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Analytical solution and numerical simulation of the thermal entrance region problem for laminar flow through a circular pipe
Publikationstyp
Journal Article
Date Issued
2020-04-01
Sprache
English
Author(s)
Institut
TORE-URI
Volume
11
Issue
2
Article Number
2050013
Citation
International Journal of Modeling, Simulation, and Scientific Computing 2 (11): 2050013 (2020-04-01)
Publisher DOI
Scopus ID
In this paper, the assumptions implicited 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, other important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail. A comparison with the previous study available in literature has been done and found an excellent agreement with the published data.
Subjects
dimensionless variables
Nusselt number
Runge-Kutta method
temperature
thermal boundary layer
Thermal entrance region