THE ONSET OF CONVECTION CAUSED BY BUOYANCY DURING TRANSIENT HEAT-CONDUCTION IN DEEP FLUIDS

The onset of convection in a thermal layer generated by transient heat conduction in deep fluid is examined. It is generally accepted that b uoyancy driven convection predominates in deep fluids while surface te nsion driven convection can occur only in very thin layers of liquid. The occurrence of buoyancy convection can be predicted from convention al linear stability analysis for steady-state heat conduction. Its res ults are summarised in terms of critical Rayleigh numbers. The point o f instability in transient heat conduction is, however, less well unde rstood. Its onset in deep fluids is determined by the mode and rate of cooling. In this paper, the judicial application of transient heat co nduction equations and a newly defined transient local Ra with the app ropriate boundary conditions has allowed the tracking of the time and spatial development of local hydrodynamic equilibrium to the point of instability. The onset of convection can be predicted from the maximum transient Ra whose values are the same as those previously obtained b y linear stability analysis for the same boundary conditions. The crit ical times and critical depths for stable diffusion in fluids (i.e. wi thout convection) can thus be determined accurately. Agreement with ob served values from the literature is very good. The mode and rate of h eat conduction are confirmed to be the controlling factors in determin ing the time of onset of convection. Copyright (C) 1996 Elsevier Scien ce Ltd