Geodesic
On one method for analytical solution of Graetz--Nusselt problem
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 193-198.

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An approximate analytic solution of heat transfer problem for fluid flow in a circular tube is found using the method of separation of variables, based on the introduction of additional boundary conditions. It is shown that already in the fourth approximation over the range of dimensionless axial coordinate $0{,}0025 \le x\infty $, the difference between the exact and the obtained solution does not exceed 3 %.
Keywords: Graetz–Nusselt problem, analytical methods, orthogonal methods, additional boundary conditions. 
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A. V. Eremin; N. M. Budylnikov. On one method for analytical solution of Graetz--Nusselt problem. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 193-198. http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a24/

[1] Petukhov B. S., Heat Transfer and Resistance in the Laminar Flow of Liquids in Tubes, Energiya, Moscow, 1967, 412 pp.

[2] Tsoi P. V., Methods of Calculating Mass-Transfer Problems, Energoatomizdat, Moscow, 1984, 414 pp.

[3] Kudinov V. A., Kartashov É. M., Kalashnikov V. V., Analytical Solutions of the Problems of Heat- and Mass Transfer and Thermal Elasticity for Multilayer Structures, Vyssh. shk., Moscow, 2005, 430 pp.