Application of the finite element method to natural convection heat transfer from the open vertical channel

The finite element method is used together with the variational principle of the local potential to obtain approximate numerical solutions for steady-state laminar natural convection from the open vertical channel with uniform wall temperature. The natural boundary conditions generated by the variational technique are invoked at the channel entrance and exit. The restriction has so far been observed that fluid velocity may be vertical only. Temperatures and upward velocities respectively are obtained for Rayleigh and Grashof number ranges from 0.1 to 10,000,000. Nusselt and Reynolds number correlations compare very closely with those for the finite difference solution by Bodoia and Osterle, and less well with a solution for the single vertical wall.