<p>This study investigates the effect of temperature-dependent viscosity on the onset of magnetohydrodynamic (MHD) instability in a non-Newtonian Navier–Stokes–Voigt (NSV) fluid, which has not been addressed in the existing literature. The threshold of the convective instability is determined using the linear stability theory and the resulting eigenvalue problem is solved analytically as well as numerically using the Galerkin procedure. It is observed that the overstability mode of convection occurs only within a specific range of the magnetic Prandtl number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$P_{rm}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mrow> <mi mathvariant="italic">rm</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. The threshold range of the magnetic Prandtl number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$P_{rm}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mrow> <mi mathvariant="italic">rm</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> at which overstability mode of convection likely enhances with increasing the magnetic Chandrasekhar number <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Q_{M}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mi>M</mi> </msub> </math></EquationSource> </InlineEquation> and the Prandtl number <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$P_{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> while, it declines with increasing the Kelvin–Voigt factor <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda$</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. The stabilizing parameters are the magnetic Chandrasekhar number <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Q_{M}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mi>M</mi> </msub> </math></EquationSource> </InlineEquation>, Kelvin–Voigt factor <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda$</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>, and magnetic Prandtl number <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$P_{rm}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mrow> <mi mathvariant="italic">rm</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, which enhance system stability. In contrast, the destabilizing parameters are the viscosity variation parameter <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$F$</EquationSource> <EquationSource Format="MATHML"><math> <mi>F</mi> </math></EquationSource> </InlineEquation> and the Prandtl number <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_1073_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$P_{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, both of which reduce stability. Additionally, several existing results are recovered as limiting cases of this study, which validates the analysis and broadens its applicability.</p>

Influence of temperature reliant viscosity on the magnetohydrodynamic instability in a Navier–Stokes–Voigt fluid

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发表日期：

2025年10月29日

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A. M. Mohamad,
Dhananjay Yadav,
Mukesh Kumar Awasthi,
Ravi Ragoju,
Amit Mahajan,
Mohammad Hassan

摘要

This study investigates the effect of temperature-dependent viscosity on the onset of magnetohydrodynamic (MHD) instability in a non-Newtonian Navier–Stokes–Voigt (NSV) fluid, which has not been addressed in the existing literature. The threshold of the convective instability is determined using the linear stability theory and the resulting eigenvalue problem is solved analytically as well as numerically using the Galerkin procedure. It is observed that the overstability mode of convection occurs only within a specific range of the magnetic Prandtl number $P_{rm}$ $P_{rm}$ . The threshold range of the magnetic Prandtl number $P_{rm}$ $P_{rm}$ at which overstability mode of convection likely enhances with increasing the magnetic Chandrasekhar number $Q_{M}$ $Q_{M}$ and the Prandtl number $P_{r}$ $P_{r}$ while, it declines with increasing the Kelvin–Voigt factor $\lambda$ $λ$ . The stabilizing parameters are the magnetic Chandrasekhar number $Q_{M}$ $Q_{M}$ , Kelvin–Voigt factor $\lambda$ $λ$ , and magnetic Prandtl number $P_{rm}$ $P_{rm}$ , which enhance system stability. In contrast, the destabilizing parameters are the viscosity variation parameter $F$ $F$ and the Prandtl number $P_{r}$ $P_{r}$ , both of which reduce stability. Additionally, several existing results are recovered as limiting cases of this study, which validates the analysis and broadens its applicability.