ANALYTICAL MODELING OF COMPLEX HEAT EXCHANGE UNDER FREE CONVECTION ON A VERTICAL PLATE

Abstract

The purpose of this article is to analytically model a complex heat transfer process that includes radiation heat transfer, natural convection, and slip conditions on a flat surface immersed in a stationary gas.

Research into the combined effect of natural convective heat transfer with thermal radiation is an integral part of solving heat transfer problems, providing an understanding of the fundamental concepts of changing the dynamics of a working fluid.

This article analytically describes the case of stationary natural convection near a heated vertical plate placed in a large volume of gas. The gas is stationary and has a constant temperature T∞. The temperature of the heated plate Tw is also constant. We consider the case Tw > T∞. The results obtained will also be valid for the case Sr >> 1.

As a result of mathematical transformations, equations for the velocity and temperature profiles, average velocity, flow rate, thickness of the boundary moving layer, and the Nusselt number are obtained. During the solution of the problem, it was found that the increase in the slip effect accelerates the boundary layer due to the presence of convection and a velocity jump on the surface. The radiation effect gives a slight acceleration of the boundary layer. The obtained Nusselt number distributions showed that the effect of radiation significantly intensifies the heat transfer process, in contrast to the slip effects, which almost do not affect the dynamics of heat transfer improvement.