<p>This study examines the onset of thermal instability in a horizontal ferrofluid layer saturating a Darcy–Brinkman porous medium. The ferrofluid layer is confined between fluid-permeable, magnetically responsive boundaries and subjected to a uniform vertical magnetic field. A novel aspect of this work is the explicit incorporation of magnetically permeable boundary conditions along with magnetic-field-dependent (MFD) viscosity and porous resistance, enabling effective control of ferrofluid convection. A linear stability analysis based on the normal mode approach is employed to derive the associated eigenvalue problem, and the validity of the principle of exchange of stability is established. The critical Rayleigh number is then obtained using a single-term Galerkin method. The analysis revealed that an increase in MFD viscosity and magnetic susceptibility delays the onset of convection, whereas higher values of the magnetic buoyancy parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ (M_1) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and medium permeability <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ (k_0) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> promote instability. The nonlinear magnetization parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$(M_3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> exhibits a dual influence, acting as a destabilizing factor for weak viscosity variation but contributing to stabilization as magnetic effects on viscosity become stronger. A transition in the nature of magnetically permeable boundaries from free to rigid significantly enhances system stability, with the rigid–rigid configuration being the most stable. The influence of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$M_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$M_3$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> on the characteristic size of convection cells is also examined. The study provides useful physical insight into the control of ferrofluid convection with relevance to thermal management applications.</p>

Convective instability in a ferrofluid-saturated Darcy–Brinkman porous layer with magnetic-field-dependent viscosity and permeable magnetic boundaries

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发表日期：

2026年4月28日

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Pankaj Kumar,
Abhishek Thakur,
Awneesh Kumar

摘要

This study examines the onset of thermal instability in a horizontal ferrofluid layer saturating a Darcy–Brinkman porous medium. The ferrofluid layer is confined between fluid-permeable, magnetically responsive boundaries and subjected to a uniform vertical magnetic field. A novel aspect of this work is the explicit incorporation of magnetically permeable boundary conditions along with magnetic-field-dependent (MFD) viscosity and porous resistance, enabling effective control of ferrofluid convection. A linear stability analysis based on the normal mode approach is employed to derive the associated eigenvalue problem, and the validity of the principle of exchange of stability is established. The critical Rayleigh number is then obtained using a single-term Galerkin method. The analysis revealed that an increase in MFD viscosity and magnetic susceptibility delays the onset of convection, whereas higher values of the magnetic buoyancy parameter $ (M_1) $ $(M_{1})$ and medium permeability $ (k_0) $ $(k_{0})$ promote instability. The nonlinear magnetization parameter $(M_3)$ $(M_{3})$ exhibits a dual influence, acting as a destabilizing factor for weak viscosity variation but contributing to stabilization as magnetic effects on viscosity become stronger. A transition in the nature of magnetically permeable boundaries from free to rigid significantly enhances system stability, with the rigid–rigid configuration being the most stable. The influence of $M_1$ $M_{1}$ and $M_3$ $M_{3}$ on the characteristic size of convection cells is also examined. The study provides useful physical insight into the control of ferrofluid convection with relevance to thermal management applications.