Thermomagnetic pump and thermomagnetic convection in a closed hydrodynamic loop

A thermomagnetic pump is understood as a heated section of a convective loop with a ferrofluid with a non-uniform magnetic field imposed on this section. The part of the heat generated in the pump is transferred by the ferrofluid and absorbed in a cooling radiator, and the other part is dissipated in the environment. The aim of the work is to search for a functional relationship between the velocities of thermomagnetic convection and pump parameters. The problem is solved analytically in the approximation of small Reynolds numbers for a pump containing an electric heater with a circular channel. Equations are obtained that determine the velocity of the convective flow in a parametric form, taking into account the geometry and magnetic field strength and the field dependence of the pyromagnetic coefficient of the ferrofluid. The role of the parameter is played by the spatial decrement of the temperature decay along the contour axis. It is shown that in the case of low Biot numbers the velocity of the flow increases according to the root law with increasing heater power and does not depend on the diameter of the channel. The analytical results are compared with the experimental data for combined (thermomagnetic and gravitational) convection. Neglecting gravitational convection at high heater power leads to an underestimation of the flow velocity by 20–30%. It can be expected that in the case of reduced gravity, the resulting formulas will describe the flow velocity with an accuracy of a coefficient close to unity.