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Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder

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Summary

Consideration is given to analyse the sub-micron deposition from a laminar free convection boundary layer developing on a heated isothermal vertical cylinder. A finite-difference method, as proposed by Cebeci and Smith [28], has been used to theoretically calculate the local cumulative particle deposition, with the thermophoretic velocity being that proposed by Talbot et al. [19]. It was demonstrated that the thermophoresis has a pronounced effect on the particle transfer but only a slight effect on the very smaller particles (<0.01 μm) and that the effect increases with particle size and distance along the cylinder. Experiments were also conducted using mono-disperse flourescent uranin, particles with mean diameter of 0.05 μm. A calibrated flourimeter was used to measure the mass of the particles deposited at different axial locations of the cylinder. Results showed similar trends to the theoretical model, but absolute values of the deposits were greater than theoretical predictions.

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Abbreviations

C :

Non-dimensional particle concentration

D :

Brownian diffusion coefficient (K BT/(3πμdp))

d p :

Particle diameter

f :

Non-dimensional stream function

g:

Gravitational acceleration

H :

Non-dimensional temperature

k :

Thermophoretic coefficient

K B :

Boltzmann constant (=1.38×10−23 J/K)

N :

Particle flux

N t :

Dimensionless thermophoresis parameter (k(Tw−T∞)/T∞)

Pr:

Prandtl number

r :

Radius co-ordinate

r o :

Radius of solid rod

Sc:

Schmidt number

T :

Absolute temperature

u :

Velocity inx-direction

v :

Velocity iny-direction

v t :

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 :

Cartesian co-ordinates

ψ:

Stream function

η:

Similarity variable

ξ:

Stretchedx co-ordinate

μ:

Viscosity of fluid

υ:

Kinematic viscosity

α:

Coefficient of thermal reflection

β:

Volumetric coefficient of thermal expansion

o :

Reference conditions

w :

Wall conditions

∞:

Conditions far from the surface

References

  1. Fiebig, M., Hilgenstock, M., Riemann, H. A.: The modified chemical vapor deposition process in a concentric annulus. Aerosol Sci. Tech.9, 237–249 (1988).

    Google Scholar 

  2. Weinberg, M. C.: Thermophoretic deposition of particles in laminar flow in a concentric annulus. J. A. Ceram. Soc.66, 439–443 (1983).

    Google Scholar 

  3. Otani, Y., Emi, H., Kanaoka, C., Kato, K.: Determination of deposition velocity onto a wafer for particles in the size range between 0.03 and 0.8 μm. J. Aerosol Sci.20, 787–796 (1989).

    Google Scholar 

  4. Cooper, D. W., Miller, R. J., Wu, J. J., Peter, M. H.: Deposition of submicron aerosol particles during integrated circuit manufacturing: Theory. Part. Sci. Techn.8, 209–224 (1990).

    Google Scholar 

  5. Ye, Y., Pui, D. Y. H., Liu, B. Y. H., Opiolka, S., Blumhorst, S., Fissan, H.: Thermophoretic effect of particle deposition on a free standing semiconductor wafer in a clean room. J. Aerosol. Sci.22, 63–72 (1991).

    Google Scholar 

  6. Goren, S. L.: Thermophoresis of aerosol particles in the laminar boundary layer on a flat surface. J. Colloid Interface Sci.61, 77–85 (1977).

    Google Scholar 

  7. Gokoglu, S. A., Rosner, D. E.: Thermophoretically augmented mass transfer rate to solid walls across laminar boundary layers. AIAA J.24, 172–179 (1986).

    Google Scholar 

  8. Park, H. M., Rosner, D. E.: Combined inertial and thermophoretic effects on particle deposition rates in highly loaded systems. Chem. Eng. Sci.44, 2233–2244 (1989).

    Google Scholar 

  9. Walker, K. L., Homsy, G. M., Geyling, F. T.: Thermophoretic deposition of small particles in laminar tube flow. J. Colloid Interface Sci.107, 21–37 (1979).

    Google Scholar 

  10. Stratman, F., Fissan, H.: Non-dimensional investigation of sub-micron particle transport on cooled laminar boundary layer tube flow. J. Aerosol Sci.22, 211–214 (1991).

