<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 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.</p></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 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.

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

Faculty of Computer Science and Information Technology

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

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

Published Online: Sep 22, 2020

Page range: 293 - 298

Received: Apr 12, 2019

Accepted: Jun 27, 2020

DOI: https://doi.org/10.2478/prolas-2020-0045

Keywords
linear stability, Boussinesq approximation, collocation method

© 2020 Andrei Kolyshkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Sep 22, 2020

Page range: 293 - 298

Received: Apr 12, 2019

Accepted: Jun 27, 2020

DOI: https://doi.org/10.2478/prolas-2020-0045

Keywordslinear stability, Boussinesq approximation, collocation method

© 2020 Andrei Kolyshkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
linear stability, Boussinesq approximation, collocation method