Geodesic
Initial boundary value problem on the motion of a viscous heat-conducting liquid in a vertical pipe
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 5-16

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The initial-boundary value problem arising in a modeling an unsteady unidirectional convective flow in vertical heat exchangers with an arbitrary cross section is researched. An a priori estimate in $L_2$ is obtained and uniqueness of the problem solution is proved. For a rectangular and circular sections solution was found in the form of double Fourier series. Sufficient conditions for stabilization of solution to rest with increasing time are given.
Keywords: initial boundary value problem, a priori estimate, Fourier series
Mots-clés : convection. 
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     title = {Initial boundary value problem on the motion of a viscous heat-conducting liquid in a vertical pipe},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a0/}
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Victor K. Andreev; Alyona I. Uporova. Initial boundary value problem on the motion of a viscous heat-conducting liquid in a vertical pipe. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 5-16. http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a0/