A successful general fluid-to-fluid similarity theory for heat transfer at supercritical pressure

The present paper introduces a successful and general fluid-to-fluid similarity theory for heat transfer to fluids at supercritical pressure, having a high degree of universality. This work shortly follows the recent publication of a “local” successful similarity theory developed for fluids at supercritical pressures in a range of conditions in which the values of their molecular Prandtl number were quantitatively similar, extending its conclusions to the case of different molecular Prandtl numbers. The reason why this further step requested a short time to be elaborated is due to recognising that previous work by the Authors had actually already solved the related problems, though in a slightly different way, now interpreted in a more significant frame owing to a better problem understanding. The present similarity theory is based on first ideas developed more than one and a half decade ago by one of the authors, while addressing flow stability of supercritical fluids in heated channels, which encountered immediate problems to be applied in a straightforward way to heat transfer. These ideas were revised and considerably improved during the PhD thesis of the other author, also overcoming a sort of prejudicial assumption that finally resulted to limit their applicability. More recently, published DNS data triggered further reflections on the role of the Prandtl number, leading to the mentioned “local” form of the successful similarity theory. This led to the present step, by just recognising that the mentioned PhD thesis had already proposed a sufficient rationale to extend this local interpretation to a broader range of conditions. The rather convincing results presented herein, obtained making use of RANS CFD analyses with four different fluids, demonstrate the interesting capabilities of this final form of the theory. The establishment of an effective set of dimensionless numbers for heat transfer problems is hoped to pave the way for the development of the still lacking successful engineering heat transfer correlations for supercritical pressure fluids. It further calls for dedicated experiments needed to confirm the suitability of the present theory beyond any reasonable doubt.