Examination of a new finite element method applied to convection heat transfer

A new finite element formulation for two-dimensional viscous flow and convection heat transfer is presented. The current method was designed in particular to be competitive with finite difference methods in terms of storage requirements, solution times, and range of applicability. Novel features of the formulation include the use of a streamline upwind approximation for the advection terms and an equal order velocity and pressure approximation.The current paper focuses on the features of the method which allow the formulation to be competitive with available finite difference methods. The method is illustrated by application to two examples including a natural convection example and a forced convection example.