A general numerical method for the prediction of convective heat and mass transfer processes has been formulated. The method has been designed to handle irregular-shaped domains and work with highly non-uniform grids. In its present form, the method is capable of solving steady, plane two-dimensional elliptic problems. The formulation is based on primitive variables, however, and its key ideas do not have any inherent limitations with respect to their extension to unsteady, three-dimensional problems. Further, considerable importance has been attached to the interpretation of the formulation in terms of physically meaningful quantities like fluxes, forces, and sources and an effort has been made to avoid the use of any mathematical notation that may be unfamiliar to the practicing engineer.

In problems which do not involve the calculation of fluid flow, the calculation domain is discretized into three-node triangular elements. In all other problems, the domain is first discretized into six-node triangular macroelements;​ then each macroelement is divided into four three-node triangular subelements. No restrictions are placed on either the shape or the size of these elements. Following this domain triangulation, each node is associated with a polygonal control volume.

The nature of the problem being solved determines the forms of the interpolation functions for the dependent variables. In conduction- type problems, all dependent variables are interpolated linearly in each three-node element. In problems involving fluid flow, however, special interpolation functions are used in each three node element, for all dependent variables except pressure. These interpolation functions are exponential in the direction of an element-averaged velocity vector and linear in a direction normal to it;​ they respond to an element Peclet number, reducing to a completely linear form when it approaches zero. The use of these functions enables the proposed method to successfully handle problems in the low to high Peclet number range.

In the formulation of the proposed method, appropriate conservation laws are imposed on the polygonal control volumes associated with the nodes. The resulting sets of integral conservation equations are then approximated by algebraic equations, using the interpolation functions discussed above. These algebraic equations, which are non- linear and coupled, in general, are solved by an iterative procedure similar to the method of successive approximations. In each cycle of this procedure, the pressure, the velocity components, and all other dependent variables are solved for in a sequential manner. programs.

The proposed method has been implemented in a number of computer Using these programs, several test problems have been solved. These include conduction-type problems, convection-diffusion problems, fluid flow problems, forced convection problems, and a natural convection problem. Whenever possible, the solutions to these problems have been compared with either analytical solutions or solutions available in the published literature. The results are very encouraging.