Skin-Friction and Forced Convection from Rough and Smooth Plates

Abstract

Since the 1930s, theories of skin-friction drag from plates with rough surfaces have been based by analogy to turbulent flow in pipes with rough interiors. Failure of this analogy at small fluid velocities has frustrated attempts to create a comprehensive theory. Utilizing the concept of a self-similar roughness that disrupts the boundary layer at all scales, this investigation derives formulas for a rough or smooth plate’s skin-friction coefficient and forced convection heat transfer given its characteristic length, root-mean-squared (RMS) height-of-roughness, isotropic spatial period, Reynolds number, and the fluid’s Prandtl number. This novel theory was tested with 456 heat transfer and friction measurements in 32 data-sets from one book, six peer-reviewed studies, and the present apparatus. Compared with the present theory, the RMS relative error (RMSRE) values of the 32 data-sets span 0.75% through 8.2%, with only four data-sets exceeding 6%. Prior work formulas have smaller RMSRE on only four of the data-sets.

Keywords

• skin-friction
• forced-convection
• height-of-roughness