Skip to main content
SpringerLink
Log in

Approximate integration op nonstationary equations of a diffusion or thermal boundary layer

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

An approximate method is proposed for integrating the nonstationary equations of a diffusion or thermal boundary layer using the known steady solution in the planar or axisymmetric case. It is shown that the proposed method is exact in problems involving mass or heat transfer of reacting drops and bubbles in a laminar flow of a viscous incompressible fluid and also particles moving in an ideal fluid. An integral equation is obtained for the local diffusion or heat flux in the case of abrupt “activation” of a reaction on the surface of a particle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. L. G. Loitsyanskii, Laminar Boundary Layers [in Russian], Fizmatgiz, Moscow (1962), p. 479.

    Google Scholar 

  2. H. Schlichting, Boundary Layer Theory, McGraw-Hill, New York (1968).

    Google Scholar 

  3. V. G. Levich, Physicochemical Hydrodynamics [in Russian], Fizmatgiz, Moscow (1959), p. 699.

    Google Scholar 

  4. A. D. Polyanin and P. A. Pryadkin, “Two problems of convective diffusion to the surface of blunt bodies,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 104 (1978).

    Google Scholar 

  5. V. G. Levich, V. S. Krylov, and V. P. Vorotilin, “Theory of unsteady diffusion from a moving drop,” Dokl. Akad. Nauk SSSR,161, 648 (1965).

    Google Scholar 

  6. E. Ruckenstein, “Mass transfer between a single drop and continuous phase,” Int. J. Heat Mass Transfer,10, 1785 (1967).

    Google Scholar 

  7. B. T. Chao, “Transient heat and mass transfer to translating droplet,” Trans. ASME, Ser. C, J. Heat Transfer,91, 273 (1969).

    Google Scholar 

  8. Yu. P. Gupalo, A. D. Polyanin, P. A. Pryadkin, and Yu. S. Ryazantsev, “Unsteady mass transfer for a drop in a stream of viscous fluid,” Prikl. Mat. Mekh.,42, 441 (1978).

    Google Scholar 

  9. Yu. P. Gupalo, A. D. Polyanin, P. A. Pryadkin, and Yu. S. Ryazantsev, “Integration of the nonstationary heat transfer equation of bodies moving in a fluid,” Prikl. Mat. Mekh.,43, 1119 (1979).

    Google Scholar 

  10. A. D. Polyanin, “Integration of the nonlinear nonstationary equations of convective heat and mass transfer,” Dokl. Akad. Nauk SSSR,251, 817 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow

    Yu. P. Gupalo, A. D. Polyanin & Yu. S. Ryazantsev

Authors
  1. Yu. P. Gupalo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Polyanin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. S. Ryazantsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 87–92, September–October, 1982.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupalo, Y.P., Polyanin, A.D. & Ryazantsev, Y.S. Approximate integration op nonstationary equations of a diffusion or thermal boundary layer. Fluid Dyn 17, 725–729 (1982). https://doi.org/10.1007/BF01090153

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01090153

Keywords

Search

Navigation