Effect of nonlinear temperature and concentration profiles on the stability of a layer of fluid with chemical reaction

Abstract

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 nonlinear stability with exponential decay of finite amplitude perturbations is achieved and the Galerkin technique is utilized to solve the resulting eigenvalue problem obtained from linear and nonlinear 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 nonlinear results show the existence of subcritical instability.