Governing Equations

It will be fair to say that the early developments in CFD and heat and mass transfer began with calculation of boundary layers. The term boundary layer is applied to long and thin flows: long in the streamwise direction and thin in the transverse direction. The term applies equally to flows attached to a solid boundary (wall boundary layers) as well as to jets or wakes (free-shear layers).

Calculation of boundary layer phenomena received a considerable boost following the development of a robust numerical procedure by Patankar and Spalding. This made phenomena that were either impossible or too cumbersome to calculate by means of earlier methods (similarity, nonsimilarity, and integral) amenable to fast and economic computation. The procedure, for example, permitted use of variable properties, allowed for completely arbitrary variations of boundary conditions in the streamwise direction, and led to several new explorations of diffusion and source laws. Thus, calculation of free or forced flames or wall fires could be carried out by considering the detailed chemistry of chemical reactions. Similarly, calculation of turbulent flows (and development of turbulence models, in particular) could be brought to a substantial level of maturity through newer explorations of diffusion and source laws governing transport of variables that characterise turbulence. Computer programs based on the Patankar–Spalding procedure are available in. There are also other methods, for example, the Keller–Box method described in.