Modeling of heat and mass transfer processes in non-linearly viscous fluid film flows

Abstract

The problem of heat and mass transfer in a liquid film of a nonlinearly viscous fluid flowing down the surface of a body of revolution under the influence of gravity is considered. The axis of the body is located at a certain angle to the vertical, and the film of liquid flows down from its top. It is assumed that the thermal and diffusion Prandtl numbers are large and the main changes in the temperature and diffusion fields occur in thin boundary layers near the solid wall and near the free surface separating the liquid and gas. A curvilinear orthogonal coordinate system (ξ, η, ζ) connected with the surface of the body is introduced. To describe the flow of a liquid film, a model of a viscous incompressible liquid is used, which is based on differential equations in partial derivatives - the equations of motion and continuity. As boundary conditions, the conditions of adhesion are used on the surface of a solid body, as well as the conditions of continuity of stresses and the normal component of the velocity vector - on the surface separating the liquid and gas. To simulate heat and mass transfer in a liquid film, the equations of thermal and diffusion boundary layers with boundary conditions of the first and second kind are used. To close the system of differential equations, the Ostwald-de-Ville rheological model is used. To simplify the system of differential equations, the small parameter method is used, in which the relative film thickness is selected. It is assumed that the generalized Reynolds number is of the order of unity. The solution of the equations of continuity and motion (taking into account the main terms of the expansion) is obtained in an analytical form. To determine the unknown film thickness, an initial-boundary-value problem is formulated for a first-order partial differential equation. The solution to this problem is found numerically using a running count difference scheme. To reduce the dimension of the problem for the equations of the boundary layer, the local similarity method is used. To integrate simplified equations, the finite-difference method is used.