A linear and nonlinear stability analyses are carried out for a double‐diffusive chemically reactive fluid layer with viscosity being a function of temperature and pressure. The linear stability analysis is studied when the stabilizing salt gradient acts against the destabilizing thermal gradient. The effect of reaction parameters and variable viscosity on the stability of the system is studied for heated below, salted above, and the heated and salted below models with Rigid–Rigid boundary conditions. Chebyshev pseudospectral method is applied to determine the numerical solutions.

In the present study, double‐diffusive convection with chemical reaction in a Darcy–Brinkman porous layer, heated and salted below, has been investigated. Linear analysis is performed with the help of the normal mode technique, and nonlinear analysis is performed with the help of the energy method. The effect of the thermal contribution of the chemical reaction is found to be more effective on the convective instability in comparison with the solutal contribution of the chemical reaction. The reaction parameters k 1 , k 2 enhance the onset of convection in the stationary mode, however, in oscillatory mode, the onset of convection is seen to be delayed. The effect of solute Rayleigh number R s , Darcy number D a , is depicted graphically.

Investigation of the onset of thermosolutal convection with chemical reaction is carried out for different types of basic temperature and concentration gradients using linear theory and energy method. An unconditional non-linear stability with exponential decay of finite amplitude perturbations is achieved and the Galerkin technique is utilized to solve the resulting Eigen-value problem obtained from linear and non-linear analysis. The numerical scheme is validated with existing results and the results are obtained for linear, parabolic, inverted parabolic, piecewise linear, oscillatory and step-function profiles of temperature and concentration gradients. The linear and non-linear results show the existence of subcritical instability.

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