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The present research investigates the flow characteristics of a Carreau-Yasuda fluid, which is non-Newtonian in nature, passing through a membrane composed of biporous layered cylindrical particles, utilizing a variable permeability approach. The process of formulating the governing equations entails utilizing both the empirical particle-in-cell model and a heat transfer approach. The structure of the proposed research is configured so that fluid flow near the solid core of the cylindrical particle is governed by the Brinkman-Forchheimer equation with variable permeability. In the intermediate region enveloping the Brinkman-Forchheimer region, the fluid flow is regulated by the Brinkman equation with variable permeability. Meanwhile, the peripheral region, adjacent to the hypothetical cell surface, is governed by the Stokes equation due to its non-porous nature. The thermal equations in a steady-state condition are simplified under viscous dissipation. The nonlinearity and coupling of equations arise in the study of Carreau-Yasuda fluid flow through a biporous layered cylindrical particle. This is attributed to the inclusion of a nonlinear inertia term in the Brinkman-Forchheimer equation, variable permeability, and a nonlinear correlation between shear stress and strain in the Carreau-Yasuda fluid. In addressing this issue, the empirical regular perturbation method is employed to derive asymptotic solutions for the governing equations under conditions of high permeability and low Weissenberg number. Additionally, a numerical approach utilizing the NDSolve command in Mathematica software is applied to illustrate graphical analyses under conditions of low permeability and Weissenberg number. The flow profiles' expressions are employed for analyzing the membrane permeability, Kozeny constant, and temperature variation. The graphical discussion delves into the influence of various control parameters, such as Carreau-Yasuda fluid parameters, variable permeability parameters, and Forchheimer number, on hydrodynamic and thermal quantities like fluid velocity, membrane permeability, Kozeny constant, temperature variations, and Nusselt number. The notable finding of the present study is that increasing variable permeability parameters in both the Forchheimer and Brinkmann regions, along with the Forchheimer number, lead to a decrease in fluid velocity and temperature profiles across the flow domain, ultimately resulting in a reduced Nusselt number profile. The present study includes a comparative analysis with existing works, focusing on reduced cases, and reveals that the findings closely match with the previously published studies on membrane filtration processes. The findings of the current study show potential for enhancing our comprehension of crucial physical and biological applications, such as filtration processes in wastewater treatment, characteristics of petroleum reservoir rocks, and the dynamics of blood flow through smooth muscle cells. |
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