Numerical study of free convection in a thin layer between coaxial horizontal cylinders
We consider free convection in 2D and 3D horizontal cylindrical layers with the inner hot and outer cold boundary at Ra (Rayleigh number) in range (4∙103 ÷ 4∙105) and the ratio δ ≈ 1:20 of the layer width to inner radius. Prandtl number was 0,71, fluid properties were taken for air at 293 K.It was s...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-01-01
|
| Series: | Case Studies in Thermal Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214157X22008437 |
| _version_ | 1797956264714567680 |
|---|---|
| author | Alexander Fedotov Yana Tsitavets Andrey Elyshev |
| author_facet | Alexander Fedotov Yana Tsitavets Andrey Elyshev |
| author_sort | Alexander Fedotov |
| collection | DOAJ |
| description | We consider free convection in 2D and 3D horizontal cylindrical layers with the inner hot and outer cold boundary at Ra (Rayleigh number) in range (4∙103 ÷ 4∙105) and the ratio δ ≈ 1:20 of the layer width to inner radius. Prandtl number was 0,71, fluid properties were taken for air at 293 K.It was shown that the flow in a 2D cylindrical layer can be divided into three regions. Stable symmetric convective rolls are formed in the layer’s upper part; regions with the transient flow appear at the lateral sides; transitional regions between the upper and the lateral regions have convective rolls of an unusual asymmetric shape.The flow in a 3D cylindrical layer in the upper part is organized into a spatially stable convective roll pattern. With increase of the Rayleigh number (Ra), roll pattern becomes suppressed by a transient plume pattern.The global Nu (the Nusselt number) is proportional to 0,0019∙Ra0,567 for the 2D case and to 0,22∙Ra0,192 for the 3D case. The 2D problem provides a reasonable estimation of the Nusselt number for Rayleigh number up to 4∙104 and overestimates Nu for higher Rayleigh number, which agrees with Lyapunov exponent values. |
| first_indexed | 2024-04-10T23:46:19Z |
| format | Article |
| id | doaj.art-ca3b5336378c4a129fa22854cd2f78a8 |
| institution | Directory Open Access Journal |
| issn | 2214-157X |
| language | English |
| last_indexed | 2024-04-10T23:46:19Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Case Studies in Thermal Engineering |
| spelling | doaj.art-ca3b5336378c4a129fa22854cd2f78a82023-01-11T04:29:07ZengElsevierCase Studies in Thermal Engineering2214-157X2023-01-0141102606Numerical study of free convection in a thin layer between coaxial horizontal cylindersAlexander Fedotov0Yana Tsitavets1Andrey Elyshev2Nature-inspired Engineering Center, University of Tyumen, Volodarskogo Str. 6, Tyumen, 625003, Russia; Physics Faculty, Belarusian State University, Nezalezhnasci av., 2, Minsk, 220030, Belarus; Corresponding author. Nature-inspired Engineering Center, University of Tyumen, Volodarskogo Str. 6, Tyumen, 625003, Russia.Nature-inspired Engineering Center, University of Tyumen, Volodarskogo Str. 6, Tyumen, 625003, Russia; Physics Faculty, Belarusian State University, Nezalezhnasci av., 2, Minsk, 220030, Belarus; Corresponding author. Nature-inspired Engineering Center, University of Tyumen, Volodarskogo Str. 6, Tyumen, 625003, Russia.Nature-inspired Engineering Center, University of Tyumen, Volodarskogo Str. 6, Tyumen, 625003, RussiaWe consider free convection in 2D and 3D horizontal cylindrical layers with the inner hot and outer cold boundary at Ra (Rayleigh number) in range (4∙103 ÷ 4∙105) and the ratio δ ≈ 1:20 of the layer width to inner radius. Prandtl number was 0,71, fluid properties were taken for air at 293 K.It was shown that the flow in a 2D cylindrical layer can be divided into three regions. Stable symmetric convective rolls are formed in the layer’s upper part; regions with the transient flow appear at the lateral sides; transitional regions between the upper and the lateral regions have convective rolls of an unusual asymmetric shape.The flow in a 3D cylindrical layer in the upper part is organized into a spatially stable convective roll pattern. With increase of the Rayleigh number (Ra), roll pattern becomes suppressed by a transient plume pattern.The global Nu (the Nusselt number) is proportional to 0,0019∙Ra0,567 for the 2D case and to 0,22∙Ra0,192 for the 3D case. The 2D problem provides a reasonable estimation of the Nusselt number for Rayleigh number up to 4∙104 and overestimates Nu for higher Rayleigh number, which agrees with Lyapunov exponent values.http://www.sciencedirect.com/science/article/pii/S2214157X22008437ConvectionRayleigh-bénardNusseltLyapunovCoaxial cylinders |
| spellingShingle | Alexander Fedotov Yana Tsitavets Andrey Elyshev Numerical study of free convection in a thin layer between coaxial horizontal cylinders Case Studies in Thermal Engineering Convection Rayleigh-bénard Nusselt Lyapunov Coaxial cylinders |
| title | Numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| title_full | Numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| title_fullStr | Numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| title_full_unstemmed | Numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| title_short | Numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| title_sort | numerical study of free convection in a thin layer between coaxial horizontal cylinders |
| topic | Convection Rayleigh-bénard Nusselt Lyapunov Coaxial cylinders |
| url | http://www.sciencedirect.com/science/article/pii/S2214157X22008437 |
| work_keys_str_mv | AT alexanderfedotov numericalstudyoffreeconvectioninathinlayerbetweencoaxialhorizontalcylinders AT yanatsitavets numericalstudyoffreeconvectioninathinlayerbetweencoaxialhorizontalcylinders AT andreyelyshev numericalstudyoffreeconvectioninathinlayerbetweencoaxialhorizontalcylinders |