A transient formulation of entropy and heat transfer coefficients of Newton's cooling law with the unifying entropy potential difference in compressible flows

Abstract

The original Newton's law of cooling is considered an ideal convection model of a point source ignoring conduction, but its unknown convection conductance and inconsistent thermal potential difference make it difficult to further elucidate the transient heat transfer mechanism of convection because of the no-slip condition at the interface between a body and a fluid. For this purpose, both the convective entropy transfer theory and the hypothesis of the isothermal velocity sublayer are developed to recast Newton's law of cooling into a standard Ohm's law form via the unified entropy driving force and the unambiguous entropy transfer coefficient. An explicit expression for the transient heat transfer coefficient is presented theoretically and experimentally in compressible flows by virtue of the product of the free-stream velocity, the volumetric thermal capacity of the fluid, and the near-wall velocity constant. The unified thermal potential difference is established between the body temperature and the total temperature (reduced to the ambient temperature for incompressible fluids). The physical mechanism of convection mode in the original Newton's cooling law is reasonably explained by the entropy transfer theory and entropy transfer efficiency, and the formulae for the entropy flux vector driven by the standard entropy potential difference and the rate of entropy generation are obtained. The analytical heat transfer coefficients as well as the standard thermal driving forces are validated by comparison with the forced convection experiment with a maximum error of 4.6 % in incompressible flows and the previous Newton's benchmark cooling experiments with the maximum error of 6.7 % in compressible flows. The effects of radiation on the total heat transfer coefficient are also analyzed quantitatively.