Turbulent Flow in a Rectangular Microchannel: Development and Validation of Correlations for Nusselt Number and Friction Factor

Accurate prediction of turbulent heat transfer and pressure drop in rectangular microchannels remains limited, as most existing correlations are constrained by narrow geometric ranges, low Reynolds numbers, or a single working fluid. To address this gap, the present study develops new correlations for the local and mean Nusselt number and the Darcy friction factor in rectangular microchannels with three-sided heating under turbulent flow. To establish the new models, a database of 40 conjugate three-dimensional CFD simulations was generated in ANSYS Fluent using the SST k-ω turbulence model. The simulations span hydraulic diameters of 200?1000 µm, aspect ratios of 0.25-2, Reynolds numbers of 2500-12,000, and Prandtl numbers of 4-12.5, covering a substantially broader parameter space than previously available studies. The resulting correlations incorporate the effects of asymmetric heat input and wall conduction, and are validated against in-house experiments using both water and acetone. All predictions remain within the ±15% experimental uncertainty. The proposed closed-form correlations are straightforward to implement and offer reliable predictive capability for the design and optimization of microchannel heat sinks operating under realistic three-wall heating conditions.