Unidirectional Heat-Gravitational Motion of Viscous Fluid in A Flat Channel with A Given Flow Rate

This paper touches upon an initial-boundary-value problem that describes the unidirectional heat-gravitational motion of fluid in a plane channel in the case of solid immobile upper and lower walls with temperature distribution thereon and in the case of a heat-insulated upper wall. The motion is caused by a joint effect of the longitudinal temperature gradient and given nonstationary flow rate. The initial-boundary-value problem is inverse relative to the pressure gradient along the channel. An exact stationary solution is obtained. A solution of the nonstationary problems in Laplace images is determined, and the results of numerical calculations are presented.