Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer

• Main Authors: Belhocine, Ali, Wan Omar, Wan Zaidi
• Format: Article
• Language: English
• Published: ACI Avances en Ciencias e Ingenierías 2019
• Subjects: TJ Mechanical engineering and machinery
• 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

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.