<p>This study inspects the influences of the Cattaneo–Christov flux model on the flow of Casson nanofluid on a heated, dual-directional elongating surface. It considers the effects of space and temperature-based heat sources. The study also investigates how variable porous effects on the sheet affect fluid momentum by altering the inter-spacing and radius of nanoparticles. The leading equations have been changed to dimension-free notation and then have been solved through bvp4c technique. The outcome of this work has revealed that for an upsurge in the inclination angle of the magnetic field with flow system, variable porous factor, and magnetic factor, there is a decline in all velocities for small and large sizes of nanoparticles inter-spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="106" /> </InlineMediaObject> <EquationSource Format="TEX">$h = 5/2\,\,\& \,\,7/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo>=</mo> <mn>5</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mspace width="0.166667em" /> <mspace width="0.166667em" /> <mo>&</mo> <mspace width="0.166667em" /> <mspace width="0.166667em" /> <mn>7</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and their radius say <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="117" /> </InlineMediaObject> <EquationSource Format="TEX">$Rp = 3/2\,\,\& \,\,5/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>p</mi> <mo>=</mo> <mn>3</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mspace width="0.166667em" /> <mspace width="0.166667em" /> <mo>&</mo> <mspace width="0.166667em" /> <mspace width="0.166667em" /> <mn>5</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Thermal distribution has augmented for escalation in radiation factor, thermophoresis, Brownian motion factors, and space/thermal-dependent heat source factors. These findings help in optimizing cooling systems in electronics, aerospace, and nuclear reactors. It enhances heat transfer in solar energy, medical treatments, and industrial processes, leading to better performance, energy savings, and enhanced material durability. The skin frictions <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{\text{fx}} Re_{\text{x}}^{1/2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mtext>fx</mtext> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mrow> <mtext>x</mtext> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq4.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{\text{fy}} Re_{\text{y}}^{1/2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mtext>fy</mtext> </msub> <mi>R</mi> <msubsup> <mi>e</mi> <mrow> <mtext>y</mtext> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation> have retarded more significantly for large inter-particle space and radius say <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$h = 7/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo>=</mo> <mn>7</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14304_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">$Rp = 5/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>p</mi> <mo>=</mo> <mn>5</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The comparison of current results with published work reveals a close alignment between our findings and the previously published dataset.</p>

Impact of nanoparticle radius and inter-particle space on nanofluid flow on an extending surface: CCHF model with variable heat sources

期刊论文
发表日期：

2025年5月31日

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Humaira Yasmin

摘要

This study inspects the influences of the Cattaneo–Christov flux model on the flow of Casson nanofluid on a heated, dual-directional elongating surface. It considers the effects of space and temperature-based heat sources. The study also investigates how variable porous effects on the sheet affect fluid momentum by altering the inter-spacing and radius of nanoparticles. The leading equations have been changed to dimension-free notation and then have been solved through bvp4c technique. The outcome of this work has revealed that for an upsurge in the inclination angle of the magnetic field with flow system, variable porous factor, and magnetic factor, there is a decline in all velocities for small and large sizes of nanoparticles inter-spaces $h = 5/2\,\,\& \,\,7/2$ $h = 5 / 2 & 7 / 2$ and their radius say $Rp = 3/2\,\,\& \,\,5/2$ $R p = 3 / 2 & 5 / 2$ . Thermal distribution has augmented for escalation in radiation factor, thermophoresis, Brownian motion factors, and space/thermal-dependent heat source factors. These findings help in optimizing cooling systems in electronics, aerospace, and nuclear reactors. It enhances heat transfer in solar energy, medical treatments, and industrial processes, leading to better performance, energy savings, and enhanced material durability. The skin frictions $C_{\text{fx}} Re_{\text{x}}^{1/2}$ $C_{fx} R e_{x}^{1 / 2}$ and $C_{\text{fy}} Re_{\text{y}}^{1/2}$ $C_{fy} R e_{y}^{1 / 2}$ have retarded more significantly for large inter-particle space and radius say $h = 7/2$ $h = 7 / 2$ and $Rp = 5/2$ $R p = 5 / 2$ . The comparison of current results with published work reveals a close alignment between our findings and the previously published dataset.