Modified Grid Clustering Technique to Predict Heat Transfer Coefficient in a Duct of Arbitrary Cross Section Area

Abstract

A simple straightforward mathematical method has been developed to cluster grid nodes on a boundary segment of an arbitrary geometry that can be fitted by a relevant polynomial. The method of solution is accomplished in two steps. At the first step, the length of the boundary segment is evaluated by using the mean value theorem, then grids are clustered as desired, using relevant linear clustering functions. At the second step, as the coordinates cell nodes have been computed and the incremental distance between each two nodes has been evaluated, the original coordinate of each node is then computed utilizing the same fitted polynomial with the mean value theorem but reversibly.

The method is utilized to predict Nusselt number distribution in a hybrid cross section area duct, non-circular non-rectangular, for laminar incompressible flow under Uniform Wall Temperature condition. The results have been compared with the published data and the agreement has been found very well.