Linear Stability of a Convective Flow in an Annulus with a Nonlinear Heat Source

JP Journal of Heat and Mass Transfer 2019
Ilmārs Iltiņš, Marija Iltiņa, Andrejs Koliškins, Valentīna Koliškina

Linear stability of a convective motion in a tall vertical annulus is analyzed in the paper. The base flow is generated by a non-linear heat source. The base flow velocity and temperature distributions are obtained numerically solving the system of the Navier-Stokes equations under the Boussinesq approximation. Linear stability problem is solved for axisymmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results show that there are three destabilizing factors: (1) the increase of the gap between the cylinders, (2) the increase of the Frank-Kamenetsky parameter characterizing the rate and intensity of a chemical reaction and (3) the increase of the Prandtl number.

Keywords
linear stability, nonlinear heat sources, Arrhenius law
DOI
10.17654/HM018020315
Hyperlink
http://www.pphmj.com/abstract/12964.htm

Iltiņš, I., Iltiņa, M., Koliškins, A., Koliškina, V. Linear Stability of a Convective Flow in an Annulus with a Nonlinear Heat Source. JP Journal of Heat and Mass Transfer, 2019, Vol. 18, No. 2, pp.315-329. ISSN 0973-5763. Available from: doi:10.17654/HM018020315

Publication language
English (en)