Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation

Proceedings of the Latvian Academy of Sciences, Section B: Natural, Exact, and Applied Sciences 2020
Andrejs Koliškins, Valentīna Koliškina, Inta Volodko, Ilmārs Iltiņš

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 axisymmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.

Keywords
Boussinesq approximation; Collocation method; Linear stability
DOI
10.2478/prolas-2020-0045
Hyperlink
https://www.sciendo.com/article/10.2478/prolas-2020-0045

Koliškins, A., Koliškina, V., Volodko, I., Iltiņš, I. Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation. Proceedings of the Latvian Academy of Sciences, Section B: Natural, Exact, and Applied Sciences, 2020, Vol. 74, No. 4, pp.293-298. ISSN 1407-009X. Available from: doi:10.2478/prolas-2020-0045

Publication language
English (en)