A mathematical model governing steady laminar flow of an incompressible fluid subjected to a steady magnetic field including internal heating due to Joule effect, heart transfer due to conduction and convection, and thermally induced buoyancy forces has been developed. The thermal buoyancy was accounted for via Boussinesq approximation. To demonstrate effects of the Lorentz and Joule heating on the blood flow, two configurations have been chosen. The first configuration consists of a closed rectangular container (two-dimensional), and the second is a three-dimensional pipe with rectangular cross section. Results of test cases with and without applied magnetic field demonstrate influence of the magnitude of the magnetic field on the recirculating blood flow instability.
