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.

中文翻译：

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用于预测热边界层的广义 Levèque 方程的解析解和数值模拟

摘要 本文重新检验了Levesque 近似中的隐式假设，并利用所开发的解说明了无量纲温度分布和热边界层厚度。通过定义相似变量，控制方程和边界条件被简化为典型的无量纲形式，以便在入口区域获得解析解。提出了一个相对简单的数学方案，通过该方案可以严格地获得具有相似变量的层流传热的入口区域温度解。然后，将解析解与在 FORTRAN 代码下使用四阶龙格编程的数值解进行核对。库塔法 (RK4)。最后，从该分析中获得的其他重要热结果，例如；详细讨论的热入口区域的近似努塞尔数。分析结果与文献中可用的已发表数据进行了比较，发现了良好的一致性。