A numerical study of fluid flow and heal transfer around periodic cylinder arrays under laminar cross flow conditions is presented. The investigation considers flow in sparse square and triangular arrays, with fluid fractions ranging from 0.80-0.99 and particle Reynolds numbers from about 3-160. Volume averaging of the microscopic flow field variables is used to ascertain the functional form of coefficients appearing in the macroscopic (porous media) equations. Frictional losses are shown to follow Darcy＇s law when the Darcian Reynolds number is of the order of one, while significant non-Darcy effects are seen at higher Reynolds numbers. The validity of the Forchheimer and Ergun correlations is shown to be suspect for flow in this highly porous media. Local thermodynamic equilibrium is relaxed in order to explore cylinder-to-fluid convective heal transfer. Power-law relationships for frictional losses and Nusselt number are shown to correlate Well with detailed simulation results.