ON THE NUSSELT MODULUS AS A FUNCTION OF FRICTION FACTOR, REYNOLDS AND PRANDTL MODULI, FOR HEAT TRANSFER TO A FLUID FLOWING TURBULENTLY THROUGH A TUBE OF CIRCULAR SECTION

Abstract

Theoretical expressions for the Nusselt modulus and radial temperature distribution in terms of Reynolds number, Prandtl number, the ratio k of the eddy diffusivities for heat and momentum, and the friction factor are developed for the case of heat transfer from a tube of circular section to a fluid flowing turbulently through it. The results, appropriate to fluids with Prandtl numbers greater than 1/2k, are derived on the assumption of the constancy of fluid properties and require a linear longitudinal temperature gradient in the tube itself. They enable the effect of the insulating "laminar" and "buffer" layers adjacent to the tube wall to be demonstrated at various Prandtl numbers and are appropriate for correlation with experiment for the investigation of the constancy or otherwise of the ratio of the eddy diffusivities for heat and momentum implicit in the momentum transfer analogy.A similar result is worked out on the vorticity transfer analogy for the particular case of Prandtl number equal to 1/k′ and is found to be invalid for such a configuration. Here k′ is the ratio of the eddy diffusivities for heat and vorticity.