One-Directional Thermogravitational Movement of Viscous Fluid in a Flat Channel with a Given Flow Rate
E. N. Cheremnykh1,2
1Institute of Computational Modeling Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russia, 660036
2Siberian Federal University, Krasnoyarsk, Russia, 660036
Keywords: Oberbeck-Boussinesq equations, convection, numerical experiments
Abstract
This paper touches upon an initial-boundary-value problem that describes the unidirectional thermogravitational 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.
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