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<p>This research investigates the role of thermally radiating ternary hybrid nanofluid flow in an axisymmetric finite flexible duct. The inner surface of the duct is equipped with the metachronal arrangement of motile cilia waves. These waves are responsible for the development of fluid motion. The current physical model is developed by keeping in view the demanding application such as robotics, microfluidics, geothermal/ solar thermal systems, biological and cellular processes. To incorporate the above applications, momentum and energy equation is modeled in the presence of thermal radiation, viscous dissipation, Joule heating, magnetic field, and porous medium effects. This study treats water as a base fluid, whereas for the mixture ternary hybrid nanofluid, copper, titanium dioxide, and silicon dioxide are chosen as nanoparticles. The governed mathematical model is examined under the principal of long wavelength <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14697_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left(\lambda \to \infty \right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>λ</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mfenced> </math></EquationSource> </InlineEquation> and low Reynolds number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14697_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left(Re\ll 1\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>R</mi> <mi>e</mi> <mo>≪</mo> <mn>1</mn> </mfenced> </math></EquationSource> </InlineEquation>. Closed-form exact solutions for the temperature, momentum, and pressure gradient profiles are attained using the famous Blasius equation. For the easy understanding of attained results, graphs and tables are also presented. Flowlines investigation is also discussed using the streamlines pattern. Moreover, it is revealed from the current study that the local skin friction increases with an increase in the Darcy parameter; however, the local Nusselt number decreases with an increase in the radiation parameter.</p>

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Impact of radiating ciliated walls influenced by Cu–TiO2–SiO2/H2O nanofluid flow in an axisymmetric duct

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • M. N. Abrar,
  • Raheela Razzaq,
  • Bandar Almohsen,
  • Ali Akgül

摘要

This research investigates the role of thermally radiating ternary hybrid nanofluid flow in an axisymmetric finite flexible duct. The inner surface of the duct is equipped with the metachronal arrangement of motile cilia waves. These waves are responsible for the development of fluid motion. The current physical model is developed by keeping in view the demanding application such as robotics, microfluidics, geothermal/ solar thermal systems, biological and cellular processes. To incorporate the above applications, momentum and energy equation is modeled in the presence of thermal radiation, viscous dissipation, Joule heating, magnetic field, and porous medium effects. This study treats water as a base fluid, whereas for the mixture ternary hybrid nanofluid, copper, titanium dioxide, and silicon dioxide are chosen as nanoparticles. The governed mathematical model is examined under the principal of long wavelength \(\left(\lambda \to \infty \right)\) λ → ∞ and low Reynolds number \(\left(Re\ll 1\right)\) R e ≪ 1 . Closed-form exact solutions for the temperature, momentum, and pressure gradient profiles are attained using the famous Blasius equation. For the easy understanding of attained results, graphs and tables are also presented. Flowlines investigation is also discussed using the streamlines pattern. Moreover, it is revealed from the current study that the local skin friction increases with an increase in the Darcy parameter; however, the local Nusselt number decreases with an increase in the radiation parameter.