SOLUTION OF THE PILE EQUATION FOR A BARE CYLINDRICAL SYSTEM OF HEXAGONAL CROSS-SECTION
K.C. Hines, D.W. Holbrough · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1957
It is shown that the diffusion equation for a cylindrical reactor with hexagonal cross-section may be solved as an infinite series, the terms of which involve Bessel functions of order 6n, where n = 0, 1, 2,...... for the successive terms of the series. Considering in succession additional terms of the series a sequence is obtained for the eigenvalue which converges rapidly. In this way a value is found for the eigenvalue of a bare system. The contour of zero flux was evaluated in the approximations for which one, two......, terms of the series solution were included. When three terms are included this contour of zero flux was found to follow the hexagonal boundary quite closely. (auth)