This paper presents a derivation of the empirical Colburn analogy and discusses its implications. Key words: heat transfer, Colburn, j factor, turbulence, power law, log-law, wall layer
The physical background behind the success of the Sieder-Tate correction in heat transfer is analysed. The equivalent correction for mass transfer correlations is based on the ratio of diffusivities at the wall and bulk concentrations. This correctio
n is not required if the Prandtl/Schmidt numbers are evaluated at the wall layer conditions and the Reynolds number at the bulk conditions. This technique brings heat and mass transfer coefficients into agreement.
This paper presents a technique that collapses existing experimental data of heat transfer in pipe flow of Newtonian and power law fluids into a single master curve. It also discusses the theoretical basis of heat, mass and momentum analogies and the
implications of the present analysis to visualisations of turbulence.
Numerous studies in the past 40 years have established that turbulent flow fields are populated by transient coherent structures that represent patches of fluids moving cohesively for significant distances before they are worn out by momentum exchang
e with the surrounding fluid. Two particular well-documented structures are the hairpin vortices that move longitudinally above the wall and ejections inclined with respect to the wall that bring the fluid from the transient viscous layers underneath these vortices into the outer region of the boundary layer. It is proposed that the Karman universal constant in the logarithmic law the sine of the angle between the transient ejections and the direction normal to the wall. The edge of the buffer layer is represented by a combination of the Karman constant and the damping function in the wall layer. Computation of this angle from experimental data of velocity distributions in turbulent shear flows matches published traces of fronts of turbulence obtained from the time shifts in the peak of the correlation function of the velocity. Key works: Turbulence, coherent structures, Karman constant, mixing-length, shear layers
