Skin-Friction and Forced Convection from Rough and Smooth Plates

TL;DR

This paper develops a new theory for skin-friction and heat transfer from rough and smooth plates using self-similar roughness concepts, validated by extensive experimental data, improving accuracy over previous models.

Contribution

It introduces a novel formula based on self-similar roughness to predict skin-friction and heat transfer, addressing limitations of earlier pipe-roughness analogies.

Findings

RMSRE of 0.75% to 8.2% across data-sets

Four data-sets exceeded 6% error, fewer than prior models

New formulas outperform previous ones in accuracy

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 slow velocities has frustrated attempts to create a comprehensive theory. Utilizing the concept of a self-similar roughness which 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.