On the Calculation of Heat and Mass Transfer in Laminar and Turbulent Boundary Layers

The effects of surface topography on momentum and mass transfer in a turbulent boundary layer

“…Taylor ( 1977). However, as in $3, the method of analysis described by Davies & Bourne (1956) was found to be the most convenient to apply to wind-tunnel conditions. This is based on solving equation 14using the velocity profile form (12) with aneddydiffusivity distribution, applying over the main part of the boundary-layer thickness.…”

“…Secondly, it was noted from Davies & Bourne (1956) that an expression for eddy diffusivity, based on experimental results in the flat-plate case, could be written in the form…”

“…The velocity profile ( 1 2 ) was taken to represent u over the limited range of evaporating areas tested on the upwind slope of the ridge. The corresponding E distribution is obtained by using i-/p = ~a u / a y , with T = r 0 = constant, in the region from the surface up to 3 mm say (which determines evaporation or heat transfer), The method of sources described in detail by Davies & Bourne (1956) for a flat surface can now be followed exactly except for the different numerical values of the parameters. They showed that, by neglecting the presence of sub-layers as a first approximation and extrapolating the velocity profile (12) right down to the actual surface, a convenient expression for evaporation from a surface of length 1 could be obtained, which was in good agreement with experiments over flat surfaces.…”

“…The distribution of eddy viscosity was then evaluated for the limited downstream ridge lengths considered. The eddy-diffusivity distribution in the inner layer adjacent to these limited areas of ridge surface follows by applying Reynolds analogy, and a convenient method of calculating evaporation (Davies & Bourne 1956) can be used. This is valid for cases in which the thickness of the momentum boundary layer varies significantly in the downstream direction, and contains a vapour boundary layer whose thickness also varies in this direction.…”

“…The two-dimensionality of the problem restricts its applicability, but the results indicate the considerable changes in gas concentration caused by a curved surface on a turbulent boundary layer. The eddydiffusivity distribution in the inner layer, used to calculate evaporation, does not give good results for concentration profiles, and an expression for eddy diffusivity, applied by Davies & Bourne (1956) over the main thickness of the boundary layer, is modified by assuming an approximate similarity in shape of the velocity profiles over the limited range of the leading slope of the ridge. A solution of the two-dimensional equation is obtained, and experiments on gas concentration distributions over a ridge surface in a wind tunnel are used to test the method of calculation.…”