Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation
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| Format: | Artículo científico |
| Sprache: | en |
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Universidad Distrital Francisco José de Caldas
2018
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| _version_ | 1876450340417568768 |
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| author | Ali Belhocine |
| author_facet | Ali Belhocine |
| contents | Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation Ali Belhocine Wan Zaidi Wan Omar Multidisciplinarias (Ciencias Sociales) Runge Temperature Kutta method Nusselt number Thermal boundary layer In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero, and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. 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. 2018 artículo científico 0124-2253 https://www.redalyc.org/articulo.oa?id=504373148002 en http://www.redalyc.org/revista.oa?id=5043 Revista Científica application/pdf Universidad Distrital Francisco José de Caldas Revista Científica (Colombia) Num.1 Vol.31 |
| format | Artículo científico |
| id | redalyc_504373148002 |
| institution | Redalyc |
| language | en |
| publishDate | 2018 |
| publisher | Universidad Distrital Francisco José de Caldas |
| spellingShingle | Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation Ali Belhocine Multidisciplinarias (Ciencias Sociales) Runge Temperature Kutta method Nusselt number Thermal boundary layer Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation Ali Belhocine Wan Zaidi Wan Omar Multidisciplinarias (Ciencias Sociales) Runge Temperature Kutta method Nusselt number Thermal boundary layer In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero, and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. 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. 2018 artículo científico 0124-2253 https://www.redalyc.org/articulo.oa?id=504373148002 en http://www.redalyc.org/revista.oa?id=5043 Revista Científica application/pdf Universidad Distrital Francisco José de Caldas Revista Científica (Colombia) Num.1 Vol.31 |
| title | Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation |
| topic | Multidisciplinarias (Ciencias Sociales) Runge Temperature Kutta method Nusselt number Thermal boundary layer |
| url | https://www.redalyc.org/articulo.oa?id=504373148002 |