Transient confined natural convection with internal heat generation

Abstract

Numerical studies are conducted to describe the time-dependent adjustment of natural convection in a square cavity. A steady flow field had been established by maintaining different temperatures at the two vertical sidewalls, and this effect is represented by the external Rayleigh number Ra-E. A uniform internal heat generation, which is measured by a properly defined internal Rayleigh number Ra-I, is switched on impulsively at t=0. The ensuing process of settlement to final state, for large Ra-E and Ra-I, and Pr similar to O(1), is depicted by solving the governing equations numerically. When the effect of internal heating is small, the major circulation cell, which has been driven by external heating, remains little affected, and this pattern is termed stage I. When Ra-I/Ra-E is moderately large, an additional oppositely directed circulation cell appears in the upper corner region of the heated sidewall, which is denoted stage II. When Ra-I/Ra-E is very large, three stages are encompassed. The qualitative flows of the first two stages correspond to those described earlier. In stage III, the whole cavity is occupied by two oppositely directed circulation cells. The final-state features are consistent with the preceding experimental visualizations for the flow dominated by internal heating effects. Time histories of the average Nusselt number on the wall are analyzed, and the overall time characterizing the global adjustment is shown to scale with Ra-I(-1/4). (C) 1997 by Elsevier Science Inc.