We propose a mathematical model and method of its approximate solution for circulating flows, induced by an alternating magnetic field in a channel filled with a non-magnetic liquid and injected a drop of a ferrofluid, soluble in this liquid. One side of the channel is closed by an impermeable wall. This model imitates a thrombosed blood vessel. The aim of this work is development of a mathematical background for a method of intensification of thrombolytics transport in the thrombosed vessels, with the help of an alternating magnetic field.