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Effect of thermophoresis on submicron particle deposition from a forced laminar boundary layer flow onto an isothermal moving plate

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Summary

Similarity solutions for the problem of a continuously moving surface in a stationary incompressible fluid, including the combined effects of convection, diffusion, wall velocity and thermophoresis are derived for the case in which both the surface temperature and stretching velocity vary as a power law. Calculations for an isothermal moving plate clearly show the importance of thermophoresis on particle deposition.

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Abbreviations

A :

Arbitrary constants

B :

Arbitrary constants

C :

Non-dimensional particle concentration

D :

Brownian diffusion coefficient\(\left( { = \frac{{K_B T}}{{3\pi \mu d_p }}} \right)\)

d p :

Particle diameter

f :

Non-dimensional stream function

Gr:

Grashof number

g :

Gravitational acceleration

H :

Non-dimensional temperature

I :

Parameter of thermophoretic effect\(\left( { = \frac{{T_\infty }}{{T_w - T_\infty }}} \right)\)

k :

Thermophoretic coefficient

K B :

Boltzmann constant (1.38×10−23 J/K)

L :

Characteristic length

n :

Arbitrary constants

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

r p :

Particle radius

Sc:

Schmidt number

Sh:

Sherwood number

T :

Absolute temperature

u :

Non-dimensional velocity inx-direction

v:

Non-dimensional velocity iny-direction

vt:

Thermophoretic velocity

V d :

Deposition velocity of particle

V d o :

Diffusional deposition velocity of particle

V d th :

Deposition velocity of particle with the effect of thermophoresis

x, y :

Cartesian co-ordinates

ψ:

Stream function

η:

Similarity variable

τ:

Fluid shear stress or relaxation time of particle

μ:

Viscosity of fluid

v :

Kinematic viscosity

λ:

Mean free path of gas molecules

β:

Volumetric coefficient of thermal expansion (=1/T ∞ for an ideal gas)

o :

Reference conditions

w :

Wall conditions

∞:

Conditions far from the surface

′:

Dimensional values

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  1. M. C. Chiou

    Present address: Department of Vehicle Engineering, National Huwei Institute of Technology, 64 Wenhua Road, Huwei, Yunlin, Taiwan

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    Chiou, M.C. Effect of thermophoresis on submicron particle deposition from a forced laminar boundary layer flow onto an isothermal moving plate. Acta Mechanica 129, 219–229 (1998). https://doi.org/10.1007/BF01176747

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    • DOI: https://doi.org/10.1007/BF01176747

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