Regression analysis of squeezing-induced hybrid nanofluid flow in Darcy-Forchheimer porous medium

• Published in: Applied mathematics and mechanics Vol. 46; no. 1; pp. 193 - 208
• Main Authors: Muhammad, K., Sarfraz, M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Compressing; Cooling systems; Electrons; Flow velocity; Fluid flow; Fluid- and Aerodynamics; Gold; Heat; Heat flux; Heat transfer; Magnetic flux; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nanofluids; Nanomaterials; Ohmic dissipation; Parallel plates; Partial Differential Equations; Porous media; Pressure gradients; Regression analysis; Regression models; Resistance heating; Silicon dioxide; Skin friction; Statistical analysis; Thermal management; Thermal relaxation; Darcy-Forchheimer medium; Joule heating; regression analysis; 76D05; hybrid nanofluid; 80A20; numerical solution; 35Q79; squeezing flow; 76S05; O361; 76W05; convective boundary condition; magnetohydrodynamic (MHD); O175.2
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3202-9

This article presents a mathematical model addressing a scenario involving a hybrid nanofluid flow between two infinite parallel plates. One plate remains stationary, while the other moves downward at a squeezing velocity. The space between these plates contains a Darcy-Forchheimer porous medium. A mixture of water-based fluid with gold (Au) and silicon dioxide (SiO 2 ) nanoparticles is formulated. In contrast to the conventional Fourier’s heat flux equation, this study employs the Cattaneo-Christov heat flux equation. A uniform magnetic field is applied perpendicular to the flow direction, invoking magnetohydrodynamic (MHD) effects. Further, the model accounts for Joule heating, which is the heat generated when an electric current passes through the fluid. The problem is solved via NDSolve in MATHEMATICA. Numerical and statistical analyses are conducted to provide insights into the behavior of the nanomaterials between the parallel plates with respect to the flow, energy transport, and skin friction. The findings of this study have potential applications in enhancing cooling systems and optimizing thermal management strategies. It is observed that the squeezing motion generates additional pressure gradients within the fluid, which enhances the flow rate but reduces the frictional drag. Consequently, the fluid is pushed more vigorously between the plates, increasing the flow velocity. As the fluid experiences higher flow rates due to the increased squeezing effect, it spends less time in the region between the plates. The thermal relaxation, however, abruptly changes the temperature, leading to a decrease in the temperature fluctuations.