Finite element simulation of thin liquid film flow and heat transfer including a hydraulic jump

A numerical simulation has been performed to investigate planar and radial #ows of thin liquid "lm subject to constant wall temperature or constant wall heat #ux, considering the surface tension e!ect. To simulate the variation of the "lm height including a hydraulic jump, an Arbitrary Lagrangian}Eulerian (ALE) method is adopted in describing the governing equations. An iterative split algorithm is used to improve the continuity constraint in time marching of the governing equations which are discretized by Streamline Upwind Petrov}Galerkin (SUPG) "nite element method. It has been shown clearly that the surface tension has to be considered in order to describe realistically a hydraulic jump preceded by a capillary ripple. The variation of the "lm height is in good agreement with the existing experimental data. Physical aspects of how the #owrate as well as temperature-dependent #uid properties a!ect the formation of the hydraulic jump and the variation of the Nusselt number are discussed rationally