A thermal non-equilibrium perspective on mixed convection in a vertical channel

Abstract

This paper addresses the influence of thermal non-equilibrium state on fully developed mixed convection in a vertical channel filled with porous medium. The non-Darcy-Brinkman-Forchheimer extended model has been considered. The governing equations are solved numerically by spectral collocation method and analytically for a special case (form drag equal to zero). The governing parameters for this problem are Rayleigh number (Ra), Darcy number (Da), Forchheimer number (F), inter-phase heat transfer coefficient (H), and porosity-scaled thermal conductivity ratio (γ). Special attention is given to understand the effect of thermal non-equilibrium parameters: H and γ on the rates of heat transfer and fluid flow profiles, for both buoyancy assisted as well as opposed cases. A comprehensive investigation indicates that, in case of buoyancy assisted flow, for each Ra considered in this study and when γ ≤ 1, there exists a minimum value Ho of H such that the heat transfer rate of fluid (Nuf) at the wall is an increasing function in [0, Ho]. Furthermore, as H is varied beyond Ho, Nuf decreases. Initially the decay of Nuf is fast, but later on it becomes smooth and slow. Similar results are also observed in buoyancy opposed case for very small values of γ. Variation of velocity profile as a function of γ indicates that change in velocity profile is sudden and abrupt. For H > 6, when γ = 0.01, Da = 10−2, |Ra| = 103 and F = 102, flow separation and point of inflection are completely died out from the profile. Overall, for both the cases, on increasing H makes the flow profile smooth (stabilizes the flow) and recovers the system equivalent to equilibrium state, whereas, γ destabilizes the flow by inviting point of inflection or flow separation on the velocity profile.