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

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... gated 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.