Abstract
We use the energy method to obtain the non-linear stability threshold for thermosolutal convection porous media of Brinkman type with reaction. The obtained non-linear boundaries for different values of the reaction terms are compared with the relevant linear instability boundaries obtained by Wang and Tan (Phys Lett A 373:776–780, 2009). Using the energy theory we obtain the non-linear stability threshold below which the solution is globally stable. The compound matrix numerical technique is implemented to solve the associated system of equations with the corresponding boundary conditions. Two systems are investigated, the heated below salted above case and the heated below salted below case. The effect of the reaction terms and Brinkman term on the Rayleigh number is discussed and presented graphically.
Highlights
Convection in porous media has attracted the attention of many researchers and has been an area of great interest in addition to its wide range of applications
Bdzil and Frisch [15] performed a linear stability analysis where the fluid catalysed at the lower boundary of the layer and they developed their work in Bdzil and Frisch [16] and a similar work carried by Gutkowicz-Krusin and Ross [17]
Wang and Tan [1] extended the previous work of Pritchard and Richardson [28] in which Wang and Tan [1] considered Darcy-Brinkman model and used normal mode analysis to carry out a linear instability analysis
Summary
Convection in porous media has attracted the attention of many researchers and has been an area of great interest in addition to its wide range of applications. Thermal convection in porous media and stability analysis returns back to Horton and Rogers [2], Lapwood [3] and Nield and Barletta [4]. The problem of double-diffusive convection in porous media is well investigated by Nield [5], Rudraiah et al [6], Wollkind and Frisch [7,8], Nield and Bejan [9], Ingham and Pop [10,11], Vafai [12,13] and
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
