<p>This study explores mixed convection of Williamson nanofluid over a vertical stretching sheet, considering Joule heating and viscous dissipation. Nanoparticle addition improves ternary hybrid nanofluid performance, with the Williamson model describing non-Newtonian flow in porous media. Zinc oxide <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(ZnO)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>Z</mi> <mi>n</mi> <mi>O</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, graphene oxide <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\left(GO\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>G</mi> <mi>O</mi> </mfenced> </math></EquationSource> </InlineEquation>, and magnesium oxide <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\left(MgO\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>M</mi> <mi>g</mi> <mi>O</mi> </mfenced> </math></EquationSource> </InlineEquation> are regarded as nanoparticles, with blood serving as the base fluid. The governing equations are transformed into dimensionless partial differential equations (PDEs), treated as ordinary differential equation (ODEs) using the local non-similarity (LNS) approach, and solved with MATLAB bvp4c tool. Using numerical analysis, the temperature and velocity distributions are shown graphically. The Nusselt number and reduced skin friction coefficient values for various physical parameters are computed, examined, and presented in tables. We validate strong validation by comparing these results with available data for particular limiting instances. Porosity and thermal radiation are the main topics of this study. Important parameters are analyzed in detail along with a graphical representation of how they affect liquid flow, including the porosity parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\left(N\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>N</mi> </mfenced> </math></EquationSource> </InlineEquation>, Prandtl number <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\left(Pr\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>P</mi> <mi>r</mi> </mfenced> </math></EquationSource> </InlineEquation>, radiation parameter <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\left(Rd\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>R</mi> <mi>d</mi> </mfenced> </math></EquationSource> </InlineEquation>, magnetic parameter <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\left(M\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>M</mi> </mfenced> </math></EquationSource> </InlineEquation>, and Williamson fluid parameter. As porosity and magnetic characteristics rise, so does the lowered skin friction coefficient. Moreover, increasing the Williamson parameter and Eckert number reduces the fluid velocity while raising the temperature within the thermal boundary layer. Lastly, the current work will have important in industrial manufacturing, heat exchangers, chemical engineering, energy systems, environmental engineering, biomedical applications, aerospace engineering, and HVAC systems.</p>

Mixed convection analysis of Williamson ternary hybrid nanofluid flow over a vertical stretching sheet: non-similar analysis

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发表日期：

2026年7月2日

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Amara Bibi,
Umer Farooq

摘要

This study explores mixed convection of Williamson nanofluid over a vertical stretching sheet, considering Joule heating and viscous dissipation. Nanoparticle addition improves ternary hybrid nanofluid performance, with the Williamson model describing non-Newtonian flow in porous media. Zinc oxide $(ZnO)$ $(Z n O)$ , graphene oxide $\left(GO\right)$ $(G, O)$ , and magnesium oxide $\left(MgO\right)$ $(M, g, O)$ are regarded as nanoparticles, with blood serving as the base fluid. The governing equations are transformed into dimensionless partial differential equations (PDEs), treated as ordinary differential equation (ODEs) using the local non-similarity (LNS) approach, and solved with MATLAB bvp4c tool. Using numerical analysis, the temperature and velocity distributions are shown graphically. The Nusselt number and reduced skin friction coefficient values for various physical parameters are computed, examined, and presented in tables. We validate strong validation by comparing these results with available data for particular limiting instances. Porosity and thermal radiation are the main topics of this study. Important parameters are analyzed in detail along with a graphical representation of how they affect liquid flow, including the porosity parameter $\left(N\right)$ $(N)$ , Prandtl number $\left(Pr\right)$ $(P, r)$ , radiation parameter $\left(Rd\right)$ $(R, d)$ , magnetic parameter $\left(M\right)$ $(M)$ , and Williamson fluid parameter. As porosity and magnetic characteristics rise, so does the lowered skin friction coefficient. Moreover, increasing the Williamson parameter and Eckert number reduces the fluid velocity while raising the temperature within the thermal boundary layer. Lastly, the current work will have important in industrial manufacturing, heat exchangers, chemical engineering, energy systems, environmental engineering, biomedical applications, aerospace engineering, and HVAC systems.