Thermoconvective explosion in a ferromagnetic liquid

V. G. Bashtovoi - B. M. Berkovskii - A. K. Sinitsyn

Abstract
An isothennal mechanical-equilibrium state of a ferromagnetic liquid, located in gravitational and nonhomogeneous magnetic fields, becomes unstable with determined values of the parameters. It is shown that, with a linear dependence of the magnetic moment of the liquid on temperature, the convection arising is capable of autodevelopment. The temperature and the rate of motion of the liquid increase with time. An analogy can be noted between the process under consideration and the phenomenon of thermal explosion in chemical kinetics. A numerical mathematical study is carried out using the example of an infinite vertical plane-parallel channel, on whose walls an identical constant temperature is maintained. When critical values of the parameters are attained, positive perturbations break down the mechanical-equilibrium state of the liquid, and it starts to move upward along the gradient of the magnetic field. With given sources of heat due to the magnetocaloric effect, this movement is accompanied by an accelerated heating up of the liquid. Along with infinitely small perturbations, a study is also made of perturbations of finite value. A study is made of the effect of the value of the finite perturbations on the stability of the mechanical equilibrium of the liquid, and of the effect of various factors on the character of their development with time. It is demonstrated that the least stable system is that which relates to finite perturbations of the velocity. Numerical evaluations are given of the temperature and of the rate of the convection arising in the liquid.