A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure

This paper reports the influence of local thermal non-equilibrium state between solid porous matrix and saturated fluid on natural convection in enclosure. The two dimensional steady flow is induced by constant heat flux on side walls of the enclosure, when both horizontal walls are insulated. The governing equations are solved numerically by ADI method and analytically by using parallel flow assumption valid for slender enclosure. A comparative study has been made between convection in square cavity and the same in slender enclosure. Numerical experiments indicate that in comparison with square cavity, where a sharp decrease of local heat transfer rate for fluid (Nuf) takes place up to a certain small value of interface heat transfer coefficient (H), in slender enclosure a smooth decrease of Nuf has been observed in the entire range of H when conductivity ratio (γ) is very small. However, for relatively high values of γ (e.g., γ = 10), Nuf is almost independent of H in both geometries. For a given γ, when the value of H is relatively very high, up to a certain value of Ra the difference between both solid as well as fluid temperature rates is negligible. Corresponding temperature contours of two phases becomes almost identical in magnitude as well as patterns point of view, which indicates that equilibrium state between two phases is achieved. Finally, in equilibrium state maximum heat transfer rate used to take place at a certain value (Ao) of aspect ratio, lying in between 1 and 1.5, and is almost independent of all equilibrium parameters. In case of non-equilibrium state, Ao acts as an increasing function of γ.