Geodesic
On a spectral problem for convection equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 88-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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Spectral problems for stationary unidirectional convective flows in vertical heat exchangers at various boundary temperature conditions are considered. The constant temperature gradient on the vertical walls is used as a spectral parameter. The heat exchanger cross-section can be of an arbitrary shape. The general properties of the spectral problem solutions are established. Solutions are obtained in an analytical form for rectangular and a circular cross sections. The critical values of temperature gradient at which convective flow arises are found. The corresponding vertical velocity profiles are constructed. The properties of solutions of a new transcendental equation for the spectral values are studied.
Keywords: spectral problem, eigenfunctions, eigenvalues.
Mots-clés : convection 
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Victor K. Andreev; Alyona I. Uporova. On a spectral problem for convection equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 88-100. http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a9/

[1] V.K.Andreev, Y.A.Gaponenko, O.N.Goncharova, V.V.Pukhnachev, Mathematical Models of Convection, Walter de Gruyter GmbH $\$ Co, KG, Berlin–Boston, 2012 | MR

[2] V.V.Pukhnachev, “Symmetries in the Navier-Stokes equations”, Uspehi Mehaniki, 2006, no. 6, 3–76 (in Russian)

[3] S.N.Aristov, D.V.Knyazev, A.D.Polyanin, “Exact solutions of the Navier-Stokes equations with a linear dependence of the velocity components on two spatial variables”, Theoretical Foundations of Chemical Engineering, 43:5 (2009), 642–662 | DOI

[4] O.A.Ladyzhenskaya, Boundary value problems of mathematical physics, Fizmatlit, Nauka, 1973 (in Russian) | MR

[5] A.D.Polyanin, A Handbook of Linear Equations in Mathematical Physics, Fizmatlit, Nauka, 2001 (in Russian)

[6] V.G.Watson, The theory of Bessel functions, Publishing house of foreign literature, 1949 (in Russian)

[7] M.Abramovitz, I.Stegan, Special Functions Handbook, Fizmatlit, Nauka, 1979 (in Russian)

[8] I.S.Gradshtein, I.M.Ryzhik, Tables of integrals, sums, series and products, Fizmatlit, Nauka, 1963 (in Russian) | MR

[9] M.A.Lavrentyev, B.V.Shabat, Methods of Theory of Complex Variable Functions, Nauka, M., 1973 (in Russian) | MR