<p>This article seeks to analyze the mass and heat transfer of a bioconvective tangent hyperbolic nanofluid as it flows through an expandable Riga wedge, considering influences such as thermophoresis, chemical reactions, Brownian motion, and a heat source. This exploration encompasses stream calculations with modified Hartmann numbers, notably in the unstable tangent hyperbolic fluid stream situation. This work aims to enforce heat transportation with homogeneous inclusion of nano-species. The present study highlights the coupled impact of bioconvection, activation energy, and chemical reaction in tangent hyperbolic nanofluids along an extendable Riga wedge-a geometrical setting that has rarely been discussed in the open literature. Minimal studies have been conducted to address such complex relations with realistic applications in high-performance heat exchangers, biomedical devices, and electronic coolers. The novelty ensues when considering bioconvection-biochemical reactions and activation energy in tangent hyperbolic nanofluid flow over a rarely analyzed expanding Riga wedge configuration. New insights obtained in the optimization of heat and species transfer with this modern numerical solution are also useful for engineering and biomedicine. Additionally, this work finds immense practical relevance in designing, among others, efficient heat exchangers, electronic cooling, and biomedical fluid transportation systems. A pair of similarity transformations is being used to acquire dimensionless forms of the fluid regulating equations. The numerical analysis is conducted using the RK-4 method in conjunction with the shooting technique. The effects of several parameters on the motile density profiles, temperature, concentration, and non-dimensional velocity are graphically represented. Analyses are conducted on the effects of pertinent parameters on skin friction, heat transfer coefficient, Sherwood number, and motile density coefficient. It is noticed that when the modified Hartmann number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14051_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$M_\mathrm{{h}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mi mathvariant="normal">h</mi> </msub> </math></EquationSource> </InlineEquation> is elevated, the velocity profile <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14051_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">$f'(\eta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of the tangent hyperbolic fluid increases faster than that of Newtonian fluid. In the presence of Pr and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14051_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$B_\mathrm{{i}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mi mathvariant="normal">i</mi> </msub> </math></EquationSource> </InlineEquation>, the local Nusselt number <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14051_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$-\theta '(0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <msup> <mi>θ</mi> <mo>′</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> increases.</p>

Bioconvection for Riga wedge flow of tangent hyperbolic nanofluids in the presence of activation energy and mass suction

期刊论文
发表日期：

2025年4月30日

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Guoning Li,
Sohaib Abdal,
Biaofeng Zhang,
Nehad Ali Shah,
Zarwa Fatima

摘要

This article seeks to analyze the mass and heat transfer of a bioconvective tangent hyperbolic nanofluid as it flows through an expandable Riga wedge, considering influences such as thermophoresis, chemical reactions, Brownian motion, and a heat source. This exploration encompasses stream calculations with modified Hartmann numbers, notably in the unstable tangent hyperbolic fluid stream situation. This work aims to enforce heat transportation with homogeneous inclusion of nano-species. The present study highlights the coupled impact of bioconvection, activation energy, and chemical reaction in tangent hyperbolic nanofluids along an extendable Riga wedge-a geometrical setting that has rarely been discussed in the open literature. Minimal studies have been conducted to address such complex relations with realistic applications in high-performance heat exchangers, biomedical devices, and electronic coolers. The novelty ensues when considering bioconvection-biochemical reactions and activation energy in tangent hyperbolic nanofluid flow over a rarely analyzed expanding Riga wedge configuration. New insights obtained in the optimization of heat and species transfer with this modern numerical solution are also useful for engineering and biomedicine. Additionally, this work finds immense practical relevance in designing, among others, efficient heat exchangers, electronic cooling, and biomedical fluid transportation systems. A pair of similarity transformations is being used to acquire dimensionless forms of the fluid regulating equations. The numerical analysis is conducted using the RK-4 method in conjunction with the shooting technique. The effects of several parameters on the motile density profiles, temperature, concentration, and non-dimensional velocity are graphically represented. Analyses are conducted on the effects of pertinent parameters on skin friction, heat transfer coefficient, Sherwood number, and motile density coefficient. It is noticed that when the modified Hartmann number $M_\mathrm{{h}}$ $M_{h}$ is elevated, the velocity profile $f'(\eta )$ $f^{'} (η)$ of the tangent hyperbolic fluid increases faster than that of Newtonian fluid. In the presence of Pr and $B_\mathrm{{i}}$ $B_{i}$ , the local Nusselt number $-\theta '(0)$ $- θ^{'} (0)$ increases.