Phenomenological theory on refrigeration effect of practical type-I superconductor.

In accordance with the phenomenological theory of thermodynamics, we discussed the Magnetocaloric effect of type-I superconductors, which are exposed to a varying magnetic field. It is concluded theoretically that the refrigeration effect is closely associated with demagnetization effect for practical specimens, which is different from the situation for ideal superconductor sample having no demagnetization effect. From the thermodynamic formulation of superconductivity, we deduced the integrating function of the thermal effect. By numerical calculation, we found a quantitative relation between the refrigeration effect and the demagnetizing factor which is determined by the shape of the sample.