A second-order approximation to natural convection for large Rayleigh numbers and small Prandtl numbers

The present investigation is concerned with a problem described by Schultz (1973), who provided a numerical solution for the flow of a fluid in a heated closed cavity. The procedures employed by various investigators to obtain numerical results for this problem are evaluated. No evidence is found that any one of the considered methods have produced results for large Rayleigh numbers and small Prandtl numbers with small grids and second order boundary approximations. The current investigation provides a method which produces such results. The selected procedure involves the use of a rectangular array of nodes which is placed over the region considered in the problem. The solution of the obtained difference equations is discussed, and the results are presented in a number of tables and graphs. It is found that the employed second-order method is superior to the method used by Schultz.