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ACI Avances en Ciencias e Ingenierías

SECTION A: EXACT SCIENCES

Vol. 11 No. 2 (2019)

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

DOI
https://doi.org/10.18272/aci.v11i2.968
Submitted
October 25, 2017
Published
2019-05-12

Abstract

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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