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Double-diffusive convection induced by selective absorption of radiation in a fluid overlying a porous layer

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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.

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References

  1. Beavers GS, Joseph DD (1967) Boundary conditions at a naturally permeable wall. J Fluid Mech 30:197–207

    Article  ADS  Google Scholar 

  2. 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

    Article  MATH  Google Scholar 

  3. Chang MH (2004) Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer. Phys Fluids 16:3690–3698

    Article  ADS  Google Scholar 

  4. Chang MH (2006) Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow. Phys Fluids 18:1–10

    Article  Google Scholar 

  5. 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

    Article  MathSciNet  MATH  Google Scholar 

  6. Hill AA (2003) Convection due to the selective absorption of radiation in a porous medium. Contin Mech Thermodyn 15:275–285

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Hill AA (2004) Convection induced by the selective absorption of radiation for the Brinkman model. Contin Mech Thermodyn 16:43–52

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hill AA (2004) Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source. Dyn Atmos Ocean 38:57–67

    Article  ADS  Google Scholar 

  10. Hill AA (2005) Double-diffusive convection in a porous medium with a concentration based internal heat source. Proc R Soc A 461:561–574

    Article  ADS  MATH  Google Scholar 

  11. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Hirata SC, Goyeau B, Gobin D (2009) Stability of thermosolutal natural convection in superposed fluid and porous layers. Transp Porous Media 78:525–536

    Article  Google Scholar 

  15. Krishnamurti R (1997) Convection induced by selective absorption of radiation: a laboratory model of conditional instability. Dyn Atmos Ocean 27:367–382

    Article  ADS  Google Scholar 

  16. 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

    Article  ADS  Google Scholar 

  17. Malashetty MS, Biradar BS (2011) The onset of double diffusive reaction-convection in an anisotropic porous layer. Phys Fluids 23:064102

    Article  ADS  Google Scholar 

  18. 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

    Article  ADS  Google Scholar 

  19. Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York

    Google Scholar 

  20. Straughan B (2001) Surface-tension-driven convection in a fluid overlying a porous layer. J Comput Phys 170:320–337

    Article  ADS  MATH  Google Scholar 

  21. 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

    Article  MATH  Google Scholar 

  22. Straughan B (2002) Global stability for convection induced by absorption of radiation. Dyn Atmos Ocean 35:351–361

    Article  ADS  Google Scholar 

  23. Straughan B (2004) The energy method, stability, and nonlinear convection. Applied mathematical sciences, Springer, New York

    MATH  Google Scholar 

  24. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Princewill Baysa Olali

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  1. Princewill Baysa Olali
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Correspondence to Princewill Baysa Olali.

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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

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  • DOI: https://doi.org/10.1007/s11012-012-9594-6

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