In this study, numerical simulations by single- and two-phase models of nanofluids turbulent forced convection in a three-dimensional arc rib-grooved channel with constant wall temperature are investigated. The elliptical, coupled, steady-state, three-dimensional governing partial differential equations for turbulent forced convection of nanofluids are solved numerically using the finite volume approach. The average Nusselt number of arc rib-grooved channels is found to improve more with smaller rib-grooved height ratios, and some ratios of arc rib-grooved pitch. In addition, the optimization of this problem is also presented by using the response surface methodology (RSM) and the genetic algorithm (GA) method. It is found that the objective function E is better at Re=10,000, and the arc rib-groove has a 42.1% enhancement.