  The investigation of thermal convection of a fluid with the dependence of
thermal diffusivity on temperature in a vertical Hele Shaw cell heated from
below has been fulfilled theoretically.The expression for equilibrium
temperature distribution in a cavity has been derived analytically. It has been
found that the dependence of temperature on the vertical coordinate looks like
a square rootlaw.The linear stability of mechanical equilibrium state against
small normal perturbations has been investigated by means of Galerkin method.
It has been shown that the most dangerous perturbation in a cavity under
considerationis described by the mode which corresponds to the two vortexsteady
flow. The numerical simulation of overcritical steady and oscillatory flows has
been carried out in the approximation of plane trajectories.This simplification
of theoretical modelis consistent with all experimental data on thermal
convection in similar cavities. It has been shown that the inclusion of the
dependence of thermal diffusivity on temperature into the mathematical model
leads to the up down symmetry breakdown for the small values of over
criticality.
