Ciliary Flow of Jeffery Nanofluid with Mixed Convection in a Curved Porous Channel: A Numerical Approach

The double-diffusive, cilia-induced flow of time-dependent (Jeffery) nanofluids in porous curved channels simulates complex biological transport, supporting respiratory therapies, advanced drug delivery, and treatments for reproductive and mucosal tissues. It also improves oil recovery, heat transfer in microdevices, and the efficient transport of genetic material and pollutants in environmental and biotechnological systems. This paper presents a numerical analysis of the double-diffusive, cilia-induced flow of a non-Newtonian Jeffery nanofluid through a porous medium in a curved channel. A modified Darcy’s law is used to simulate the porous region, and curvilinear coordinates are used to convert the flow equations into a wave frame. The model is rectified by assuming a long wavelength and a low Reynolds number. The NDSolve tool in Mathematica is used to solve the nonlinear system to get a numerical data with highest accuracy. It is concluded that the velocity falls with solutal Grashof number in the range $$\:1<{G}_{rc}<7$$ , the Darcy number $$\:1<Da<5$$ , and Jeffery fluid parameter $$\:1<\beta\:<4$$ but inverse readings are visualized for the nanoparticles Grashof number $$\:0.5<{G}_{rf}<6.5$$ . While temperature rises with Brinkman number and it falls with Prandtl number. The pressure gradient rises with curvature parameter and Jeffery fluid parameter and falls with Hartmann number. Bolus size increases with thermal Grashof number and curvature parameter and decreases with rising solutal Grashof number. Comprehensive 2D and 3D visualizations provide practical interpretations of the effects of parameters on the flow structure and graphically verify these conclusions.