The onset of buoyancy-driven convection in fluid layers with temperature-dependent viscosity

A theoretical analysis of thermal instability driven by buoyancy forces under a time-dependent temperature field of conduction is conducted in an initially quiescent, horizontal liquid layer. The dependency of viscosity on temperature is considered and the propagation theory is employed for the stability analysis. For large Prandtl number systems, the critical condition of the onset of buoyancy-driven convection is obtained as a function of the Rayleigh number and also the viscosity contrast and it is compared with available experimental data. It is evident that the growth period is required until the growing instabilities are detected experimentally, which is dependent upon the viscosity contrast.