Convective Transport Finite Element Analog

A finite element method for solving two-dimensional steady convective heat transfer problems is presented and applied to three test cases for verification. The fully nonlinear momentum equations are cast in fourth-order streamfunction form and functionals for the heat and streamfunction equations are formed by the Galerkin Method. Cubic interpolants are used to form the stiffness matrices and a Newton Raphson weighted average iteration scheme is used to solve the coupled problem. Three cavity problems are analyzed: (1) A shear driven homogeneous cavity; (2) the hot wall cavity problem; and (3) a shear driven stably stratified cavity problem. Nonlinear solutions to the last two problems were achieved by incremental loading. When compared to previous solutions the approach is very stable and converges quite rapidly with a minimum of computer storage.