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The problem of forced convection in a cell of plane-parallel layer of nematic liquid crystal, both the boundaries of which are free and isothermal, has been discussed. However much artificial seem the boundary conditions first proposed by Rayleigh, these permit an obtaining of simple exact solution of the boundary value problem, by means of which some most important features of the problem are elucidated. In particular it proved possible to excite convective motions in the absence of reorientation of the liquid crystal director.