Computation Study of Magnetized Darcy-Forchheimer Tangent Hybrid Nanofluid Flow Bounded by Stretchable Surface using Three-Stage Lobatto IIIA Scheme.

Abstract

Current research explores the intricate dynamics of Darcy–Forchheimer flow in a magnetized tangent hyperbolic hybrid nanofluid. , incorporating the effects of heat and mass transfer, thermal radiation, and a porous medium. Hybrid nanofluids, renowned for their enhanced thermal conductivity and modified rheological behavior, have emerged as transformative materials in energy and industrial applications. The governing nonlinear partial differential equations (PDEs) are reformulated into ordinary differential equations (ODEs) using similarity transformations and solved numerically via a three-stage Lobatto scheme with the help of MATLAB, ensuring computational precision. The study provides a comprehensive analysis of the influence of the Forchheimer number, porosity parameter, magnetic field intensity, and nanoparticle shape factor on flow behavior. Results reveal that increasing the shape factor significantly enhances thermal conductivity, while the Forchheimer effect and porous resistance govern the velocity distribution. A notable observation is that higher values of the Weissenberg number (We), magnetic parameter (M), rotational parameter (λ), and Forchheimer number (Fr) lead to a reduction in velocity boundary layer thickness, whereas the temperature profile exhibits a pronounced increase. Furthermore, the presence of thermal radiation introduces substantial modifications to heat transfer characteristics, optimizing energy transport mechanisms. The findings demonstrate strong alignment with existing literature, reinforcing the robustness of the proposed model. This study offers valuable insights into the complex interplay between magnetohydrodynamics (MHD), porous media, and hybrid nanofluid dynamics, highlighting their potential for next-generation applications in cooling technologies, biomedical systems, and sustainable energy solutions.