Numerical analysis of non-similar convection flows of a two-phase nanofluid past a semi-infinite vertical plate with thermal radiation

This research presents a computational investigation of non-linear, steady-state, incompressible laminar boundary-layer flow over a semi-infinite vertical plate using the Darcy–Forchheimer model along with Buongiorno’s nanofluid model. Thermal convection and radiative heat and mass transfer of nanoparticles are considered. The research investigation fills a significant gap in the literature regarding the effects of Darcy–Forchheimer drag and heat radiation. The dimensionless nonlinear boundary value problem with associated wall and free stream boundary conditions is solved with the robust second-order accurate implicit finite-difference Keller Box technique to solve complex coupled nonlinear PDEs with high accuracy. The intricate interactions inside the fluid are clarified through extensive numerical simulations. An excellent correlation is obtained when our current code is validated using previous research from the literature, which had adopted numerous numerical techniques to solve the research problems. This study presents a novel non-similar analysis of two-phase nanofluid convection incorporating thermal radiation effects, which is rarely addressed in existing literature. The research uniquely captures the combined influence of Brownian motion, thermophoresis, and radiation on flow and heat transfer characteristics. The findings provide novel and creative insights into the structure of nanofluids in porous media, advancing our knowledge of fluid dynamics, heat, and mass transfer. It is observed that with increasing Darcy number ( Da ), there is a substantial increase in velocity, but temperature and concentration profiles decay; conversely, as Forchheimer number ( Fs ) enhances, velocity is depreciated; however, temperature and concentration profiles are elevated steadily. Moreover, increasing Brownian motion ( Nb ) enhances both velocity and temperature but reduces the concentration profile. Additionally, the velocity and temperature profiles are appreciated when thermal radiation ( R ) values are enhanced, but concentration decays. Temperature and velocity are reduced as the Prandtl number ( Pr ) increases, while concentration is elevated. Additionally, surface contour graphs and isothermal graphs are studied in detail. This current study has practical implications for enhancing the design and optimization of cooling systems, electronic thermal management, and energy systems, in circumstances where accurate control of temperatures and effective heat transmission are essential. By addressing the current research gap, this study makes major advances in the fields of thermal sciences and nanofluid technology dynamics.