Journal of engineering physics

, Volume 39, Issue 4, pp 1146–1150 | Cite as

Use of the WKB method to investigate connective heat transfer in a micropolar fluid

  • N. P. Migun
Article
  • 16 Downloads

Abstract

A general approximate solution is obtained for problems of heat transfer associated with a flow of micropolar fluid in a plane channel with boundary conditions of the first and second kind and its accuracy is determined.

Keywords

Boundary Condition Heat Transfer Statistical Physic Approximate Solution Plane Channel 

Notation

To and Tw

temperatures of entrance section and wall of channel, respectively

dp/dx

pressure gradient

x1, x2

longitudinal and transverse coordinates, respectively (or x and y)

Pe=2vmNh/a

Peclet number

vmN

mean velocity of Newtonian fluid with viscosity μ+ϰ/2 in channel of width 2h

α

boundary condition parameter

2h

width of channel

vx and vz

nonzero components of velocity and microrotation of micropolar fluid

a and λ

thermal diffusivity and thermal conductivity of fluid

ϰ, μ, and γ

viscosities of micropolar fluid

qw

heat flux density on wall

ɛn and Yn(y)

eigenvalues and eigenfunctions of Sturm-Liouville problem

Cn

constants that can be determined by using orthogonality of eigenfunctions

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Literature cited

  1. 1.
    B. S. Petukhov, Heat Transfer and Resistance in a Laminar Flow of Fluid in Tubes [in Russian], Énergiya, Moscow (1967).Google Scholar
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    A. C. Bringen, “Theory of micropolar fluids,” J. Math. Mech.,16, No. 1, 1–16 (1966).Google Scholar
  3. 3.
    J. R. Sellars, M. Tribus, and J. S. Klein, “Heat transfer to laminar flow in a round tube or flat conduit—the Graetz problem extended,” Trans. ASME,78, No. 2, 441–448. (1956).Google Scholar
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    V. L. Kolpashchikov and N. P. Migun, “Heat transfer in a micropolar fluid,” Vestn. B. Gos. Univ., Ser. 1, No. 3, 42–47 (1977).Google Scholar
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    V. L. Kolpashchikov, N. P. Migun, and P. P. Prokhorenko, “Heat transfer in a micropolar fluid with forced convection and boundary conditions of second kind,” Vestsi Akad. Nauk BSSR, Ser. Fiz.-Energ. Navuk, No. 3, 96–102 (1978).Google Scholar
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    B. M. Smol'skii, Z. P. Shul'man, and V. M. Gorislavets, Rheodynamics and Heat Transfer of Nonlinearly Viscoplastic Materials [in Russian], Nauka i Tekhnika, Minsk (1970).Google Scholar
  7. 7.
    V. L. Kolpashchikov, N. P. Migun, P. P. Prokhorenko, and V. I. Lis, “Heat transfer in a microstructured fluid with boundary conditions of third kind,” Inzh.-Fiz. Zh.,37, No. 1, 43–49 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • N. P. Migun
    • 1
  1. 1.Physicotechnical InstituteAcademy of Sciences of the Belorussian SSRMinsk

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