Three dimensional simulations and stability analysis for convection induced by absorption of radiation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 5 May 2015
Abstract
Purpose
The purpose of this paper is to investigate a model for convection induced by the selective absorption of radiation in a fluid layer. The concentration based internal heat source is modelled quadratically. Both linear instability and global nonlinear energy stability analyses are tested using three dimensional simulations. The results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.
Design/methodology/approach
The author introduce the stability analysis of the problem of convection induced by absorption of radiation in fluid layer, then the author select a situations which have very big subcritical region. Then, the author develop a three dimensions simulation for the problem. To do this, first, the author transform the problem to velocity – vorticity formulation, then the author use a second order finite difference schemes. The author use implicit and explicit schemes to enforce the free divergence equation. The size of the Box is evaluated according to the normal modes representation. Moreover, the author adopt the periodic boundary conditions for velocity and temperature in the $x, y$ dimensions.
Findings
This paper explores a model for convection induced by the selective absorption of radiation in a fluid layer. The results demonstrate that the linear instability thresholds accurately predict the onset of instability. A three-dimensional numerical approach is adopted.
Originality/value
As the author believe, this paper is one of the first studies which deal with study of stability of convection using a three dimensional simulation. When the difference between the linear and nonlinear thresholds is very large, the comparison between these thresholds is very interesting and useful.
Keywords
Acknowledgements
This work was supported by a scholarship from the Iraqi ministry of higher education and scientific research. The author would like to thank anonymous referees for their comments that have led to improvements in the manuscript.
Citation
Harfash, A.J. (2015), "Three dimensional simulations and stability analysis for convection induced by absorption of radiation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 4, pp. 810-824. https://doi.org/10.1108/HFF-08-2013-0250
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited