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<p>This work analyzes the unsteady natural convection&#xa0;flow of a non-Newtonian magnetohydrodynamic Williamson nanofluid via an oscillating vertical porous plate immersed in a saturated porous medium. The Buongiorno nanofluid formulation is used to examine the physical significance of Brownian and thermophoretic motion of nanoparticles. In thermal and solutal fields, this study includes the combined consequences of chemical reaction, Joule heating, heat absorption/generation, and cross-diffusion processes described by Soret and Dufour effects. The Boussinesq approximation is implemented to investigate the natural convection. The Williamson constitutive equation is used to simulate the fluid's nonlinear rheological behavior, incorporating shear-thinning properties important for complex industrial and biological applications. The governing nonlinear partial differential equations for energy, momentum, and concentration of nanoparticles are developed by using the considered assumptions. A system of coupled equations is obtained after nondimensionalization of equations, and the implicit Crank-Nicolson finite difference technique is used to determine numerical results. The numerical and graphical significance of emergent parameters, including the thermal Grashof number, Williamson fluid parameter, solutal Grashof number, Soret and Dufour numbers, porosity parameter, chemical reaction rate, and heat sink or source coefficients on the flow, thermal, and solutal fields are investigated. A thorough parametric study shows that the&#xa0;increment in&#xa0;the Williamson parameter decreases the thickness of the velocity boundary layer because of higher shear-thinning effects. The thermal Grashof number enhances buoyancy-driven flow and rises the velocity of fluid, but higher values of the porosity parameter&#xa0;reduce the velocity field. By combining mass diffusion and heat flow, the Dufour effect improves temperature profiles, whereas the Soret number raises concentration profiles. The concentration of nanoparticles is substantially decreased by the reaction parameter, and the generation of heat promotes the development of thermal boundary layers.</p>

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Numerical analysis of Williamson nanofluid flow past an oscillating vertical porous plate: influence of Soret, Dufour, and chemical reaction effects

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Albara Alrawashdeh,
  • Muhammad Awais,
  • Hakim Al Garalleh,
  • Raja Farrukh Riaz

摘要

This work analyzes the unsteady natural convection flow of a non-Newtonian magnetohydrodynamic Williamson nanofluid via an oscillating vertical porous plate immersed in a saturated porous medium. The Buongiorno nanofluid formulation is used to examine the physical significance of Brownian and thermophoretic motion of nanoparticles. In thermal and solutal fields, this study includes the combined consequences of chemical reaction, Joule heating, heat absorption/generation, and cross-diffusion processes described by Soret and Dufour effects. The Boussinesq approximation is implemented to investigate the natural convection. The Williamson constitutive equation is used to simulate the fluid's nonlinear rheological behavior, incorporating shear-thinning properties important for complex industrial and biological applications. The governing nonlinear partial differential equations for energy, momentum, and concentration of nanoparticles are developed by using the considered assumptions. A system of coupled equations is obtained after nondimensionalization of equations, and the implicit Crank-Nicolson finite difference technique is used to determine numerical results. The numerical and graphical significance of emergent parameters, including the thermal Grashof number, Williamson fluid parameter, solutal Grashof number, Soret and Dufour numbers, porosity parameter, chemical reaction rate, and heat sink or source coefficients on the flow, thermal, and solutal fields are investigated. A thorough parametric study shows that the increment in the Williamson parameter decreases the thickness of the velocity boundary layer because of higher shear-thinning effects. The thermal Grashof number enhances buoyancy-driven flow and rises the velocity of fluid, but higher values of the porosity parameter reduce the velocity field. By combining mass diffusion and heat flow, the Dufour effect improves temperature profiles, whereas the Soret number raises concentration profiles. The concentration of nanoparticles is substantially decreased by the reaction parameter, and the generation of heat promotes the development of thermal boundary layers.