In the present study, a thermodynamic model is proposed to analyze and assess the performance, through energy and exergy, of a cascade active magnetic regenerative (AMR) refrigerator operation a regenerative Brayton cycle. This cascade refrigeration system works with Gd x Tb 1Àx alloys as magnetic materials where the composition of the alloy varies for di®erent stages. In this model, the heat transfer°uid considered is a water-glycol mixture (50% by weight). The refrigeration capacity, total power consumption, coe±cients of performance (COP), exergy e±ciency and exergy destruction rate of a cascade AMR refrigeration (AMRR) system are determined. To understand the system performance more comprehensively, a parametric study is performed to investigate the e®ects of several important design parameters on COP and exergy e±ciency of the system. A : Heat transfer area, m 2 B : constant magnetic¯eld, H c : speci¯c heat, J kg K À1 COP : coe±cient of performance D : diameter of the regenerator section, m ‡ Corresponding author.Int. J. Air-Cond. Ref. 2013.21. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 01/02/15. For personal use only. d P : diameter of the particles, m E : x : exergy°ow rate, W h : convection coe±cient, W m À2 K À1 H : magnetic¯eld, T (N A À1 m À1 Þ H max : maximum magnetic¯eld, T k : thermal conductivity, W m À1 K À1 L : length of the regenerator, m m : mass, kg _ m : mass°ow rate, kg s À1 M : magnetization per unit mass, A m 2 kg À1 MCM : Magnetocaloric material Nu : Nusselt number Pr : Prandtl number _ Q : heat transfer rate, W Re : Reynolds number s : speci¯c entropy, J kg À1 K À1 t : time coordinate, s T : temperature, K V : volume, L x : axial position, m x : mass fraction W : : work, kW ÁP : pressure drop, PaGreek Letters " : porosity 0 : permeability of free space (m kg s À2 A À2 Þ : density kg m À3 : e±ciency 1 : demagnetization time step (s) 2 : hot to cold°uid°ow time step (s) 3 : magnetization time step (s) ¼ density kg m À3 4 : cold to hot°uid°ow time step (s) : cycle time (s)