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Spatially periodic temperature modulation of a compressible fluid

journal contribution
posted on 2023-05-17, 19:18 authored by Chen, MJ, Lawrence ForbesLawrence Forbes

A spatially periodic temperature modulation is gradually applied at the lower boundary of a layer of compressible fluid. The temperature from the lower wall diffuses into the layer and induces various convection patterns. As the amplitude of the temperature modulation is increased, non-linear effects, including those due to the inclusion of compressibility, become more prominent. An accurate numerical scheme is developed to capture the full time-dependent behaviour here. Spectral methods will be used throughout this work to provide accurate representations of the various solution components and allow for the efficient implementation of a variety of boundary conditions.

Three different types of modulation are considered, namely a pure cosine as well as rounded triangle and rounded square profiles, where the latter two of these have applications in various physical situations. Interest lies in how the nature of the convection and temperature diffusion change as the amplitude of these modulations is increased. Both no-slip and slip conditions will be implemented on the upper and lower boundaries of the layer and the differences between the two will be considered for selected cases.


Publication title

European Journal of Mechanics B: Fluids








School of Natural Sciences


Gauthier-Villars/Editions Elsevier

Place of publication

23 Rue Linois, Paris, France, 75015

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Copyright 2013 Elsevier Masson SAS

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  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences