2020
DOI: 10.2478/prolas-2020-0045
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Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation

Abstract: Linear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that… Show more

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Cited by 1 publication
(3 citation statements)
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“…Wide gaps between the walls of the annulus are not considered in the present study (the values of η that are used in the paper are η = 0.6 and η = 0.7). As was shown in [1,20], asymmetric perturbations (depending on the angular coordinate ϕ) are the most unstable for very large gaps (small values of η), which is why only axisymmetric perturbations are considered in the present paper. In the future, we plan to investigate the role of the radius ratio on the stability boundary as well as to consider different Prandtl numbers by analyzing both axisymmetric and asymmetric perturbations.…”
Section: Discussionmentioning
confidence: 86%
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“…Wide gaps between the walls of the annulus are not considered in the present study (the values of η that are used in the paper are η = 0.6 and η = 0.7). As was shown in [1,20], asymmetric perturbations (depending on the angular coordinate ϕ) are the most unstable for very large gaps (small values of η), which is why only axisymmetric perturbations are considered in the present paper. In the future, we plan to investigate the role of the radius ratio on the stability boundary as well as to consider different Prandtl numbers by analyzing both axisymmetric and asymmetric perturbations.…”
Section: Discussionmentioning
confidence: 86%
“…where E is the activation energy, R is the universal gas constant, Q 0 is a constant and T is the absolute temperature. Models with internal heat generation given by (1) are used in practice in order to describe processes during biomass thermal conversion [20,21,23] with the objective to obtain cleaner and more efficient sources of energy. Instability is a desirable phenomenon in this case since it enhances fluid mixing, which, in turn, leads to more efficient energy conversion.…”
Section: Mathematical Formulation Of the Problemmentioning
confidence: 99%
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