A Theoretical Analysis of the Recovery Factor for High Speed Turbulent Flow,
Experimental data for turbulent boundary-layer and tube flow of air generally are in support of this relationship. A semi-empirical formulation also has been proposed for the recovery factor by Rotta which is in agreement with equation. This formulation is based on the usual eddy-diffusivity approach to turbulence.
In order to provide additional insight into the effects of viscous dissipation, a very simple and straightforward formulation is now presented for the recovery factor on the basis of surface-renewal-and-penetration model. This model was first set forth by Dankwerts for turbulent mass transfer at a fluid-solid interface, but has been subsequently adapted to a broad range of turbulent transport processes for fluid-solid interfaces. The elementary surface-renewal-and-penetration model is based on the assumption that eddies intermittently move from the turbulent core into the close vicinity of the transport surface. During the residency of elements of fluid at the surface, simple one-dimensional unsteady molecular transfer is assumed to occur.
Journal of Heat Transfer
Thomas, L. C. and Chung, Benjamin T.F., "A Theoretical Analysis of the Recovery Factor for High Speed Turbulent Flow," (1973). Mechanical Engineering Faculty Research. 1036.