The performance of an explicit algebraic stress model (EASM) is assessed in predicting the turbulent flow and forced heat transfer in both straight and wavy ducts, with rectangular, trapezoidal and triangular cross-sections, under fully developed conditions. A comparison of secondary flow patterns, including velocity vectors and velocity and temperature contours, are shown in order to study the effect of waviness on flow dynamics, and comparisons between the hydraulic parameters, Fanning friction factor and Nusselt number, are also presented. In all cases, isothermal conditions are imposed on the duct walls, and the turbulent heat fluxes are modeled using gradient-diffusion type models. The formulation is valid for Reynolds numbers up to 105 and this minimizes the need for wall functions that have been used with mixed success in previous studies of complex duct flows. In addition, the present formulation imposes minimal demand on the number of grid points without any convergence or stability problems. Criteria in terms of heat transfer and friction factor needed to choose the optimal wavy duct cross-section for industrial applications among the ones considered are discussed.