Straughan, B. (2021) 'Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order.', Rendiconti del Circolo Matematico di Palermo Series 2 .
We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.
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|Publisher Web site:||https://doi.org/10.1007/s12215-020-00588-1|
|Publisher statement:||This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.|
|Date accepted:||28 December 2020|
|Date deposited:||21 April 2021|
|Date of first online publication:||18 January 2021|
|Date first made open access:||21 April 2021|
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