The exact solution of nonlinear stress-free convection under the influence of magnetic fields

This paper aims at transforming nonlinear equations (Navier-Stokes, energy and magnetic induction) in steady state into ordinary high order differential equations. The exact solution for it has been found using a suitable transformation. The second goal is studying the state conditions of heating from below in a horizontal layer and studying the influence of the magnetic field on the phenomenon of convection itself. This model paper has uncovered the properties of electricity-conducting fluid elements. These properties have been disclosed neither in theory nor in practice. This study has been applied on the stress-free boundaries. All of which have realistic manifestation, in nature. They study convection in geophysics and astrophysics. Results have been illustrated in three dimensions to generalize the study and use it practically.