<p>The paper presents the results of mathematical modeling of convective heat exchange and magnetic hydrodynamics of liquid in a spherical layer. The influence of boundary conditions for the azimuthal component of magnetic induction on the heat exchange of an electrically conductive liquid, the structure of its flow, the field of magnetic induction, and the distribution of local Nusselt numbers for the case of magnetic Reynolds numbers less than one is investigated. The values of magnetic Reynolds numbers and the moments of time at which the intensity of heat exchange on the inner and outer surfaces of the liquid layer becomes the same are determined.</p>