TRANSIENT LAMINAR NATURAL CONVECTION IN AN ENCLOSURE FROM STEADY FLOW STATE TO STATIONARY STATE

Abstract

The aim of this numerical study is to investigate the transient natural convection in a two-dimensional enclosure of which the upper and lower walls are adiabatic. Initially t = 0, the left wall is at a higher temperature than the right wall, and the fluid of the enclosure is at a steady flow state. At time t > 0, the temperature of the left wall descends to that of the right wall. This causes the flow of the fluid in the enclosure to change. As time increases, the flow decays. Finally, the flow ceases and the fluid becomes stationary. During the computing process, a penalty finite-element method with a Newton-Raphson iteration algorithm and a backward difference scheme dealing with the time term are adopted to solve the governing equations. A skyline method is used to reduce massive computer memory. The effect of Rayleigh number on the heat transfer mechanism during the transient process is examined by investigating the Ra = 10⁴ case, in which conduction heat transfer is dominant, and the Ra = 10⁶ case, in which convection is dominant. In both cases, only one cell exists at the initial steady flow state. Wren the boundary condition changes, another cell forms. As time increases, the two cells become symmetric to the vertical centerline. For the Ra = 10⁴ case, only the right cell transfers heat to the left cell. However, for the Ra = 10⁶ case, the two cells transfer heat to each other during the transient process. Besides the flow field, the temperature distribution and the local Nusselt number distributions along the left and right walls during the transient process are also examined in detail.