Correlation of thermophoretically-modified small particle diffusional deposition rates in forced convection systems with variable properties, transpiration cooling and/or viscous dissipation

Abstract

Rational correlations are developed and presented for making engineering predictions of small particle diffusional deposition rates in the presence of thermophoresis, transpiration cooling, viscous dissipation and/or variable fluid properties. We propose and find that the effects of these phenomena on the convective-diffusion mass transfer Stanton number can be simply expressed in the product form: ▪ where the first function accounts for particle transport by convective processes normal to the deposition surface, and the second function accounts for the spatial variability of the thermophoretic drift velocity, as influenced by viscous dissipation (mainly outside of the Brownian diffusion sublayer). Correlations of this particular form, when tested against rigorous numerical boundary layer (BL) calculations, gave average errors of only 7% for all laminar BL cases (0 ⩽ Ma e ⩽ 2; 0.5 ⩽; T w / T e ⩽ 1; 0 ⩽ α T, p Le ⩽ 1.5; B ⩽ 5), and 2% for all turbulent BL cases (0.5 ⩽ T w/T e ⩽ 1; 0 ⩽ α T,p Le ⩽ 1.5; 0.9 × 10 4 ⩽ Re ⩽ 3 × 10 7; B ⩽ 5), respectively.