Abstract
A linear instability analysis for the inception of double-diffusive convection with a concentration based internal heat source is presented. The system encompasses a layer of fluid which lies above a porous layer saturated with the same fluid. Detailed stability characteristics results are presented for key physical parameters including the solute Rayleigh number, depth ratio of the fluid to porous layer and strength of radiative heating.
Similar content being viewed by others
References
Beavers GS, Joseph DD (1967) Boundary conditions at a naturally permeable wall. J Fluid Mech 30:197–207
Capone F, Gentile M, Hill AA (2011) Double-diffusive penetrative convection simulated via internal heating in an anisotropic porous layer with throughflow. Int J Heat Mass Transf 54:1622–1626
Chang MH (2004) Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer. Phys Fluids 16:3690–3698
Chang MH (2006) Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow. Phys Fluids 18:1–10
Dongarra JJ, Straughan B, Walker DW (1996) Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl Numer Math 22:399–434
Hill AA (2003) Convection due to the selective absorption of radiation in a porous medium. Contin Mech Thermodyn 15:275–285
Hill AA (2004) Convection induced by the selective absorption of radiation for the Brinkman model. Contin Mech Thermodyn 16:43–52
Hill AA (2004) Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium. Contin Mech Thermodyn 16:305–318
Hill AA (2004) Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source. Dyn Atmos Ocean 38:57–67
Hill AA (2005) Double-diffusive convection in a porous medium with a concentration based internal heat source. Proc R Soc A 461:561–574
Hill AA, Carr M (2010) Sharp global nonlinear stability for a fluid overlying a highly porous material. Proc R Soc Lond A 466:127–140
Hill AA, Carr M (2010) Nonlinear stability of the one domain approach to modelling convection in superposed fluid and porous layers. Proc R Soc Lond A 466:2695–2705
Hill AA, Straughan B (2009) Global stability for thermal convection in a fluid overlying a highly porous material. Proc R Soc Lond A 465:207–217
Hirata SC, Goyeau B, Gobin D (2009) Stability of thermosolutal natural convection in superposed fluid and porous layers. Transp Porous Media 78:525–536
Krishnamurti R (1997) Convection induced by selective absorption of radiation: a laboratory model of conditional instability. Dyn Atmos Ocean 27:367–382
Kumar A, Bhadauria BS (2011) Double diffusive convection in a porous layer saturated with viscoelastic fluid using a thermal non-equilibrium model. Phys Fluids 23:054101
Malashetty MS, Biradar BS (2011) The onset of double diffusive reaction-convection in an anisotropic porous layer. Phys Fluids 23:064102
Malashetty MS, Tan W, Swamy M (2009) The onset of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer. Phys Fluids 21:084101
Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York
Straughan B (2001) Surface-tension-driven convection in a fluid overlying a porous layer. J Comput Phys 170:320–337
Straughan B (2002) Effect of property variation and modelling on convection in a fluid overlying a porous layer. Int J Numer Anal Methods Geomech 26:75–97
Straughan B (2002) Global stability for convection induced by absorption of radiation. Dyn Atmos Ocean 35:351–361
Straughan B (2004) The energy method, stability, and nonlinear convection. Applied mathematical sciences, Springer, New York
Straughan B, Walker DW (1996) Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems. J Comput Phys 127:128–141
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Olali, P.B. Double-diffusive convection induced by selective absorption of radiation in a fluid overlying a porous layer. Meccanica 48, 201–210 (2013). https://doi.org/10.1007/s11012-012-9594-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-012-9594-6