Geodesic
On a spectral problem for convection equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 88-100

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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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     title = {On a spectral problem for convection equations},
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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/