Stability analysis of Electro-thermo convection of binary fluid with chemical reaction in a horizontal porous layer

Abstract

In the present article, we illustrate the onset of electro-thermo convection of a binary fluid in a horizontal porous layer subject to fixed temperatures and chemical equilibrium on the bounding surfaces. The state of convection is considered, when the solubility of dissolved components depends on temperature. We use linear stability analysis to investigate how the vertical electric field and dissolution or precipitation of the component affects the onset of convection. Darcy-Brinkman’s law and Boussinesq approximation are employed with the equation of state taken to be linear with respect to temperature and concentration. We present a comparative study for four different bonding surfaces in linear case and weakly non-linear study in free-free (F/F) case for different controlling parameters. From the linear stability analysis, we find that the larger value of AC electric Rayleigh number (Rea) and Damköler number enhance (χ) the onset of convection whereas the larger value of inverse Darcy number delay (Da-1) the onset of convection. The stability criteria for different bounding surfaces are given as F/R>R/R>R/F>F/F (where F represents free and R stands for rigid bounding surfaces). The effect of parameters is qualitatively same for all surfaces but differs quantitatively. We are getting same kind of results for limiting cases such as pure electro convection, pure double diffusive electro-convection and pure thermal double diffusive convection. From weakly non-linear stability analysis, we show heat and mass transfer effect for unsteady and steady cases for same parameters. With increasing value of Rea and χ, enhance the unsteady and steady convection whereas reverse is obtained with increasing Da-1. We also draw streamlines, isotherms and isohalines in unsteady case for different times (0.001,0.03,0.06,0.1) as well as in steady case for different Rayleigh number (at critical Rayleigh number and more than critical). These plots represent state of conduction and convection.