Effect of particulate thermophoresis in reducing the fouling rate advantages of effusion-cooling

To predict small particle diffusional mass transfer (deposition), including particle thermophoresis, transpiration cooling and variable properties, the coupled ordinary differential equations governing self-similar laminar boundary layers are solved numerically. Under typical combustion turbine conditions, although diffusional deposition rates can be dramatically reduced by transpiration cooling (eg by some 5-decades for mainstream submicron particles corresponding to a Schmidt number of about 10² (or d_p ≈ 0.7 × 10^?2μm) and a wall transpiration-cooled to $\text{T}{}_{\mathrm{<mtext>w</mtext>}}\text{T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.8}$) actual deposition rate reductions will be smaller than previously expected (by about 1 decade for particles with Sc ≈ 10²), owing to thermophoretic particle drift ‘caused’ by the colder wall. Such micro-droplets, small enough to behave like ‘heavy molecules’ in combustion systems, are often important because they can cause adherence of the much larger, supermicron, ash particles which inertially impact on the same surface