Raising the turbine inlet gas temperature is an effective strategy for improving turbomachinery efficiency; however, it imposes severe thermal loads on turbine blades. To enhance blade cooling performance, this study employs computational fluid dynamics (CFD) to investigate the influence of sinusoidal ribs on turbulent flow and heat transfer in rectangular internal cooling channels. Numerical simulations demonstrate that sinusoidal rib configurations achieve superior heat transfer enhancement with reduced pressure losses across a wide Reynolds number range (Re = 20,000–90,000) compared to conventional transverse rib geometries. This improvement is quantified by higher normalized Nusselt numbers (Nu/Nu0) and lower normalized friction factors (f/f0). Through systematic parametric analysis, the study elucidates how key geometric parameters—amplitude, wave number, and rib height—regulate flow and heat transfer performance. The study ranks nine pre-specified sinusoidal rib configurations under uniform heat flux conditions and identifies SR-I and SR-C as top performers for different design criteria, providing quantitative guidance for the preliminary design of turbine blade cooling channels.