Improved Point-Matching Techniques Applied to Multi-Region Heat Transfer Problems

An analytical method is presented which extends the series solution of the Laplace and Poisson equations with irregular boundary conditions to multi-cell problems. The method employs a least-squares technique of satisfying the boundary conditions on the irregular boundaries and eliminates the use of a finite number of boundary points to satisfy these conditions. The technique is applied to the calculation of the fully developed temperature distribution of a constant-velocity fluid flowing parallel to a semi-infinite square array of circular nuclear fuel rods. The bounding wall of the array is located such that the flow area of the cell associated with the rod adjacent to the wall is different from the (equal) areas of all the other cells. The series solution is compared to a finite-difference solution for a sample case of two cells. The results for the semi-infinite array indicate that while the array temperature distribution is markedly affected by the difference in flow areas, the Nusselt numbers of the rods are relatively unaffected. Typical results are presented for a pitch-to-diameter of 1.2; the flow area of the first cell is 3.67 percent greater than the area of the other cells.