A numerical investigation of turbulent forced convection in a three-dimensional channel with periodic ribs on the lower channel wall is conducted. The lower wall is subjected to a uniform heat flux condition while the upper wall insulated. This study was conducted to investigate the forced convection, flow friction, and performance factor in a horizontal air and air/mist cooled rectangular duct, with various shaped ribs. Calculations are carried out for square ribs (case A), triangular ribs (case B), and trapezoidal ribs (case C and case D) cross sections over a range of Reynolds numbers (8000–20,000), constant mist mass fraction (6%), and fixed rib height and pitch. To investigate turbulence model effects, computations based on a finite volume method are carried out by utilizing three turbulence models: the standard k-, Omega Reynolds stress, and shear stress transport turbulence models. The predicted results from using several turbulence models reveal that the shear stress transport turbulence model provides better agreement with available measurements than others. It is found that the average mist cooling enhancement is about 1.8 times. The air/mist provides the higher heat transfer enhancement over air with trapezoidal-shaped ribs (38°, case C).