Impact of constant Heat Source/sink on Natural convection flow in a vertical Channel: A non-linear Boussinesq approximation Approach

Abstract

This study aims to investigate the impact of a constant source/sink on natural convection flow between two vertical walls within a porous medium. The problem is solved analytically for the steady, fully developed Brinkman extended Darcy model. The influence of the source/sink parameter ), Darcy number, and viscosities ratio  on fluid velocity as well as temperature is obtained in this research work. All the results are shown graphically for the variations of their relevant parameters, such as Darcy number, heat source/sink parameter, and ratio of viscosities. The result illustrates that the velocity profile is more in the case of nonlinear density variation with temperature (NDT) than linear density variation with temperature (LDT). There is enhancement in the temperature profile with the increment in source/sink parameter. The mathematical expressions for the skin friction were also obtained at both the walls. Mass flow rate in the channel is also derived analytically. Outcome of the study indicates that the nature of flow validates the previous research done in the same area.