DIRECT NUMERICAL SIMULATION OF NATURAL CONVECTION BOUNDARY-LAYER FLOW OF LOW PRANDTL NUMBER FLUID

In solar heating and ventilation systems, the unsteadynatural convection boundary-layer flow of air formed adjacent to thevertical plane where solar radiation is absorbed is the key to determine thethermal performance of the systems. For a Pr<1 linearly-stratified fluid,scaling analysis demonstrates that the development of the boundary layer atthe start-up stage is independent of the height but depends on time,while the scaling laws at the steady state stage are quite different fromthose at the end of the start-up stage; they depend only on Pr andthe linear stratification parameter. Direct numerical simulation resultsshow that the scaling laws obtained from the scaling analysis reveal themain dependences, however, they also show that there are further dependenceof the scaling laws on Pr which can be obtained by direct numericalsimulation results.