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<p>This study investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics of Cu and TiO<sub>2</sub> water-based Williamson nanofluids over a nonuniformly stretching flat surface embedded in a porous medium. Motivated by the growing demand for efficient heat and mass transfer systems in industrial applications, the model incorporates the nonlinear rheology of the Williamson fluid, enhanced thermal properties of Cu and TiO<sub>2</sub> nanoparticles, nonuniform stretching velocities and the interplay of heat sources, viscous dissipation, and porous medium permeability. The governing partial differential equations (PDEs) are reduced to a system of ordinary differential equations (ODEs) using similarity transformations and solved numerically using MATLAB’s built-in bvp4c solver. The solutions are validated against previously published results, showing excellent agreement. Parametric studies reveal that increasing the magnetic field intensity (<i>M</i>) reduces the velocity profiles due to the Lorentz force, with Cu–H<sub>2</sub>O exhibiting up to 12% stronger reduction compared to TiO<sub>2</sub>–H<sub>2</sub>O. Higher porosity parameter values (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(k_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>) enhance both velocity and temperature profiles, with a 15% rise in temperature observed for Cu–H<sub>2</sub>O at <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(k_p=0.3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>k</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </math></EquationSource> </InlineEquation>, highlighting the role of porosity in reducing flow resistance. Additionally, temperature profiles increase with <i>M</i>, indicating improved heat retention, while entropy generation number (<InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(N_\textrm{G}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mtext>G</mtext> </msub> </math></EquationSource> </InlineEquation>) rises with <i>M</i>, <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(k_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> and Eckert number (Ec) due to viscous and thermal dissipation. Comparative analysis shows that Cu–H<sub>2</sub>O consistently outperforms TiO<sub>2</sub>–H<sub>2</sub>O in terms of heat transfer and entropy generation, owing to its superior thermal conductivity. These findings provide practical insights into optimizing nanofluid performance for applications such as heat exchangers, energy harvesting and magnetic drug delivery, offering a comprehensive perspective on the combined effects of fluid behavior, porous media and heat source mechanisms on nanofluid dynamics.</p>

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Impact of viscous dissipation, porosity and heat source on MHD flow, thermal performance and entropy generation in Cu and TiO2 water-based Williamson nanofluids over a nonuniformly stretching surface

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Ratnamanjari Sahoo,
  • Bharat Keshari Swain,
  • Apul Narayan Dev

摘要

This study investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics of Cu and TiO2 water-based Williamson nanofluids over a nonuniformly stretching flat surface embedded in a porous medium. Motivated by the growing demand for efficient heat and mass transfer systems in industrial applications, the model incorporates the nonlinear rheology of the Williamson fluid, enhanced thermal properties of Cu and TiO2 nanoparticles, nonuniform stretching velocities and the interplay of heat sources, viscous dissipation, and porous medium permeability. The governing partial differential equations (PDEs) are reduced to a system of ordinary differential equations (ODEs) using similarity transformations and solved numerically using MATLAB’s built-in bvp4c solver. The solutions are validated against previously published results, showing excellent agreement. Parametric studies reveal that increasing the magnetic field intensity (M) reduces the velocity profiles due to the Lorentz force, with Cu–H2O exhibiting up to 12% stronger reduction compared to TiO2–H2O. Higher porosity parameter values ( \(k_p\) k p ) enhance both velocity and temperature profiles, with a 15% rise in temperature observed for Cu–H2O at \(k_p=0.3\) k p = 0.3 , highlighting the role of porosity in reducing flow resistance. Additionally, temperature profiles increase with M, indicating improved heat retention, while entropy generation number ( \(N_\textrm{G}\) N G ) rises with M, \(k_p\) k p and Eckert number (Ec) due to viscous and thermal dissipation. Comparative analysis shows that Cu–H2O consistently outperforms TiO2–H2O in terms of heat transfer and entropy generation, owing to its superior thermal conductivity. These findings provide practical insights into optimizing nanofluid performance for applications such as heat exchangers, energy harvesting and magnetic drug delivery, offering a comprehensive perspective on the combined effects of fluid behavior, porous media and heat source mechanisms on nanofluid dynamics.