A magnetic refrigerator with a cylindrical heat exchanger of porous periodic structure has been designed and numerical system performance calculations have been performed. This refrigerating machine, respectively heat pump device, can be operated with air or water as working fluid. In the article the design of the new refrigerator is outlined and the coupled basic equations of magnetism and thermodynamics are presented, which contain three independant characteristic geometrical quantities characterizing the heat exchanger structure. Magnetic fields, magnetic flux densities, and coefficients of performances (COP), etc. were investigated for magnetic inductions B0 between 1 and 5 Tesla. The obtained COP’s are promising high compared to conventional refrigeration equipment working with gas compression and expansion.