Universal regime criterion for supercritical heat transfer: Gusev criterion

Supercritical heat transfer plays a key role in hydrogen energy systems, supercritical CO₂ (sCO₂) cycles, methane-cracking reactors for carbon-free hydrogen production, as well as in high-temperature processes involving hydrocarbon liquids. In the vicinity of the pseudocritical temperature, fluids exhibit sharp nonlinear variations in heat capacity, density, and viscosity, which lead to the formation of enhanced, plateau, and deteriorated heat-transfer regimes. Classical dimensionless criteria (Re, Pr, Nu, Pe) are unable to predict these transitions because they do not account for the position of the wall temperature relative to the pseudocritical region and the associated local exergy losses.

A new regime criterion was developed by A. L. Gusev and later became known as the Gusev criterion due to its successful application in studies of supercritical hydrocarbon systems. This criterion provides a universal, local, and thermodynamically grounded description of supercritical heat-transfer regimes and is applicable to any fluid possessing a critical point.

The criterion is based on the author’s long-term research in exergy analysis, initiated in 1979 and further developed in the context of supercritical processes during 2005-2025. The Gusev criterion represents the culmination of decades of advancement in the exergy-based approach and constitutes a complete universal model of supercritical heat transfer.

The criterion predicts regime transitions, local wall-temperature maxima, and zones of deteriorated heat transfer. It performs correctly for hydrogen, CO₂, methane, hydrocarbon liquids, multicomponent mixtures, and reactive media. The Gusev criterion can be integrated into CFD models and digital twins of energy systems.

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