Numerical solutions were obtained for the fluid flow in a heat exchanger consisting of an array of diamond-shaped pin fins. The model that underlies the solutions is based on the concept of the periodic fully developed regime, whereby the velocity field repeats itself from row to row and the pressure field also repeats periodically relative to a linear axial decrease. Implementation of the model was accomplished via the finite element method, whereby the solution domain was discretized by subdividing it into an assemblage of two-dimensional, nine-noded quadrilateral elements. As a prelude to the final numerical solutions, a systematic study was performed to establish the number of elements needed for the attainment of accurate results. For validation purposes, solutions were run for arrays of circular cylindrical pin fins (i.e., tube banks) and specific arrays of diamond-shaped pin fins to enable comparisons of pressure drop predictions with available experimental data. The final set of numerical solutions encompassed 18 different arrays, parameterized by the vertex angle of the diamond-shaped fins and by the dimensionless transverse and longitudinal center-to-center distances between the fins. The results presented include representative streamline maps and isobars and an in-depth display of pressure drop information. These results are parameterized by the Reynolds number.