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The free convection of a conducting fluid in connected vertical channels

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The convection of a conducting fluid in vertical channels in a magnetic field has been studied in a series of papers (see review [1]). Motion in isolated channels was considered in these papers. The present paper solves the problem of convection in a system of two connected plane vertical channels. A solution is obtained for the problem of steady-state motion when heating occurs from the side. Equilibrium stability is also investigated for a liquid which is heated from below (the magnetohydrodynamic generalization of the problem considered previously [2]).

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  1. 1.

    S. A. Regirer, “Laminar flows of a conducting fluid in pipes and channels in the presence of a magnetic field,” Magnitnaya gidrodinamika [Magnetohydrodynamics], no. 1, 1965.

  2. 2.

    G. Z. Gershuni, E. M. Zhukhovitskii, and G. F. Shaidurov “The convective instability of a fluid in connected vertical channels,” PMM, vol. 30, no. 4, 1966.

  3. 3.

    G. Z. Gershuni and E. M. Zhukhovitskii, “The steady-state convective motion of an electrically conducting fluid between parallel plates in a magnetic field,” ZhETF, vol. 34, no. 3, 1958.

  4. 4.

    G. Z. Gershuni and E. M. Zhukhovitskii, “The convective instability spectrum of a conducting medium in a magnetic field,” ZhETF, vol. 42, no. 4, 1962.

  5. 5.

    M. I. Shliomis, “The stability of a fluid which is rotating and heated from below relative to perturbations which are periodic with time,” PMM, vol. 26, 1962.

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    E. M. Zhukhovitskii, “The stability of a nonuniformly heated fluid in a vertical elliptical cylinder,” PMM, vol. 19, no. 6, 1955.

  7. 7.

    Yih Chia-Shun, “Gravitational instability of a viscous fluid in a magnetic field.” J. Fluid Mech., vol. 22, p. 3, 1965.

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Gershuni, G.Z., Zhukhovitskii, E.M. The free convection of a conducting fluid in connected vertical channels. J Appl Mech Tech Phys 8, 21–24 (1967). https://doi.org/10.1007/BF00913202

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  • Magnetic Field
  • Convection
  • Mathematical Modeling
  • Mechanical Engineer
  • Industrial Mathematic