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Suhas V. Patankar
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, and Innovative Research, Inc., Plymouth, MN 55447, USA


The prediction of the heat transfer behavior in a given physical configuration is useful in many practical situations. The prediction can be achieved by the generalization and extension of available experimental data or by the solution of a mathematical model describing the physical problem. Because most practical situations are governed by numerous parameters, the acquisition and generalization of the relevant experimental data is often too expensive if not impossible. On the other hand, the solution of an appropriate mathematical model can be accomplished at a much lower cost. Numerical methods, thus, play a major role in the prediction of practical heat transfer situations.
Numerical methods for conduction are well-established, but the treatment of convection presents new challenges. In the presence of fluid flow, the temperature at a given point is very strongly influenced by the region on the upstream side and only weakly by the downstream points. Unless numerical methods account for this unsymmetrical behavior, the solutions can become physically unrealistic as well as difficult to obtain. Therefore, methods that contain some element of "Upstream weighing" are preferable. Many such methods have been proposed in recent years, some of them are discussed here.
Since convective heat transfer is based on an underlying fluid flow, the numerical analyst is also faced with the task of solving the equations of motion. This is a more difficult task since the momentum and continuity equations are coupled in a special way. Again successful numerical methods have been developed for this purpose, some of which are discussed in the paper.
Finally, the tasks for future research are outlined.

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