This paper presents the large eddy simulation (LES) results of turbulent heat and fluid flows in a straight square duct (SSD) at higher Reynolds numbers ranged from 10(4) to 10(6), which are based on the bulk mean velocity and the duct cross-sectional side length. A sub-grid model is proposed, which assumes that the sub-grid stress and heat flux are, respectively, proportional to the temporal increments of the filtered strain rate and temperature gradient, with the proportional coefficient determined by calibrating the friction factor. The temperature was taken as passive due to the neglect of buoyancy effect. The Taylor and Kolmogorov scales in the SSD are predicted and the results show that the LES results are better than c-DNS results. The LES results can explain why the c-DNS is applicable to the problem at a moderate Re, and reveal that the largest relative deviation of the overall mean Nusselt number is less than 10% as compared with existing experimental correlations. With the rise of Reynolds number, the mean secondary vortex pairs move towards the corners and have smaller size, while smaller vortices also occur in the instantaneous secondary flow. Empirical mode decomposition (EMD) was carried out to analyze the fluctuation of the x-averaged cross-sectional origin temperature at Re = 10(5). (C) 2009 Elsevier Ltd. All rights reserved.