NEW METHODOLOGY FOR THE COMPUTATION OF HEAT TRANSFER IN FREE SURFACE FLOWS USING A PERMEABLE WALL

Abstract

A new computational procedure for determining the structure of the free surface flow of a thin liquid film is presented. The iterative method assumes the free surface to be a porous wall where transpiration through the wall is allowed while it is maintained at constant pressure with no shear stress. The Eulerian computation uses a body-fitting coordinate system and an iterative procedure where successive improvements of the free surface geometry are attained from the velocity components on the free surface. In the final iteration, the transpiration becomes negligibly small and thereby the free surface forms a streamline. This new algorithm has an advantage over existing computational methods in that a complete two-dimensional solution of the flow field and heal transfer coefficient can be obtained and applied to complex flow problems like a hydraulic jump. The computed results include plane and radial flows involving a hydraulic jump and those flows at zero gravity where no jump can be present. The details of the flow structure, the friction coefficient, and the heat transfer coefficient are presented.