A detailed computational study was performed for the case of a wall-bounded pin-fin-array in a staggered arrangement, representative of industrial configurations designed to enhance heat transfer. In order to evaluate the level of turbulence modelling necessary to accurately reproduce the flow physics at three (3) different Reynolds numbers (3, 000, 10, 000 and 30, 000), four models were selected: two eddy-viscosity URANS models (k-ω-SST and φ-model), an Elliptic Blending Reynolds-stress model (EB-RSM) and Large Eddy Simulation (LES). Global comparisons for the pressure loss coefficients and average Nusselt numbers were performed with available experimental data which are relevant for industrial applications. Further detailed comparisons of the velocity fields, turbulence quantities and local Nusselt numbers revealed that the correct prediction of the characteristics of the flow is closely related to the ability of the turbulence model to reproduce the large-scale unsteadiness in the wake of the pins, which is at the origin of the intense mixing of momentum and heat. Eddy-viscosity-based turbulence models have difficulties to develop such an unsteadiness, in particular around the first few rows of pins, which leads to a severe underestimation of the Nusselt number. In contrast, LES and EB-RSM are able to predict the unsteady motion of the flow and heat transfer in a satisfactory manner.