Convective-radiation boundary impact on heat transfer in buoyant viscous layers

• A novel study investigates buoyancy-driven viscous boundary layer flow over a stretching surface with a combined convective-radiation (C-R) boundary condition. • The model incorporates nonlinear thermal radiation, surface emissivity, and heat transfer coefficients, introducing key dimensionless parameters like conduction-radiation and Biot numbers. • Numerical results using the Runge-Kutta shooting method show that increasing the conduction-radiation parameter reduces local skin friction by 3.45% and enhances heat transfer by 1.07%. • The findings are applicable to high-temperature manufacturing processes such as polymer extrusion and thermal treatment of materials, where precise control of heat transfer is critical. Convective–radiation boundary conditions are essential in fluid flow analysis, as they capture the combined effects of convection and radiation on heat transfer and system thermal behaviour, with applications in thermal processing, solar energy systems, and environmental heat transfer. This paper presents a novel investigation of buoyancy-driven viscous boundary layer flow over a stretching surface with a combined convective-radiation (C-R) boundary condition. The study incorporates the effects of buoyancy and nonlinear thermal radiation on flow and heat transfer. A combined C-R boundary condition is developed for the stretching sheet boundary layer flow, considering the heat transfer coefficient and surface emissivity. The governing equations and boundary conditions are non-dimensionalized, including parameters such as free convection, temperature ratio, radiation, conduction-radiation, Biot, and Prandtl numbers. Numerical solutions are obtained using the fourth-order Runge-Kutta method with a shooting technique. The influence of physical parameters on velocity and temperature profiles, as well as local skin friction and reduced Nusselt number, is thoroughly discussed. Results indicate that increasing the conduction-radiation parameter decreases local skin friction coefficient and enhances heat transfer, as evidenced by a 3.45% reduction in local skin friction coefficient and a 1.07% increase in the Nusselt number. Further, results demonstrate that boundary parameters, including the Biot number and conduction-radiation parameters, can effectively control and balance the flow and heat transfer in the boundary layer.