Geodesic
Heat transfer in Couette flow corrected for energy dissipation by the third kind boundary conditions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 136-144.

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The analytical solution of the non-linear heat transfer problem for laminar flow of liquid in plane-parallel channel (Coutte flow) corrected for energy dissipation by the third kind boundary conditions on the moving wall is obtained by the Kantorovich and the orthogonal Bubnov-Galerkin methods. The solution allows to estimate the temperature state of liquid for the small values of longitudinal coordinate, where the displacement of temperature profile to the immovable wall takes place as the investigations have shown.
Keywords: Coutte flow, heat exchange in a liquid, analytical solution, orthogonal methods, energy dissipation. 
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A. V. Eremin; N. M. Budylnikov; I. V. Kudinov. Heat transfer in Couette flow corrected for energy dissipation by the third kind boundary conditions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 136-144. http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a12/

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[2] Kudinov V. A., Kartashov É. M., Kalashnikov V. V., Analytical solutions of problem of heat and mass transfer and thermoelasticity for multilayered structures, Vyssh. Shk., Moscow, 2005, 430 pp.

[3] Kantorovich L. V., Krylov V. I., Approximate methods of higher analysis, Fizmatlit, Moscow, Leningrad, 1962, 708 pp. | MR

[4] Kudinov V. A., Kudinov I. V., “Heat transfer in Couette flow with the energy dissipation”, Energetika. Izv. Vyssh. Ucheb. Zavedeniy Energ. Obyedin., 2011, no. 2, 43–51