<p>This study explores the entropy generation characteristics in the flow of nanofluids over an unsteady stretching surface under the combined effects of magnetic field and suction/injection. The primary objective is to investigate that three different carbon-based nanoparticles Graphene, nano-diamond, and single-walled carbon nanotubes, dispersed in a water-based fluid, influence thermal performance and entropy production in magnetohydrodynamic flow scenarios. This work presents a novel comparison of high-conductivity nanofluids for precise thermal regulation applications. The flow governing partial differential equations, describing the unsteady nanofluid flow and heat transfer, are reduced to a system of ordinary differential equations through similarity transformations. These ODEs are numerically solved using MATLAB's built-in bvp4c solver. An increase in the magnetic parameter from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$M = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$M = 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> leads to a significant reduction in the momentum profiles from <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="145" /> </InlineMediaObject> <EquationSource Format="TEX">$f^{\prime}\left( {\eta = 1} \right) = 0.38101$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.38101</mn> </mrow> </math></EquationSource> </InlineEquation> for graphene nanofluid to <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="145" /> </InlineMediaObject> <EquationSource Format="TEX">$f^{\prime}\left( {\eta = 1} \right) = 0.10741$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.10741</mn> </mrow> </math></EquationSource> </InlineEquation> for nanodiamond fluid. Similarly, enhancing the injection parameter than a rise in velocity is noticed from <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="145" /> </InlineMediaObject> <EquationSource Format="TEX">$f^{\prime}\left( {\eta = 1} \right) = 0.26662$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.26662</mn> </mrow> </math></EquationSource> </InlineEquation> (nanodiamond fluid) to <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="145" /> </InlineMediaObject> <EquationSource Format="TEX">$f^{\prime}\left( {\eta = 1} \right) = 0.42372$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.42372</mn> </mrow> </math></EquationSource> </InlineEquation> (SWCNT-based nanofluid). Furthermore, an improvement in nanoparticle volume fraction <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="127" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {0.05 \le \phi \le 0.10} \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mn>0.05</mn> <mo>≤</mo> <mi>ϕ</mi> <mo>≤</mo> <mn>0.10</mn> </mrow> </mfenced> </math></EquationSource> </InlineEquation> augments the thermal boundary layer, with the wall temperature rising from <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="138" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta \left( {\eta = 1} \right) = 0.13774$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.13774</mn> </mrow> </math></EquationSource> </InlineEquation> for graphene nanofluid to <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42452_2025_7256_Article_IEq9.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="138" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta \left( {\eta = 1} \right) = 0.21466$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mfenced close=")" open="("> <mrow> <mi>η</mi> <mo>=</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.21466</mn> </mrow> </math></EquationSource> </InlineEquation> for SWCNT-based nanofluid. The results highlight the potential of nanoparticle-enhanced fluids and magnetic/injection control for optimizing heat and momentum transfer in advanced cooling, biomedical, and microfluidic systems. These findings support applications in electronics cooling, targeted drug delivery, and energy storage technologies.</p>

Modeling and analysis of entropy in MHD unsteady flow of water-based nanofluids with carbon nanoparticles

期刊论文
出版模式：

开放获取
发表日期：

2025年7月1日

查看全文

Vijendra Kumar Jarwal,
Sushila Choudhary,
Kalpna Sharma,
Prasun Choudhary

摘要

This study explores the entropy generation characteristics in the flow of nanofluids over an unsteady stretching surface under the combined effects of magnetic field and suction/injection. The primary objective is to investigate that three different carbon-based nanoparticles Graphene, nano-diamond, and single-walled carbon nanotubes, dispersed in a water-based fluid, influence thermal performance and entropy production in magnetohydrodynamic flow scenarios. This work presents a novel comparison of high-conductivity nanofluids for precise thermal regulation applications. The flow governing partial differential equations, describing the unsteady nanofluid flow and heat transfer, are reduced to a system of ordinary differential equations through similarity transformations. These ODEs are numerically solved using MATLAB's built-in bvp4c solver. An increase in the magnetic parameter from $M = 0$ $M = 0$ to $M = 3$ $M = 3$ leads to a significant reduction in the momentum profiles from $f^{\prime}\left( {\eta = 1} \right) = 0.38101$ $f^{'} (η = 1) = 0.38101$ for graphene nanofluid to $f^{\prime}\left( {\eta = 1} \right) = 0.10741$ $f^{'} (η = 1) = 0.10741$ for nanodiamond fluid. Similarly, enhancing the injection parameter than a rise in velocity is noticed from $f^{\prime}\left( {\eta = 1} \right) = 0.26662$ $f^{'} (η = 1) = 0.26662$ (nanodiamond fluid) to $f^{\prime}\left( {\eta = 1} \right) = 0.42372$ $f^{'} (η = 1) = 0.42372$ (SWCNT-based nanofluid). Furthermore, an improvement in nanoparticle volume fraction $\left( {0.05 \le \phi \le 0.10} \right)$ $(0.05 \leq ϕ \leq 0.10)$ augments the thermal boundary layer, with the wall temperature rising from $\theta \left( {\eta = 1} \right) = 0.13774$ $θ (η = 1) = 0.13774$ for graphene nanofluid to $\theta \left( {\eta = 1} \right) = 0.21466$ $θ (η = 1) = 0.21466$ for SWCNT-based nanofluid. The results highlight the potential of nanoparticle-enhanced fluids and magnetic/injection control for optimizing heat and momentum transfer in advanced cooling, biomedical, and microfluidic systems. These findings support applications in electronics cooling, targeted drug delivery, and energy storage technologies.