using a meshless radial basis function-generated finite difference (RBF-FD) method with backward Euler time discretization. Simulations are performed for \(Ra = 10^4\) , \(10^5\) , and \(10^6\) , \(Ha = 0\) , 50, and 100, magnetic-field lengths of \(H_B = 0.3\) , 0.5, and 0.7, Darcy numbers of \(Da = 10^{-4}\) , \(10^{-3}\) , and \(10^{-2}\) , wave numbers of \(N = 0\) , 1, 2, and 3, and wave amplitudes of \(A = 0\) , 0.1, 0.2, and 0.3. The effects of these parameters are analyzed through isotherms, streamlines, centerline velocity and temperature profiles, and the average Nusselt number along the heated wall. The results show that increasing the Rayleigh number significantly intensifies buoyancy-driven circulation and enhances heat transfer, leading to a \(349.01\%\) increase in the average Nusselt number as Ra rises from \(10^4\) to \(10^6\) . In contrast, increasing the Hartmann number from 0 to 100 suppresses convection and reduces the average Nusselt number by \(34.37\%\) , while extending the magnetic-field length from 0.3 to 0.7 causes a further decrease of \(30.08\%\) . Increasing the Darcy number markedly enhances thermal transport, yielding a \(140.89\%\) increase in the average Nusselt number, whereas stronger wall waviness weakens convection: increasing the wave number reduces the average Nusselt number by \(25.66\%\) , and increasing the wave amplitude from 0 to 0.3 results in a \(61.24\%\) decrease. These findings provide useful physical insight and practical guidance for the design and optimization of heat-transfer systems involving porous media and partially magnetically controlled flows.