Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 June 2023
Issue publication date: 22 June 2023
Abstract
Purpose
The onset of Darcy–Benard convection in a fluid-saturated porous layer within channeled walls can be through either the convectively amplified perturbations or absolutely unstable modes. The convective type route to formation of cellular forms has received much more interest in the literature than the absolute mode. This paper aims to explore the absolute instability mechanism on triggering the Benard convection in the presence of a uniform magnetic field acting perpendicular to the channel walls.
Design/methodology/approach
Pursuing a completely theoretical linear stability approach, the locus of wavenumbers and critical Rayleigh numbers with respect to varying Peclet numbers leading to zero complex group velocity, and hence the absolute instability onset, is formulated in closed form. The formulae also incorporate the influence of fluid movement through the porous layer.
Findings
Wanenumbers are found to be increasing in magnitude under the effect of the magnetic field. Although the magnetic field expectedly behaves in favor of stabilizing the convection through both convective and absolute instabilities by pushing the threshold value of Rayleigh number to higher values, a peculiarity exists in such a manner that the stabilizing effect of magnetic field can no longer compete against the absolute instability mechanism within the magnetized field after some critical location possessing negative part of the wavenumber.
Originality/value
The significant outcome is attributed to the exchange of instabilities as far as the absolute instability mechanism is concerned. Magnetic field is always stabilizing and no such trend is observed regarding the convective type instability.
Keywords
Acknowledgements
The work is based on the preprint cited in Turkyilmazoglu (2023). It is with license CC BY 4.0 and the preprint will certainly be modified once the article is published on Emerald Insight.
Statements and declarations: The author declares that no funds, grants or other support were received during the preparation of this manuscript.
Competing interests: The author has no relevant financial or nonfinancial interests to disclose.
Author contributions: Only the present author contributed to the entire study.
Data availability: Data can be obtained upon a reasonable request.
Citation
Turkyilmazoglu, M. (2023), "Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 8, pp. 3056-3070. https://doi.org/10.1108/HFF-04-2023-0213
Publisher
:Emerald Publishing Limited
Copyright © 2023, Emerald Publishing Limited