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


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.


Boundary Condition Heat Transfer Statistical Physic Approximate Solution Plane Channel 
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To and Tw

temperatures of entrance section and wall of channel, respectively


pressure gradient

x1, x2

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


Peclet number


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


boundary condition parameter


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


heat flux density on wall

ɛn and Yn(y)

eigenvalues and eigenfunctions of Sturm-Liouville problem


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
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    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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