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A solution for the quasi-one-dimensional linearised Euler equations with heat transfer

Yeddula, S. R., Guzmán-Iñigo, J. ORCID: 0000-0002-1833-6034 & Morgans, A. S. (2022). A solution for the quasi-one-dimensional linearised Euler equations with heat transfer. Journal of Fluid Mechanics, 936, article number R3. doi: 10.1017/jfm.2022.101


The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging–diverging nozzle with constant heat transfer for both subcritical and supercritical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.

Publication Type: Article
Additional Information: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. © The Author(s), 2022. Published by Cambridge University Press
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
SWORD Depositor:
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