A correction of porous media model for active magnetic regenerator based on a finite thermal penetration depth

A sphere-packed regenerator is often used in the active magnetic regenerator (AMR) of a magnetic refrigerator. When simulating such a regenerator, porous media instead of the practical sphere geometry is assumed and the solid refrigerants are assumed to be homogeneous in temperature. In fact, the temperature is inhomogeneous and determined by the ratio between sphere radius and thermal penetration depth. A method was used here that evaluates the influence of inhomogeneous temperature distribution inside the spheres on the cooling capacityand a correction factor was proposed to modify the porous media model under different particle diameters, frequencies and mass flow rates. Simulation results showed that the relative deviation of cooling capacity increased in the porous media AMR model with the increase of the ratio between sphere radius and thermal penetration depth. With a frequency below 3 Hz, when the particle radius was approximately 0.8 times the thermal penetration depth, the relative deviation of cooling capacity can be controlled within 5%. Comprehensively considering the pumping work and the heat transfer, a smaller diameter was selected to obtain the maximum COP value, at which the influence of thermal penetration depth can be ignored.