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 internal wall of canal.
температурное поле, теплообмен, локальный тепловой поток, цилиндрический канал в форме эллиптического кольца, краевая задача, собственные значения, собственные функции, обычное и модифицированное уравнения Матье, temperature field, heat exchange, local stream of heat, cylindrical canal in form of elliptical ring, boundary task, own values, own functions, ordinary and modificied equations of Mathieu
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