A new finite element technique for the analysis of heat transfer problems

Steady 2D natural convection in a square enclosure and forced convection in a fully developed flow in a transverse plate array are investigated numerically using a hybrid finite-element method. The method is based on a formulation using stream function, vorticity, and temperature, integrating the vorticity-transport and energy equations in a small control volume to obtain a vorticity and energy conservation law. These equations and the vorticity/stream-function relation are treated using simple triangular finite elements. Numerical results are presented graphically and compared to those obtained by upwind-finite-element and conventional finite-difference methods. Good agreement is found with the finite-difference results; stability is maintained at high Rayleigh numbers; and better accuracy is obtained than with the upwind method.