Analytical solution to heat transfer in compressible laminar flow in a flat minichannel
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Heat transfer in compressible laminar flow in mini-/micro-channels, a classical and general topic in fields of fuel cells, electronics, micro heat exchanger, etc., is revisited. Based on a two-dimensional continuum flow model, analytical solutions of the dimensionless model are achieved in closed-form symbolic algebras of Whittaker eigenfunctions, corresponding to two kinds of boundary conditions with arbitrarily prescribed wall temperature or wall heat flux. As the eigenvalues and eigenfunctions are independent on the dimensionless quantities, which influence the along-the-channel behaviors, the algorithm reveals the common features of compressible laminar thermal flows. The algorithms do not require the assumption of a linear pressure distribution, which is proved to be untenable in some cases (e.g. constant wall heat flux). The algorithms are validated well by the exact (numerical) computations in exemplary cases of both small and moderate Reynolds number, Mach number and Eckert number of air. Although expressed in a series of eigenfunctions, only several terms (sometimes one or two terms) of solutions are required for a practical computation.
Bao , C , Jiang , Z , Zhang , X & Irvine , J T S 2018 , ' Analytical solution to heat transfer in compressible laminar flow in a flat minichannel ' , International Journal of Heat and Mass Transfer , vol. 127 , no. Part C , pp. 975-988 . https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.084
International Journal of Heat and Mass Transfer
© 2018 Elsevier Ltd. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.084
DescriptionThis work was supported by the Beijing Science and Technology Project [grant number Z181100004518004] and the Fundamental Research Funds for the Central Universities [grant number FRF-GF-17-B31]. CB thanks for the China Scholarship Council (CSC) fellowship support.
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