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Bifurcation of flows of a fluid with internal heat sources in a vertical pipe

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.2250
pages 2180-2191

T. Senoo
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University,Yoshida-honmachi, Sakyo-ku, Kyoto 060-8501, Japan

K. Deguchi
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 060-8501, Japan

M. Nagata
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 060-8501, Japan

Sinopsis

The development of incompressible fluid motion in an infinitely long vertical circular pipe in the gravity field is examined numerically when internal heat sources are homogeneously distributed inside the pipe while the temperature of the pipe wall is kept constant. We carry out a linear stability analysis finding that, in contrast to the isothermal pipe flow, our thermal flow can become linearly unstable when the vertical velocity profile becomes inflectional but not totally reverse. Also, we carry out a nonlinear analysis which shows that two branches of nonlinear solutions, referred to as spirals and ribbons, bifurcate from the same neutral point determined by the linear analysis. In particular, a branch of the ribbon reaching the isothermal limit is detected in the case for a fluid with Pr = 0 where Pr is the Prandtl number. For a fluid with Pr = 7, nonlinear mode interactions with different azimuthal wavenumbers are observed.

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