The analysis of two-dimensional fluid flow and heat transfer problems in a finite rod bundle system can be effectively handled by superpositioning the effects of all cylindrical rods present. This method is not limited to symmetrical rod arrangements but can be applied to rods with arbitrary dimensions and orientations. The solution method is illustrated by solving the Poisson and the Helmholtz equations. Numerical results are presented for the solution of the Helmholtz equation in a circular flow channel containing a center rod and a ring with six peripheral rods and with Dirichlet boundary conditions specified on the wall surfaces.