Nonlinear stability of laminar flows in an inclined heated layer with an imposed magnetic field

Nonlinear stability of stationary laminar flow solutions of two inclined parallel planes filled with a hydromagnetic fluid heated from below is studied via Lyapunov direct method. In order to determine the energy stability bound for the critical Rayleigh number ( RaE) explicitly, for Ra<RaE, the laminar flow solutions of the problem are nonlinearly unconditionally and exponentially stable, and we consider just transverse perturbations. Compared with the results in the literature, conditions for the nonlinear stability obtained in this article have no restriction on the magnetic Prandtl number Pm.