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Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems

Igor V. Shevchuk (Fakultät für Informatik und Ingenieurwissenschaften, Technische Hochschule Köln, Gummersbach, Germany)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 June 2022

Issue publication date: 3 January 2023

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Abstract

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.

Keywords

Citation

Shevchuk, I.V. (2023), "Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 204-225. https://doi.org/10.1108/HFF-03-2022-0168

Publisher

:

Emerald Publishing Limited

Copyright © 2022, Emerald Publishing Limited

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