Lie reduced order modeling of unsteady thermosolutal Marangoni magnetohydrodynamic convection conjoined with chemical reaction and heat generation

An unsteady electrically conducting thermosolutal magnetohydrodynamic Marangoni convective fluid flow along a vertically inclined sheet under the effect of heat generation and chemical reaction is analyzed in this paper through Lie symmetry method. Such flow and heat transfer models are represented by nonlinear partial differential equations of order two that are usually converted to ordinary differential equations by applying similarity transformations. There exist similarity transformations to eliminate variables of the considered flow model, in the literature, however a new enhanced generalized set of similarity transformations is derived here by obtaining and employing Lie symmetries of the flow governing equations. It is shown that this generalized set of transformations not only eliminates a few dependent and independent variables of the model, indeed it introduces some arbitrary control parameters in the reduced system of equations. These parameters often act as control parameters by influencing fluid flow profiles through analytic solutions for the deduced system of equations that are acquired by rigorous analytical homotopy perturbation formulation. Here these parameters vanish due to associated boundary conditions, however this set of similarity transformations is applicable to all those flow equations which admit the symmetry generators of the form associated with the present model, hence these transformations address a wide class of fluid flow models to reveal the corresponding fluid dynamics. The obtained analytic solutions reflect the effects of the coefficients of heat generation and chemical reaction, the Hartmann number, and the Lie control parameters on velocity, temperature, and concentration profiles.