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In this work, we perform preliminary group classification of equations governing the flow of a thermo-dependent fluid in a porous medium. The detailed model is a coupled system of nonlinear partial differential equations containing two arbitrary functions. The principal Lie algebra admitted by the coupled system is given. The study also demonstrates that the forms of arbitrary functions provide an extension of this algebra via an optimal system of one-dimensional Lie subalgebras.

This paper investigates axisymmetric shapes of a ferrofluid drop immersed in a uniform magnetic field. Approximate solutions are constructed for the governing nonlinear boundary value problem using the domain perturbation method. Bifurcation and turning points are located by applying a special type of Hermite–Pade approximation.

In this paper we study the stability of the magnetostatic equilibrium through a relaxation of a magnetic field B in perfectly conducting compressible and viscous fluid. We establish stability criterion of a large class of Beltrami flows to any admissible displacement about the equilibrium configuration. We show that the field is stable to any displacement with the same 2π-periodicity as the basic flow, except the case where perturbations with wavelength much greater than the scale of the basic flow are included.