Heat transfer coefficients for fully developed internal flows with variable properties and dissipative heating

Abstract

In this paper, numerical simulations of fully developed internal flows are used to disentangle the effects of hydrodynamic and thermal boundary conditions, as well as viscous heating and property variation. Each factor affecting heat transfer is introduced independently to elementary flow simulations, such that 1D analyses may be used to characterise its effects.

Conventional adiabatic wall temperature correlations for accounting for dissipative heating were found to lose their effectiveness when dissipation makes up more than 10% of total heat flux. A more robust method is proposed whereby heat transfer is defined by separate dissipative and convective Stanton numbers. Property variation was found to be well characterised by modified film referencing, with a new formulation proposed which outperforms the classical form. Property variation could also be accounted for by power-laws on temperature ratio, but the results suggest that the exponents are not universal. It was also found that such corrections apply equally to heated and cooled flows when confounding factors are effectively controlled.

Friction and heat transfer results are then generated for more complex flows over a range of temperature gradients, with realistic constitutive relations such that all phenomena occur simultaneously. Without appropriate correction, the results appear highly scattered for both low (due to dissipation) and high (due to property gradients) temperature ratio heat transfer. The methods developed successfully condense these results onto a single unequivocal $Re$-$f$-$\mathrm{St}$ characteristic. The isolation of this characteristic from these secondary factors is invaluable for making valid comparisons between variable-property CFD results and experiments.

This investigation focuses on air at moderate temperatures, however the findings may be expected to take on greater significance in high Mach, high Prandtl number, or cryogenic applications.