Unsteady conjugate convective heat transfer in a vertical channel at a sudden heating of the bottom

Abstract

The processes of unsteady heat transfer in the mode of thermogravitational convection in a vertical channel with solid walls of finite thermal conductivity after a sudden heating from bottom was studied numerically by the finite element method in three-dimensional problem statement. The system of thermogravitational convection equations was solved in the Boussinesq approximation in the variables of vortex–vector potential of the velocity field and temperature. The calculations were performed with the Prandtl number of 10, the Grashof number of 5000, and the ratio of the thermal conductivity of solid walls to the thermal conductivity of the liquid equal to 6.29. Distributions of the unsteady temperature field into the liquid and solid walls, temperature gradient fields, and velocity fields in the liquid were obtained. The process of formation, loss of axial symmetry and subsequent development of the rising stream was shown.