Purpose

Thus, the purposes of this study are to study the limits of applicability of the self-similar solution to the problem of fluid flow, heat and mass transfer in conical gaps with small conicity angles, to substantiate the impossibility of using a self-similar formulation of the problem in the case of large conicity angles and to substantiate the absence of the need to take into account the radial thermal conductivity in the energy equation in its self-similar formulation for the conicity angles up to 4°.

Design/methodology/approach

In the present work, an in-depth and extended analysis of the features of fluid flow and heat transfer in a conical gap at small angles of conicity up to 4° is performed. The Couette-type flow arising, in this case, was modeled using a self-similar formulation of the problem. A detailed analysis of fluid flow calculations using a self-similar system of equations showed that they provide the best agreement with experiments than other known approaches. It is confirmed that the self-similar system of flow and heat transfer equations is applicable only to small angles of conicity up to 4°, whereas, at large angles of conicity, this approach becomes unreasonable and leads to significantly inaccurate results. The heat transfer process in a conical gap with small angles of conicity can be modeled using the self-similar energy equation in the boundary layer approximation. It was shown that taking into account the radial thermal conductivity in the self-similar energy equation at small conicity angles up to 4° leads to maximum deviations of the Nusselt number up to 1.5% compared with the energy equation in the boundary layer approximation without taking into account the radial thermal conductivity.

Findings

It is confirmed that the self-similar system of fluid flow equations is applicable only for small conicity angles up to 4°. The inclusion of radial thermal conductivity in the model unnecessarily complicates the mathematical formulation of the problem and at small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%). Heat transfer in a conical gap with small conicity angles up to 4° can be modeled using the self-similar energy equation in the boundary layer approximation.

Originality/value

This paper investigates the question of the validity of taking into account the radial heat conduction in the energy equation.

中文翻译：

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关于旋转锥盘系统自相似解中径向热导率的影响

目的

因此，本研究的目的是研究自相似解决方案对小锥度角锥形间隙中的流体流动、传热和传质问题的适用性限制，以证实使用自相似公式的不可能性在大锥度角的情况下的问题，并证实不需要考虑能量方程中的径向热导率在其自相似公式中的锥度角高达 4°。

设计/方法/途径

在目前的工作中，对锥度达 4° 的小角度锥形间隙中的流体流动和热传递特征进行了深入和扩展的分析。在这种情况下，出现的 Couette 型流是使用问题的自相似公式建模的。使用自相似方程组对流体流量计算进行的详细分析表明，与其他已知方法相比，它们与实验的一致性最好。经证实，自相似系统的流动和传热方程仅适用于最大 4° 的小锥度角，而在大锥度角时，这种方法变得不合理并导致明显不准确的结果。可以使用边界层近似中的自相似能量方程来模拟具有小锥度角的锥形间隙中的传热过程。结果表明，与不考虑边界层近似的能量方程相比，在高达 4° 的小锥度角下考虑自相似能量方程中的径向热导率导致努塞尔数的最大偏差高达 1.5%考虑径向热导率。

发现

经证实，流体流动方程的自相似系统仅适用于最大 4° 的小锥度角。在模型中包含径向热导率不必要地使问题的数学公式复杂化，并且在高达 4° 的小锥度角下导致努塞尔数（最大 1.5%）的偏差微不足道。可以使用边界层近似中的自相似能量方程对小锥度角达 4° 的锥形间隙中的传热进行建模。

原创性/价值

本文研究了在能量方程中考虑径向热传导的有效性问题。