In a rotary magnetic refrigerator a porous ring is turning in and out of a magnetic field region. The adiabatic demagnetization of the magnetocaloric material produces the "cold energy". This is described by a discontinuous temperature decrease, known as adiabatic temperature difference. For such a machine a physical model has been developed, based on a mapping of the magneto-thermodynamic problem. In this model, in a basic centre cell, two coupled linear partial differential equations are solved, which have been programmed in the Modelica language. The operation of a magnetic refrigerator is simulated with numerous parameters. Steady state solutions are obtained to verify the coefficient of performance under stable operation conditions. Optimal running conditions defined by maximum values of the coefficient of performance - are not presented in this article, but can now easily be obtained with the existing program. A simple regulation strategy is proposed and implemented into the program. (C) 2010 Elsevier Ltd and IIR. All rights reserved.