Radiative Free Convection From a Vertical Plate With Constant Heat Flux in a Darcy–Forchheimer Porous Medium With Nonlinear Buoyancy

Abstract

This study investigates the steady free convection flow over a vertical plate embedded in a Darcy–Forchheimer porous medium, with particular emphasis on the coupled effects of thermal radiation, nonlinear buoyancy, and porous resistance under a constant heat flux (CHF) boundary condition. Unlike most previous studies, which were limited to constant surface temperature (CST) conditions, the present formulation considers the wall temperature as an unknown to be determined as part of the solution, providing a more realistic representation of prescribed heat‐flux thermal systems. The governing boundary‐layer equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations and solved numerically with the MATLAB bvp4c solver. The effects of the radiation parameter ( R ), Darcy parameter ( λ ), Forchheimer parameter ( F ), nonlinear buoyancy parameter ( δ ), and Prandtl number (Pr) on the velocity and temperature distributions are examined. The results show that increasing the radiation parameter enhances both the velocity and temperature fields due to stronger thermal diffusion and buoyancy effects, while reducing the local Nusselt number due to increased wall temperature under CHF conditions. Furthermore, the study demonstrates that the heat‐transfer characteristics under CHF differ fundamentally from those predicted by conventional CST models, providing new physical insight into radiative free convection in Darcy–Forchheimer porous media. The findings provide a useful theoretical basis for the analysis and design of porous thermal systems operating under prescribed heat‐flux conditions.