<p>This study presents a numerical investigation of magnetohydrodynamic natural convection in a tilted wavy right-angled triangular cavity filled with a Cu–water nanofluid. The bottom wall is heated by a sinusoidal temperature distribution, the inclined wall is adiabatic, and the vertical corrugated wall is maintained at a lower temperature. The problem is relevant to thermal-management systems in which cavity geometry, nanoparticle loading, and magnetic control jointly influence heat-transfer performance. The originality of the work lies in the coupled analysis of cavity waviness, cavity inclination, magnetic-field orientation, and nanoparticle concentration in this configuration using a meshless radial basis function-generated finite-difference (RBF-FD) method combined with an implicit backward Euler time-marching scheme. The numerical model was validated against benchmark results from the literature and showed good agreement. The effects of the Rayleigh number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((10^4 \le Ra \le 10^7)\)</EquationSource> </InlineEquation>, Hartmann number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((0 \le Ha \le 60)\)</EquationSource> </InlineEquation>, nanoparticle volume fraction <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((0 \le \phi \le 0.1)\)</EquationSource> </InlineEquation>, wave number <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((0 \le N \le 3)\)</EquationSource> </InlineEquation>, wave amplitude <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((0 \le A \le 0.05)\)</EquationSource> </InlineEquation>, cavity inclination angle <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\((0^\circ \le \gamma \le 135^\circ )\)</EquationSource> </InlineEquation>, and magnetic-field orientation <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\((0^\circ \le \alpha \le 135^\circ )\)</EquationSource> </InlineEquation> were examined through streamline patterns, isotherms, and local and average Nusselt numbers. The results show that increasing <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(Ra\)</EquationSource> </InlineEquation> strengthens buoyancy-driven circulation and enhances heat transfer, whereas increasing <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(Ha\)</EquationSource> </InlineEquation> suppresses convection through Lorentz-force damping. Increasing the nanoparticle volume fraction improves thermal performance for all Rayleigh numbers; for example, when <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\phi \)</EquationSource> </InlineEquation> increases from 0 to 0.1, the average Nusselt number rises from 1.447 to 1.865 at <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(Ra=10^4\)</EquationSource> </InlineEquation>, and from 10.311 to 11.705 at <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(Ra=10^7\)</EquationSource> </InlineEquation>. Larger wave number and wave amplitude also improve heat-transfer performance, with the strongest enhancement obtained for <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(N=3\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(A=0.05\)</EquationSource> </InlineEquation>. In addition, cavity inclination and magnetic-field orientation exhibit non-monotonic effects due to the changing alignment between buoyancy and Lorentz forces. These findings provide useful guidance for the design and optimization of nanofluid-based thermal systems under magnetic control.</p>

Magnetohydrodynamic Natural Convection of Cu-Water Nanofluid in a Tilted Wavy Right-Angled Triangular Cavity: Numerical Study using Meshless RBF-FD Method

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发表日期：

2026年6月23日

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

摘要

This study presents a numerical investigation of magnetohydrodynamic natural convection in a tilted wavy right-angled triangular cavity filled with a Cu–water nanofluid. The bottom wall is heated by a sinusoidal temperature distribution, the inclined wall is adiabatic, and the vertical corrugated wall is maintained at a lower temperature. The problem is relevant to thermal-management systems in which cavity geometry, nanoparticle loading, and magnetic control jointly influence heat-transfer performance. The originality of the work lies in the coupled analysis of cavity waviness, cavity inclination, magnetic-field orientation, and nanoparticle concentration in this configuration using a meshless radial basis function-generated finite-difference (RBF-FD) method combined with an implicit backward Euler time-marching scheme. The numerical model was validated against benchmark results from the literature and showed good agreement. The effects of the Rayleigh number \((10^4 \le Ra \le 10^7)\) , Hartmann number \((0 \le Ha \le 60)\) , nanoparticle volume fraction \((0 \le \phi \le 0.1)\) , wave number \((0 \le N \le 3)\) , wave amplitude \((0 \le A \le 0.05)\) , cavity inclination angle \((0^\circ \le \gamma \le 135^\circ )\) , and magnetic-field orientation \((0^\circ \le \alpha \le 135^\circ )\) were examined through streamline patterns, isotherms, and local and average Nusselt numbers. The results show that increasing \(Ra\) strengthens buoyancy-driven circulation and enhances heat transfer, whereas increasing \(Ha\) suppresses convection through Lorentz-force damping. Increasing the nanoparticle volume fraction improves thermal performance for all Rayleigh numbers; for example, when \(\phi \) increases from 0 to 0.1, the average Nusselt number rises from 1.447 to 1.865 at \(Ra=10^4\) , and from 10.311 to 11.705 at \(Ra=10^7\) . Larger wave number and wave amplitude also improve heat-transfer performance, with the strongest enhancement obtained for \(N=3\) and \(A=0.05\) . In addition, cavity inclination and magnetic-field orientation exhibit non-monotonic effects due to the changing alignment between buoyancy and Lorentz forces. These findings provide useful guidance for the design and optimization of nanofluid-based thermal systems under magnetic control.