To address the issue of insufficient cooling efficiency in traditional thermal management solutions for high-heat-flux electronic devices, this study proposes a coupled model integrating a straight circular turbulent flow channel with a high-heat-flux chip. A carboxymethyl cellulose (CMC)-based Al₂O₃ nanofluid is selected as the working medium. The CMC base fluid exhibits typical linear viscoelastic behavior with notable viscoelastic memory decay characteristics. The addition of Al₂O₃ nanoparticles enhances the thermal conductivity of the fluid while preserving the viscoelastic properties of the base fluid, making it highly compatible with the fractional-order Maxwell constitutive model. Therefore, the Caputo fractional-order Maxwell fluid model is adopted to accurately characterize the viscoelastic memory effects of the CMC base fluid. Through user-defined functions (UDFs) in Fluent, this model is coupled with the k-ω SST turbulence model for numerical simulation. After validating the turbulence model, the influence of fractional-order parameters—namely the relaxation exponent (α) and relaxation time (λ)—on the turbulent flow structure, heat transfer performance, and temperature reduction of the electronic device is systematically investigated. The results demonstrate that the viscoelastic behavior of the fluid and turbulent fluctuations work synergistically to enhance heat transfer. Under optimized fractional-order parameters, a significant cooling effect on the electronic device is achieved. This research provides a novel cooling strategy for high-power electronic devices, and the established fractional-order modeling framework offers a valuable reference for similar thermal design and fluid dynamics studies.