Significant Effect of Radiation on Combined Convection Vertical Channel with Internal Heat Generation and Boundary Conditions of a Third Kind

Heat transfer process involving combined convection, along with the influence of radiation, within a fully developed vertical channel, holds significant importance in environmental, industrial, and engineering applications. Concerns have arisen regarding the complexity, cost, and time required to understand the heat transfer process, especially when considering radiation effects. This study aims to assess the combined impact of the Robin temperature boundary condition and radiation on flow and heat transfer, to examine the role of viscous dissipation, including its interaction with radiation, in fluid flow and heat transfer and to compare the heat transfer effectiveness under the boundary conditions of Dirichlet, Neumann, and Robin. Various dimensional parameters are systematically tested in this investigation, with particular emphasis on discussing the phenomenon of flow reversal in the presence of radiation. The numerical solution to the Boundary Value Problem (BVP) is achieved using Maple and its built-in routine, dsolve. A validation study on a previously published problem is conducted to ensure the accuracy of the computational approach, considering the added complexity of radiation effects and the transformation of the partial differential equation into an ordinary differential equation applying the similarity technique. Graphical representations of the numerical results for flow and temperature profiles, incorporating radiation effects, are presented. Notably, the occurrence of flow reversal is observed in instances where the values of internal heat generation (G), combined convection parameter (λ), and radiation effects (Rd) were substantial. Conversely, an increase in the values of the local heating exponent (p) and Biot numbers (Bi), while accounting for radiation, eliminated the occurrence of flow reversal.