<p>This study presents a numerical analysis of thermo-convective flows driven by natural convection and buoyancy forces, using a fluid–structure interaction (FSI) model. The research examines a square cavity containing a flexible, adiabatic, thin membrane that deforms elastically in response to FSI interactions. A heating plate is positioned within the cavity at various angles of inclination, influencing the flow dynamics. The analysis is based on the fundamental principles of fluid mechanics, the heat equation, and the structural dynamic equation, with the system’s interface governed by kinematic and dynamic conditions. The study employs finite volume discretization of the Navier–Stokes equations in the arbitrary Lagrangian–Eulerian (ALE) formulation for fluid flow, while the structural behavior of the membrane is modeled using finite element discretization. This research investigates the effects of varying the heating plate’s inclination angle (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14509_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">$0^{{\text{o}}} \le \phi \le 90^{{\text{o}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>0</mn> <mtext>o</mtext> </msup> <mo>≤</mo> <mi>ϕ</mi> <mo>≤</mo> <msup> <mn>90</mn> <mtext>o</mtext> </msup> </mrow> </math></EquationSource> </InlineEquation>), the Rayleigh number (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14509_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="113" /> </InlineMediaObject> <EquationSource Format="TEX">$10^{5} \le Ra \le 10^{7}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mn>5</mn> </msup> <mo>≤</mo> <mi>R</mi> <mi>a</mi> <mo>≤</mo> <msup> <mn>10</mn> <mn>7</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>), the dimensionless modulus of elasticity (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14509_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="180" /> </InlineMediaObject> <EquationSource Format="TEX">$2 \times 10^{10} \le E_{\tau } \le 5 \times 10^{11}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>10</mn> </msup> <mo>≤</mo> <msub> <mi>E</mi> <mi>τ</mi> </msub> <mo>≤</mo> <mn>5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>11</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>) of the membrane, and magnetic forces (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14509_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">$0 \le Ha \le 80$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>H</mi> <mi>a</mi> <mo>≤</mo> <mn>80</mn> </mrow> </math></EquationSource> </InlineEquation>) on fluid velocity distribution, temperature fields, and membrane deformation.</p>

Numerical study of MHD thermo-convective flows in a square cavity with a deformable wall: effects of heating plate inclination

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发表日期：

2025年7月17日

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Nesrine Abdelli,
Adel Sahi,
Mustapha Benaouicha,
Sylvain Guillou,
Hakan F. Öztop,
Massinissa Adnani,
Djamel Sadaoui

摘要

This study presents a numerical analysis of thermo-convective flows driven by natural convection and buoyancy forces, using a fluid–structure interaction (FSI) model. The research examines a square cavity containing a flexible, adiabatic, thin membrane that deforms elastically in response to FSI interactions. A heating plate is positioned within the cavity at various angles of inclination, influencing the flow dynamics. The analysis is based on the fundamental principles of fluid mechanics, the heat equation, and the structural dynamic equation, with the system’s interface governed by kinematic and dynamic conditions. The study employs finite volume discretization of the Navier–Stokes equations in the arbitrary Lagrangian–Eulerian (ALE) formulation for fluid flow, while the structural behavior of the membrane is modeled using finite element discretization. This research investigates the effects of varying the heating plate’s inclination angle ( $0^{{\text{o}}} \le \phi \le 90^{{\text{o}}}$ $0^{o} \leq ϕ \leq 90^{o}$ ), the Rayleigh number ( $10^{5} \le Ra \le 10^{7}$ $10^{5} \leq R a \leq 10^{7}$ ), the dimensionless modulus of elasticity ( $2 \times 10^{10} \le E_{\tau } \le 5 \times 10^{11}$ $2 \times 10^{10} \leq E_{τ} \leq 5 \times 10^{11}$ ) of the membrane, and magnetic forces ( $0 \le Ha \le 80$ $0 \leq H a \leq 80$ ) on fluid velocity distribution, temperature fields, and membrane deformation.