The temperature field moving liquid into half-infinite canal which has cross section in form elliptical ring at mixed boundary conditions is studied. The task is resolved by method of dividing variables. As result it is reduced at three boundary tasks for ordinary differential equations of second order. Two differential equations of three are usual and modificied equations of Mathieu. Solutions obtain for temperature field into liquid and specific heat stream on the walls of canal.
температурное поле, локальный тепловой поток, эллиптический кольцевой цилиндр, краевая задача, собственные значения, собственные функции, обычное и модифицированное уравнения Матье, temperature field, local stream of heat, elliptical cilindric canal in form of ring, boundary task, own values, own functions, ordinary and modificied equations of Mathieu
1. S.V. Ananikov, M.Yu. Sorokin, V.P. Burdikov, E.V. Chirkunov, Teoreticheskie osnovy himicheskoy tehnologii (TOHT), 38,6, 655-660 (2004).
2. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 6, 42-46 (2012).
3. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 6, 147-150 (2012).
4. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 11, 143-145 (2012).
5. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 14, 90-93 (2012).
6. S.V. Ananikov, M.Yu. Sorokin, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 18, 58-63 (2012).
7. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 15, 20, 56-61 (2012).
8. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 16, 2, 52-55 (2013).
9. S.V. Ananikov, Vestnik Kazanskogo tehnologicheskogo universiteta, 16, 3, 58-62 (2013).
10. S.V. Ananikov, M.Yu. Sorokin, Vestnik Kazanskogo tehnologicheskogo universiteta,16, 6, 58-63 (2013).
11. Mak-Lahlan N.V., Teoriya i prilozheniya funkciy Mat'e. Inostrannaya literatura. Moskva. 1953. 476s.
12. Strett M.D.O. Funkcii Lyame, Mat'e i rodstvennye im v fizike i tehnike. GNTI Ukrainy, Har'kov-Kiev. 1935. 238s.
