Abstract
The onset of convection in the Benard problem (i.e. the determination of the critical Rayleigh number) is determined, taking into account the temperature dependence of the kinematic viscosity and the expansion coefficient. The same problem is also solved when a small laminar flow is superimposed. These two problems are solved by two different techniques: a variational formulation, using the notion of ‘local potential’ and an exact numerical solution utilizing a Runge-Kutta procedure to give an improved estimate of the critical numbers. A special interest is given to the comparison between the two methods.
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