Development of Oscillatory Asymmetric Recirculating Flow in Transient Laminar Opposing Mixed Convection in a Symmetrically Heated Vertical Channel

Abstract

Detailed flow and thermal characteristics in transient laminar opposing mixed convection in a vertical plane channel subject to a symmetric heat input are numerically investigated. First, a linear stability analysis was employed to evidence the occurrence of flow bifurcation. Then, the unsteady Navier–Stokes equations along with the continuity and energy equations were respectively integrated by a third-order upwind and power-law finite-difference scheme with the resulting matrices inverted by the Fast Fourier Transform and conjugated gradient methods. Reverse flow in the form of symmetric, elongated recirculating cells is initiated earlier and is stronger in a lower Prandtl number fluid with higher opposing buoyancy and Reynolds number and longer heated section length. At a high opposing buoyancy, sudden flow asymmetry and oscillation occur simultaneously in a nearly steady flow after the initial transient. Periodic flow and thermal evolution are noted in space and time. An empirical equation for the condition for inducing flow oscillation is proposed.