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In this study, we analyzed the flow and heat transfer within a fully-developed non-linear, non-Darcy flow through a sparsely packed chemically inert porous medium in a vertical channel by considering Dirichlet, Neumann and Robin boundary conditions. A numerical solution by using Runga-Kutta method that was obtained for the Darcy-Forchheimer-Brinkman momentum equation is used to analyze the heat transfer. The Biot number influences on velocity and temperature distributions are opposite in regions close to the left wall and the right wall. Neumann condition is seen to favor symmetry in the flow velocity whereas Robin and Dirichlet conditions skew the flow distribution and push the point of maximum velocity to the right of the channel. A reversal of role is seen between them in their influence on the flow in the left-half and the right-half of the channel. This leads to related consequences in heat transport. Viscous dissipation is shown to aid flow and heat transport. The present findings reiterate the observation on heat transfer in other configurations that no significant change was observed in Neumann condition, whereas the changes are too extreme in Dirichlet condition. It is found that Robin condition is the most stable condition.

A Study of Non-linear, Non-Darcy Newtonian Liquid Flow and Heat Transfer Through Vertical Channel Using Mixed Boundary Conditions on Temperature