Triple diffusive magneto convection in a fluid-porous composite system

A study on triple diffusive magneto convection is made for a fluid – porous composite system with rigid-rigid boundaries insulated to temperature and concentration.  The porous layer of the composite system is modeled using Darcy–Brinkman model.  The method of regular perturbation approach is employed to find the eigen-value for the problem considered.  The critical Rayleigh number as criterion for the onset of convection is derived for step function, salting below and desalting above salinity profiles.  The effect of various physical parameter on the onset of convection is graphically depicted and the stability of the system is analyzed.

triple diffusive magneto convection
non uniform salinity gradients
regular perturbation technique
  1. Turner J. S.  Buoyancy Effects in Fluids. University of Cambridge (1979).
  2. Rudraiah N., Shivakumara I. S.  Double-diffusive convection with an imposed magnetic field.  International Journal of Heat and Mass Transfer.  27 (10), 1825–1836 (1984).
  3. Thompson W. B.  Thermal convection in a magnetic field.  Philosophical Magazine.  42 (335), 1417–1432 (1951).
  4. Chandrasekhar S.  Hydrodynamic and Hydromagnetic Stability. Oxford University Press, London, UK (1961).
  5. Lortz D.  A stability criterion for steady finite amplitude convection with an external magnetic field.  Journal of Fluid Mechanics.  23 (1), 113–128 (1965).
  6. Rudraiah N.  Double-diffusive magnetoconvection.  Pramana.  27, 233–266 (1986).
  7. Siddheshwar P. G., Pranesh S.  Magnetoconvection in fluids with suspended particles under $1g$ and $\mu g$.  Aerospace Science and Technology.  6 (2), 105–114 (2002).
  8. Prakash J., Kumari K., Kumar R.  Triple diffusive convection in a Maxwell fluid saturated porous layer: Darcy–Brinkman–Maxwell Model.  Journal of Porous Media.  19 (10), 87–883 (2016).
  9. Shivakumara I. S., Naveen Kumar S. B.  Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer.  International Journal of Heat and Mass Transfer.  68, 542–553 (2014).
  10. Manjunatha N., Sumithra R.  Effects of non-uniform temperature gradients on triple diffusive surface tension driven magneto convection in a composite layer.  Universal Journal of Mechanical Engineering.  7 (6), 398–410 (2019).
  11. Awasthi M. K., Kumar V., Patel R. K.  Onset of triply diffusive convection in a Maxwell fluid saturated porous layer with internal heat source.  Ain Shams Engineering Journal.  9 (4), 1591–1600 (2018).
  12. Komala B., Sumithra R.  Effects of non-uniform salinity gradients on the onset of double diffusive magneto–Marangoni convection in a composite layer.  International Journal of Advanced Science and Technology.  28 (15), 874–885 (2019).
  13. Currie I. G.  The effect of heating rate on the stability of stationary fluids.  Journal of Fluid Mechanics.  29 (2), 337–347 (1967).
  14. Vidal A., Acrivos A.  Nature of the neutral state in surface-tension driven convection.  The Physics of Fluids.  9 (3), 615 (1966).