Turbulent complex three-dimensional air flow and heat transfer inside a cross-corrugated triangular duct is numerically investigated. Four turbulence models, the standard $k\u2010\epsilon $ (SKE), the renormalized group $k\u2010\epsilon $, the low Reynolds $k\u2010\omega $ (LKW), and the Reynolds stress models (RSM) are selected, with nonequilibrium wall functions approach (if applicable). The periodic mean values of the friction factor and the wall Nusselt numbers in the hydro and thermally developing entrance region are studied, with the determination of the distribution of time-averaged temperature and velocity profiles in the complex topology. The results are compared with the available experimental Nusselt numbers for cross-corrugated membrane modules. Among the various turbulence models, generally speaking, the RSM model gives the best prediction for $2000\u2a7dRe\u2a7d20,000$. However, for $2000\u2a7dRe\u2a7d6000$, the LKW model agrees the best with experimental data, while for $6000<Re\u2a7d20,000$, the SKE predicts the best. Two correlations are proposed to predict the fully developed periodic mean values of Nusselt numbers and friction factors for Reynolds numbers ranging from 2000 to 20,000. The results are that compared to parallel flat plates, the corrugated ducts could enhance heat transfer by 40 to 60%, but with a 2 times more pressure drop penalty. The velocity, temperature, and turbulence fields in the flow passages are investigated to give some insight into the mechanisms for heat transfer enhancement.