https://doi.org/10.1140/epjp/s13360-024-05556-7
Regular Article
Thermal entrance solution for parallel plates with asymmetric arbitrary wall heat flux
1
Key Laboratory of Pulsed Power Technology (Ministry of Education), Huazhong University of Science and Technology, 430074, Wuhan, China
2
School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430074, Wuhan, China
Received:
2
June
2024
Accepted:
12
August
2024
Published online:
26
August
2024
In engineering applications, parallel plates are geometric approximations of rectangular and concentric annular ducts. For the case that one wall is thermally insulated, and the opposite wall is held at arbitrary heat flux, establishing an intuitive local Nusselt number correlation helps design and evaluate the operating status of the equipment. For the asymmetric heating case, the eigenfunctions of odd function properties are added when applying the separation of variables method. The first 14 eigenvalues are solved using numerical methods. For larger eigenvalues, an asymptotic expression is provided. A faster approximate numerical computation scheme is developed by introducing the integral method. The optimal power of the polynomial temperature approximation profile is determined by the Lèvêque solution of the region near the entrance. The theoretical computations are verified by the CFD (computational fluid dynamic) simulation. The results show that the relative error between the separation of variables method and CFD simulation is less than 0.739% in the downstream region of the thermal entrance. In the region near the entrance, the accuracy of the CFD simulation is inferior, with a relative error of 46.41%. The integral method and the separation of variables method are in good agreement across the entire region, with a relative error not exceeding 3.130%. In terms of computation speed, the integral method has significant advantages. Finally, based on the integral method, intuitive local Nusselt number correlations are proposed for various heat flux functions, including constant values, power functions, exponential functions, and sinusoidal functions. The research finds that the thermal entrance length under the asymmetric heating case is 0.16Peb. Within a wide range of x/Peb, the relative error between the correlation and analytical solution is less than 3.130%. For another arbitrary form of function, after being expanded into a polynomial, the local Nusselt number can be derived by a linear combination of the proposed correlation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
