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

Abstract

In this paper, the implicit assumptions in Levesque’s approximation are re-examined, and the dimensionless temperature distribution and the thermal boundary layer thickness were illustrated using the developed solution. By defining a similarity variable, the governing equations and boundary conditions are reduced to a typical dimensionless form in order to achieve an analytic solution in the entrance region. A relatively simple mathematical scheme was proposed by which the entrance-region temperature solution for laminar flow heat transfer with the similarity variable can be rigorously obtained The analytical solutions are then, checked against numerical solutions which were programmed under FORTRAN code using fourth-order Runge–Kutta method (RK4). Finally, other important thermal results obtained from this analysis, such as; approximate Nusselt number for the thermal entrance region which was discussed in detail. Analytical results were compared with the published data available in the literature for limiting cases, and good agreement was noticed.