    Google Scholar 

  11. Yarin, A. L., Nudlina, T. L.: Thermophoretic deposition of fine particles from longitudinal flow over a cylinder. J. Aerosol Sci.23, 87–95 (1992).

    Google Scholar 

  12. Hales, J. M., Schwendiman, L. C., Horst, T. W.: Aerosol transport in a naturally-convected boundary layer. Int. J. Heat Mass Transfer15, 1837–1850 (1972).

    Google Scholar 

  13. Mills, A. F., Wassel, A. T.: Aerosol transport in a thermally driven natural convection boundary layer. Lett. Heat Mass Transfer2, 159–168 (1975).

    Google Scholar 

  14. Mills, A. F., Hang, X., Ayazi, F.: The effect of wall suction and thermophoresis on aerosol particle deposition from a laminar boundary layer on a flat plate. Int. J. Heat Mass Transfer27, 1110–1113 (1984).

    Google Scholar 

  15. Epstein, M., Hauser, G. M., Henry, R. E.: Thermophoretic deposition of particles in natural convection flow from a vertical plate. J. Heat Transfer107, 272–276 (1985).

    Google Scholar 

  16. Nazaroff, W. W., Cass, G. R.: Particle deposition from a natural convection flow onto a vertical isothermal flat plate. J. Aerosol Sci.18, 445–455 (1987).

    Google Scholar 

  17. Sasse, A. G. B. M., Nazaroff, W. W., Grdgil, A. J.: Particle filter based on thermophoretic deposition fro natural convection flow. Aerosol Sci. Tech.20, 227–238 (1984).

    Google Scholar 

  18. Minkowycz, W. J., Sparrow, E. M.: Local nonsimilar solutions for natural convection on a vertical cylinder. J. Heat Transfer 178–183 (1974).

  19. Talbot, L., Cheng, R. K., Schefer, R. W., Willis, D. R.: Thermophoresis of particles in a heated boundary layer. J. Fluid Mech.101, 737–758 (1980).

    Google Scholar 

  20. Batchelor, G. K., Shen, C.: Thermophoretic deposition of particles in gas flowing over cold surfaces. J. Colloid Interface Sci.107, 21–37 (1985).

    Google Scholar 

  21. Chang, J. S., Ishii, T., Matsumura, S., Ono, S., Teii, S.: Theory of aerosol particle thermal deposition on a flat body in a variable property fluid. J. Aerosol Sci.18, 619–621 (1987).

    Google Scholar 

  22. Parker, G. J., Ryley, D. J.: Equipment and techniques for studing the deposition of sub-micron particles on turbine blades. Proc. Inst. Mech. Eng.184, 45–51 (1969).

    Google Scholar 

  23. Montassier, N., Boulard, D., Renoux, A.: Experimental study of thermophoretic deposition in laminar tube flow. J. Aerosol Sci.22, 677–681 (1991).

    Google Scholar 

  24. Whitby, K. T., Lundgren, D. A., Peterson, C. N.: Homogeneous aerosol generators. Int. J. Air Water Poll.9, 263–277 (1965).

    Google Scholar 

  25. El-Kady, A. A.: Deposition of sub-micron particles onto AGR fuel elements. PhD Thesis, University of Liverpool, 1989.

  26. Owen, I., El-Kady, A. A., Cleaver, J. W.: Sub-micron particle fouling of heated AGR fuel rod elements. 2nd UK National Heat Transfer Conference, Glasgow., UK, 1989.

  27. Pratsinis, S. E., Kim, K. S.: Particle coagulation, diffusion and thermophoresis in laminar tube flows. J. Aerosol Sci.20, 101–111 (1989).

    Google Scholar 

  28. Cebeci, I., Smith, A. M. O.: A finite-difference method for calculating compressible laminar and turbulent boundary layers. J. Basic Eng. 523–535 (1970).

  29. Ostrach, S.: An analysis of laminar free-convection flow and heat transfer about a plate parallel to the direction of the generating body force. NACA Rep.1111, 1–17, (1953).

    Google Scholar 

  30. Chiou, M. C., Cleaver, J. W.: Effect of thermophoresis on sub-micron particle deposition from a laminar forced convection boundary layer flow onto an isothermal cylinder. J. Aerosol Sci.22, 677–681 (1996).

    Google Scholar 

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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. Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder. Acta Mechanica 129, 163–176 (1998). https://doi.org/10.1007/BF01176743

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