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 dimensionless eq...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
ACI Avances en Ciencias e Ingenierías
2019
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| Online Access: | http://eprints.utm.my/id/eprint/88129/1/WanZaidiWanOmar2019_AnalyticalSolutionandNumericalApproaches.pdf http://eprints.utm.my/id/eprint/88129/ https://doi.org/10.18272/aci.v11i2.968 |
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| Summary: | 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. |
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