Modeling of Opposing Mixed Convection of Air in Partially Cooled Vertical Channels

Abstract

in this paper opposing laminar mixed convection in partially cooled vertical channel is investigated numerically. Temperature profiles, Nusselt number and velocity profiles at various axial locations in the cooled part of opposing buoyancy flow are presented. Streamlines and isotherms have been also plotted for different values of Grashof number, Gr. Conservation equations of continuity, momentum and energy were solved simultaneously using Finite volume method. The effect of the cooled section on the flow pattern and heat transfer performance is investigated for given Grashof numbers. The influence of axial diffusion and it's relevant to flow reversal at the entrance region of the channel was taken into account in the governing equations and particular attention is given to the ratio │Gr / Re2│. The effect of opposing bouncy forces on the hydrodynamic and thermal fields was examined for air with Re = 500, 105 ≤ │Gr ≤ │ 3*105. Reversal flow was observed near the channel wall for this opposing buoyancy flow. It was noticed that the friction factor, f•ReL ,for the ratio │Gr / Re2 │≥ 1.2 was unstable over the cooled length, becomes negative and then increases to an asymptotic value of 16 over the insulated section. The presented numerical results revealed some interesting features which may be summarized as: (i) Globally Nusselt number decreases and reaches asymptotic value at the end of the cooling section. However for Gr = -3*105 Nusselt decreases and reach a minimum value approximately equal to 3.12. (ii) For Gr up to │3ₓ105│ the Boussinesq approximation still predicts reasonably the heat transfer rate.