Convection in Air water Layer with Side Heating

摘要

This paper explores patterns and stability of the air-water thermal gravitational convection in a thin and wide horizontal container whose top and bottom walls are adiabatic while vertical sidewalls have prescribed different temperatures. A compact polynomial solution describes a slow multi-cell motion and a temperature distribution away from the sidewalls. The solution explicitly shows how the flow topology depends on the water fraction, thermal surface-tension effect, characterized by the Marangoni number Ma, and buoyancy strength characterized by the Grashof number Gr. The performed numerical simulations agree with the analytical solution for small Gr and Ma and describe changes in the flow topology for large Gr and Ma. The flow transforms into a boundary-layer pattern with jets located near the interface and container walls. The jet entrainment generates new cells in the bulk water flow. As Ma increases, the Marangoni stresses focus near the sidewalls and develop a thin thermal boundary layer near the cold wall. The performed stability study reveals that the steady convection is stable for Gr and Ma values considered. The stability is due to the favorable stratification of water density provided by the adiabatic walls. The results can be utilized for the development of efficient heat exchangers.