Numerical investigation of nonlinear convection in Buongiorno nanofluids with Darcy–Forchheimer drag using Keller box method

Abstract

This study investigates non-similar nonlinear thermal convection of a Buongiorno nanofluid through a Darcy–Forchheimer porous medium—an important problem for accurately modelling high-velocity thermal systems where Brownian motion, thermophoresis, and inertial porous-media effects coexist.  It further highlights that the governing two-dimensional PDEs are solved using the second-order accurate Keller Box Method, validated against known special cases. The discoveries offer fresh perspectives on the behavior of nanofluids in porous media, contributing to a deeper understanding of heat, mass transfer, and fluid dynamics. It is observed that with increasing Darcy number, there is a substantial hike in velocity, but temperature and concentration decay; conversely, as the Forchheimer number increases, velocity is decreased; however, temperature and concentration profiles are elevated steadily. Specific and quantitative numerical results show that increases in nanoparticle Brownian diffusion Nb elevating temperature profiles by up to ~18% and reducing concentration by ~12%, thermophoresis Nt intensifying thermal fields by ~20% while lowering near-wall velocity, and higher Darcy Da and Forchheimer Fs numbers reducing near-wall momentum by 10–15% but enhancing thermal and concentration layers by up to 17%. This current study has practical implications for enhancing the design and optimization of cooling systems, electronic thermal management, and power systems in situations where accurate temperature regulation and effective heat transport are essential. By addressing the current research gap, this study makes major advances in the fields of thermal sciences and nanofluid technology dynamics, the novelty of simultaneously integrating Buongiorno’s nanofluid theory with the nonlinear Da–Fs model in a non-similar convection framework—advancing beyond earlier studies that considered these mechanisms separately and were restricted to ODE formulations.

Journal of Naval Architecture and Marine Engineering, 23(1), 2026, PP. 41-60