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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2010, Volume 51, Issue 4, Pages 57–71
(Mi pmtf1621)
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Joint unidirectional motion of two viscous heat-conducting fluids in a tube
V. K. Andreevab a Institute of Computational Modeling, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
b Siberian Federal University, Krasnoyarsk, 660041, Russia
Abstract:
This paper studies an invariant solution of the problem of joint motion of two heat-conducting viscous immiscible fluids which have a common interface in a cylindrical tube under an unsteady pressure gradient. The problem reduces to a coupled initial-boundary-value problem for parabolic equations. A priori estimates of velocity and temperature perturbations are obtained. The steady state of the system is determined, and it is proved that if, in one of the fluids, the pressure gradient rapidly approaches zero, the perturbations of all quantities tend to zero. It is shown that if the pressure gradient has a nonzero limit, the solution reaches a steady state. In this case, the velocity field in the limit is the same as in conjugate Poiseuille flow, and the temperature is represented as a polynomial of the fourth order on the radial coordinate.
Keywords:
viscous heat-conducting fluid, interface, steady-state flow.
Received: 25.08.2009
Citation:
V. K. Andreev, “Joint unidirectional motion of two viscous heat-conducting fluids in a tube”, Prikl. Mekh. Tekh. Fiz., 51:4 (2010), 57–71; J. Appl. Mech. Tech. Phys., 51:4 (2010), 497–509
Linking options:
https://www.mathnet.ru/eng/pmtf1621 https://www.mathnet.ru/eng/pmtf/v51/i4/p57
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