On the Stability of a Convective Flow with Nonlinear Heat Sources

Armands Gritsans, Andrei Kolyshkin (), Felix Sadyrbaev and Inara Yermachenko
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Armands Gritsans: Department of Physics and Mathematics, Daugavpils University, LV-5401 Daugavpils, Latvia
Andrei Kolyshkin: Institute of Applied Mathematics, Riga Technical University, Zunda Embankment 10, LV-1048 Riga, Latvia
Felix Sadyrbaev: Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, Latvia
Inara Yermachenko: Department of Physics and Mathematics, Daugavpils University, LV-5401 Daugavpils, Latvia

Mathematics, 2023, vol. 11, issue 18, 1-24

Abstract: The linear stability of a convective flow in a vertical fluid layer caused by nonlinear heat sources in the presence of cross-flow through the walls of the channel is investigated in this paper. This study is relevant to the analysis of factors that affect the effectiveness of biomass thermal conversion. The nonlinear problem for the base flow temperature is investigated in detail using the Krasnosel’skiĭ–Guo cone expansion/contraction theorem. It is shown that a different number of solutions can exist depending on the values of the parameters. Estimates for the norm of the solutions are obtained. The linear stability problem is solved numerically by a collocation method based on Chebyshev polynomials. It is shown that the increase in the cross-flow intensity stabilizes the flow, but there is also a small region of the radial Reynolds numbers where the flow is destabilized.

Keywords: linear stability; Krasnosel’ski?–Guo theorem; bifurcation analysis; collocation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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