Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer
In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionle...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universidad San Francisco de Quito
2019-05-01
|
| Series: | ACI Avances en Ciencias e Ingenierías |
| Subjects: | |
| Online Access: | https://revistas.usfq.edu.ec/index.php/avances/article/view/968 |
| _version_ | 1797317528250220544 |
|---|---|
| author | Ali Belhocine Wan Zaidi Wan Omar |
| author_facet | Ali Belhocine Wan Zaidi Wan Omar |
| author_sort | Ali Belhocine |
| collection | DOAJ |
| description |
In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.
|
| first_indexed | 2024-03-08T03:36:20Z |
| format | Article |
| id | doaj.art-8dac4c14afbc4a1db931edc7fe7ffe2b |
| institution | Directory Open Access Journal |
| issn | 1390-5384 2528-7788 |
| language | English |
| last_indexed | 2024-03-08T03:36:20Z |
| publishDate | 2019-05-01 |
| publisher | Universidad San Francisco de Quito |
| record_format | Article |
| series | ACI Avances en Ciencias e Ingenierías |
| spelling | doaj.art-8dac4c14afbc4a1db931edc7fe7ffe2b2024-02-10T04:32:37ZengUniversidad San Francisco de QuitoACI Avances en Ciencias e Ingenierías1390-53842528-77882019-05-0111210.18272/aci.v11i2.968Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layerAli Belhocine0Wan Zaidi Wan Omar1Faculty of Mechanical Engineering, University of Sciences and the Technology of OranL.P 1505 El - MNAOUER, USTO 31000 ORAN (Algeria)Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail. https://revistas.usfq.edu.ec/index.php/avances/article/view/968Lévêque approximationThermal entrance regionThermal boundary layerDimensionless variablesTemperatureNusselt number |
| spellingShingle | Ali Belhocine Wan Zaidi Wan Omar Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer ACI Avances en Ciencias e Ingenierías Lévêque approximation Thermal entrance region Thermal boundary layer Dimensionless variables Temperature Nusselt number |
| title | Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer |
| title_full | Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer |
| title_fullStr | Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer |
| title_full_unstemmed | Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer |
| title_short | Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer |
| title_sort | analytical solution and numerical approaches of the generalized leva¨que equation to predict the thermal boundary layer |
| topic | Lévêque approximation Thermal entrance region Thermal boundary layer Dimensionless variables Temperature Nusselt number |
| url | https://revistas.usfq.edu.ec/index.php/avances/article/view/968 |
| work_keys_str_mv | AT alibelhocine analyticalsolutionandnumericalapproachesofthegeneralizedlevaqueequationtopredictthethermalboundarylayer AT wanzaidiwanomar analyticalsolutionandnumericalapproachesofthegeneralizedlevaqueequationtopredictthethermalboundarylayer |