MATHEMATICAL MODELING OF TEMPERATURE FIELDS OF THE ROTATING CYLINDER
Keywords:
temperature field, a rolling roll, boundary value problem, boundary condition, the complex Fourier series, integral Hankel transform, Laplace, Fourie, Predvoditeleva criterionAbstract
In paper we consider a solid cylinder as a simplified model of the roll. The cylinder is under the influence of heat flow, which reflects the effect of the heated metal sheet on the roll. A three-dimensional mathematical model of temperature fields in a solid cylinder, which rotates at a constant angular velocity about the axis OZ length L, as a boundary value problem of mathematical physics is presented. As a result, found the temperature field of a solid cylinder as convergent orthogonal series of Bessel functions and of Fourie.
References
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8. Golitsyna Ye. V. Matematicheskoye modelirovaniye temperaturnogo polya v polom vrashchayushchemsya tsilindre pri nelineynykh granichnykh usloviyakh / Ye.V. Golitsyna // Teplofizika vysokikh temperatur. Noyabr'-Dekabr'. – 2008. – tom 46, № 6. – S. 905 – 910.
9. Kuwashimo Kensuke Temperature distribution within a rotating cylindrical body/ Kuwashimo Kensuke, Yamada Tominori // Bull. JSME. – 1978. – Vol. 21, №152. – P. 266 – 272.
10. Lykov A.V. Teoriya teploprovodnosti / A.V. Lykov // – M., Vysshaya shkola, 1967. – 599 s.
11. Mikhlin S.G. Lineynyye uravneniya v chastnykh proizvodnykh / S.G.Mikhlin // – M., Vysshaya shkola, 1977. – 427 s.
12. Tolstov G.P. Ryady Fur'ye / G.P. Tolstov // – M., Nauka, 1980.–384 s.
13. Galitsyn A.S., Zhukovskiy A.I. Integral'nyye preobrazovaniya i spetsial'nyye funktsii v zadachakh teploprovodnosti / A.S. Galitsyn, A.I. Zhukovskiy // – Kiyev., Naukova dumka. 1979. – 561 s.
14. Grey E. Funktsii Besselya i ikh prilozheniya k fizike i mekhanike / E. Grey, G.B. Met'yuz // – M., 1949. – 386 s.
15. Akhmetshina L.G., Yamnich T.S. Mul'timodel'nyy metod nechetkoy inter-polyatsii prostranstvennykh dannykh na neravnomernoy setke / Akhmetshina L.G., // Vestnik KHNTU, Kherson, 2011, T.42, №3, –S. 56–61.
