Instabilities in the Buoyant Convective Flows Subject to High Magnetic Fields

  • Agnieszka Hudoba

    Student thesis: Doctoral ThesisDoctor of Philosophy


    The present study is devoted to the problem of the onset of instability in time dependent convective flows of an electrically conducting fluid, subject to an externally applied magnetic field and to gravity forces. Linear stability theory is applied to investigate convective flows confined by two rigid walls and opposed by the magnetic field. These magnetohydrodynamic channel flows are studied for non-zero magnetic Prandtl numbers as well as in the inductionless approximation. The following configurations are considered: the Rayleigh-Benard problem, the horizontal layer with longitudinal temperature gradient and the vertical channel with internal heating sources. The numerical results are obtained giving characteristic laws by critical values of parameters, beyond which the flows become unstable. The comparison is made between these problems for small, but non-zero Prm, with the inductionless approximation, in order to determine the validity of that approximation. The analysis of perturbations shows that the instabilities critically depend on the electrical and thermal boundary conditions and on the Prandtl (Pr), magnetic Prandtl (Prm), and Hartmann (Ha) numbers. The instabilities are driven by different mechanisms and set in either as two- or three-dimensional modes, stationary or oscillatory, depending on these parameters and on the orientation of magnetic field and gravity. New instability structures are observed in the horizontal layer heated for the side for small ranges of Prm. The MATLAB code created for the purpose of this thesis allows the study of convective flows in the presence of high magnetic fields up to Ha = 10 5 and the asymptotic relations are successfully reached for the critical values of parameters in most cases.
    Date of Award2015
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorSergei Molokov (Supervisor)

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