Моделирование конвективного теплообмена в призматических каналах с различной геометрией сечения

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Моделирование конвективного теплообмена в призматических каналах…
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Modeling of convective heat transfer in prismatic channels
of different cross section geometry
© N.V. Kiryukhina1, A.K. Gorbunov 2, N.A. Silaeva2
1 Kaluga State University named after K.E. Tsiolkovsky, Kaluga, 248023, Russia
2Kaluga Branch of Bauman Moscow State Technical University, Kaluga, 248000, Russia
The article describes a mathematical model of heat transfer in developed laminar flow in
prismatic channels of rectangular and triangular cross-sections, including the equation
of fluid motion and the energy equation with boundary conditions of the second kind on
the channel walls. The analytical solutions for the velocity field have been derived from
the equations of liquid motion. Solution of the energy equation has been obtained by nu-
merical method of finite differences. The computational algorithm was based on the dif-
ference scheme approximating the boundary value problem, based on five-point pattern.
This algorithm implements programs allowing calculation of the velocity and tempera-
ture fields in the channels and determination of the local and average heat transfer char-
acteristics. In future we plan to build an algorithm and to develop a program for the nu-
merical solution of the problem of convective heat transfer in channel of more complex
geometry with projections on the walls.
Keywords: convective heat transfer, mathematical modeling, finite difference method.
REFERENCES
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Moscow, Nauka Publ., 1978, 736 p.
[2] Mikheev M.A., Mikheeva I.M. Osnovy teploperedachi [Fundamentals of Heat
Transfer]. 2nd ed. Moscow, Energiya Publ., 1977, 344 p.
[3] Dulnev G.N. Teoriya teplo- i massoobmena [Theory of Heat and Mass Trans-
fer]. St. Petersburg, Reseach University ITMO Publ., 2012, 194 p.
[4] Fletcher C.A.J. Computational Techniques for Fluid Dynamics. London, et al.,
1988. [Russian edition: Fletcher C. Vychislitelnye metody v dinamike
zhidkostey. Tom 1: Osnovnye polozheniya i obschie metody (Computational
methods in fluid dynamics. Vol. 1: Fundamentals and general methods) Mos-
cow, Mir Publ., 1991, 504 p.].
Kiryukhina N.V. graduated from Kaluga Pedagogical Institute named after
K.E. Tsiolkovsky. Ph.D., assoc. professor of the General Physics Department at Kaluga
State University named after K.E. Tsiolkovsky. Research interests: Thermal physics,
physics teaching theory and methods. e-mail:
Gorbunov A.K. (b. 1947) graduated from Moscow Institute of Physics and Tech-
nology. Dr. Sci. (Phys.&Math.), head of the Physics Department at Kaluga branch of
Bauman Moscow State Technical University. The author of several articles on condensed
matter physics. e-mail:
Silaeva N.A. (b. 1968) graduated from the Kaluga Pedagogical Institute named after
K.E. Tsiolkovsky. The senior lecturer of the Physics Department at Kaluga branch of
Bauman Moscow State Technical University. The author of several articles on strength
characteristics of the material properties. e-mail: