<p>This study investigates thermosolutal convection of a Casson-based ternary hybrid nanofluid within an inverted wavy T-shaped cavity—a complex geometry relevant for advanced thermal management systems. The problem addresses the challenge of accurately modeling buoyancy-driven flow in porous, radiative environments using non-Newtonian hybrid nanofluids, which are increasingly important in energy and electronics cooling applications. A higher-order compact (HOC) numerical scheme is employed to discretize the governing equations, enabling precise resolution of sharp gradients in flow and temperature fields. The model incorporates the effects of porous media (via the Darcy–Brinkman formulation) and thermal radiation, offering a comprehensive analysis of system performance. Key dimensionless parameters, including the Darcy number (Da), Rayleigh number (Ra), Lewis number (Le), Casson fluid parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\gamma$</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>), and wall undulation amplitude (<i>d</i>), are systematically varied. Quantitative findings highlight significant enhancement in transport performance: increasing Da from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$10^{-4}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$10^{-2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> raises the average Nusselt number (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Nu}}_{\text{avg}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Nu</mtext> <mtext>avg</mtext> </msub> </math></EquationSource> </InlineEquation>) by 42.8% and the average Sherwood number (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Sh}}_{\text{avg}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Sh</mtext> <mtext>avg</mtext> </msub> </math></EquationSource> </InlineEquation>) by 48.9% at <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$\gamma = 10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation>. Similarly, increasing Ra from <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$10^4$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$10^6$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>6</mn> </msup> </math></EquationSource> </InlineEquation> boosts <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Nu}}_{\text{avg}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Nu</mtext> <mtext>avg</mtext> </msub> </math></EquationSource> </InlineEquation> by 71.5% and <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Sh}}_{\text{avg}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Sh</mtext> <mtext>avg</mtext> </msub> </math></EquationSource> </InlineEquation> by 120.1% at <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq11.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$d=2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The Casson parameter exhibits a strong non-Newtonian influence, with kinetic energy (KE) rising by 1,240% as <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\gamma$</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> increases to 10 for <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14536_Article_IEq13.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Ra}} = 10^4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Ra</mtext> <mo>=</mo> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. This work is novel in applying the HOC method to a non-Newtonian ternary hybrid nanofluid in a complicated cavity, capturing complex thermofluid dynamics that are often overlooked in earlier studies. The insights gained provide a novel framework for designing high-performance systems where convective heat and mass transfer must be precisely controlled in irregular domains.</p>

Thermosolutal convection of non-Newtonian ternary hybrid nanoliquid inside an inverted wavy T-shaped cavity

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发表日期：

2025年7月29日

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Samrat Hansda,
Anirban Chattopadhyay

摘要

This study investigates thermosolutal convection of a Casson-based ternary hybrid nanofluid within an inverted wavy T-shaped cavity—a complex geometry relevant for advanced thermal management systems. The problem addresses the challenge of accurately modeling buoyancy-driven flow in porous, radiative environments using non-Newtonian hybrid nanofluids, which are increasingly important in energy and electronics cooling applications. A higher-order compact (HOC) numerical scheme is employed to discretize the governing equations, enabling precise resolution of sharp gradients in flow and temperature fields. The model incorporates the effects of porous media (via the Darcy–Brinkman formulation) and thermal radiation, offering a comprehensive analysis of system performance. Key dimensionless parameters, including the Darcy number (Da), Rayleigh number (Ra), Lewis number (Le), Casson fluid parameter ( $\gamma$ $γ$ ), and wall undulation amplitude (d), are systematically varied. Quantitative findings highlight significant enhancement in transport performance: increasing Da from $10^{-4}$ $10^{- 4}$ to $10^{-2}$ $10^{- 2}$ raises the average Nusselt number ( ${\text{Nu}}_{\text{avg}}$ ${Nu}_{avg}$ ) by 42.8% and the average Sherwood number ( ${\text{Sh}}_{\text{avg}}$ ${Sh}_{avg}$ ) by 48.9% at $\gamma = 10$ $γ = 10$ . Similarly, increasing Ra from $10^4$ $10^{4}$ to $10^6$ $10^{6}$ boosts ${\text{Nu}}_{\text{avg}}$ ${Nu}_{avg}$ by 71.5% and ${\text{Sh}}_{\text{avg}}$ ${Sh}_{avg}$ by 120.1% at $d=2$ $d = 2$ . The Casson parameter exhibits a strong non-Newtonian influence, with kinetic energy (KE) rising by 1,240% as $\gamma$ $γ$ increases to 10 for ${\text{Ra}} = 10^4$ $Ra = 10^{4}$ . This work is novel in applying the HOC method to a non-Newtonian ternary hybrid nanofluid in a complicated cavity, capturing complex thermofluid dynamics that are often overlooked in earlier studies. The insights gained provide a novel framework for designing high-performance systems where convective heat and mass transfer must be precisely controlled in irregular domains.