Analytical results were compared with the published data available in the literature for limiting cases, and good agreement was noticed. Finally, other important thermal results obtained from this analysis, such as approximate Nusselt number for the thermal entrance region which was discussed in detail.
HEAT FLUX EQUATION CODE
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 that were programmed under FORTRAN code using fourth-order Runge–Kutta method (RK4). 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. In this paper, the implicit assumptions in Leveque’s approximation are re-examined, and the dimensionless temperature distribution and the thermal boundary layer thickness were illustrated using the developed solution.
The results show that the proposed correlations are more practical and they can predict the developing, fully developed, and average Nusselt numbers with very good accuracy across a wider range of flow conditions. Moreover, the maximum and average differences for average Nusselt numbers are 4.59% and 2.01%, respectively.
The maximum and average differences between the local Nusselt numbers predicted by the proposed correlations and the analytical data are respectively 2.04% and 0.38% for fully developed flows and 9.97% and 1.35% for developing flows. The correlations use exponential and power law functions of dimensionless axial and radial lengths they are more accurate, easier to use, more similar to fundamental analytical solutions, and require fewer terms.
HEAT FLUX EQUATION SERIES
The correlations are developed based on the results of available series solutions for four fundamental boundary conditions. This study proposes new correlations for the local and average Nusselt numbers in hydrodynamically fully developed and thermally developing or fully developed regions of laminar flows. There are many problems involving heat transfer in concentric annuli which require accurate heat transfer coefficients for laminar and turbulent flows. Concentric circular annular ducts are common and important elements in fluid flow and heat transfer equipment, including chemical mixing devices and heat exchangers.
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