A phenomenological model for the heat transfer coefficient in turbulent pipe flow of power-law (PL) fluids is developed. The analysis employs a two-layer approach, separating the flow into a viscosity-dominated inner region and a turbulence-dominated outer region. By leveraging a scaling framework rooted in Kolmogorov's theory of turbulence, we derive a semi-empirical heat transfer correlation analogous to the Prandtl-Taylor analogy for Newtonian fluids. A key contribution is the introduction of a new dimensionless group, the power-law Prandtl number (${\mathrm{Pr}}_{PL}$), defined to be independent of the Reynolds number, thereby allowing for a more fundamental characterization of heat transfer in these systems. The model incorporates a single calibration function, $c_h\left(n\right)$, which depends on the power-law index $n$ and captures the influence of non-Newtonian rheology on the sublayer-to-core thermal resistance partitioning. This function is calibrated using established literature data for Carbopol solutions. The proposed correlation demonstrates excellent agreement with experimental results across a wide range of Reynolds and Prandtl numbers, achieving a normalized root-mean-square error of 1.14% with the polynomial calibration and exhibiting superior predictive accuracy compared to classical models.

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• Heat transfer
• Turbulence
• Complex fluids
• Non-Newtonian fluids