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<p>The present study investigates the effect of temperature-dependent viscosity and rotation on thermal instability in a dusty ferrofluid layer heated from below, confined by permeable boundaries. The inclusion of more general permeable boundaries introduces a novel aspect to the analysis, given its relevance across various disciplines. Using linear stability theory and normal mode analysis, the eigenvalue problem is derived and solved for both oscillatory and stationary convection modes through the application of single-term Galerkin method. Numerical computations of the threshold convective instability parameters were carried out using MATLAB R2021a, and the results are graphically displayed. The impact of key parameters on the onset of convection is analyzed for different combinations of hydrodynamic boundary conditions, providing significant insights into the stability characteristics of the system. It is found that the parameters related to temperature-dependent viscosity (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>), and rotation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T_a\)</EquationSource> </InlineEquation>) have a stabilizing effect on the system, while magnetic (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(M_1\)</EquationSource> </InlineEquation>) and dust particle (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(h^{\prime }\)</EquationSource> </InlineEquation>) parameters destabilize the system. For lower rotational intensity, the permeability of bounding surfaces facilitates the onset of convection and thus destabilizes the system. However, as the rotation exceeds a critical threshold, the rotation effect becomes more pronounced potentially counteracting the destabilizing effect of bounding permeability. The findings from previous research are obtained as specific cases within the results of the current study.</p>

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On Thermal Instability in a Rotating Dusty Ferrofluid Layer with Temperature-Dependent Viscosity and Permeable Boundaries

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Pankaj Kumar,
  • Awneesh Kumar,
  • Mandeep Kaur

摘要

The present study investigates the effect of temperature-dependent viscosity and rotation on thermal instability in a dusty ferrofluid layer heated from below, confined by permeable boundaries. The inclusion of more general permeable boundaries introduces a novel aspect to the analysis, given its relevance across various disciplines. Using linear stability theory and normal mode analysis, the eigenvalue problem is derived and solved for both oscillatory and stationary convection modes through the application of single-term Galerkin method. Numerical computations of the threshold convective instability parameters were carried out using MATLAB R2021a, and the results are graphically displayed. The impact of key parameters on the onset of convection is analyzed for different combinations of hydrodynamic boundary conditions, providing significant insights into the stability characteristics of the system. It is found that the parameters related to temperature-dependent viscosity ( \(\delta\) ), and rotation ( \(T_a\) ) have a stabilizing effect on the system, while magnetic ( \(M_1\) ) and dust particle ( \(h^{\prime }\) ) parameters destabilize the system. For lower rotational intensity, the permeability of bounding surfaces facilitates the onset of convection and thus destabilizes the system. However, as the rotation exceeds a critical threshold, the rotation effect becomes more pronounced potentially counteracting the destabilizing effect of bounding permeability. The findings from previous research are obtained as specific cases within the results of the current study.