Governing equations for AMRR system have been developed in  and .
The gradient of temperature created within the material, i.e., between the cold and the hot sides, is due to the AMRR cycles as explained in Section 1.
In addition to temperature profiles, the developed thermal model allows to obtain profiles of the energy exchanged between the fluid and material during the AMRR cycles.
Figure 2 reveals several details that are relevant to practical AMRR systems.
The technical barriers associated with the ADR cycle have been overcome by the use of a regenerator within the active magnetic regenerative refrigeration (AMRR) cycle.
The properties of the magnetocaloric material that is used in an AMRR system are primarily responsible for the system performance that can be achieved.
Because [bar]A is a constant, the fluctuations in [M.sub.i] are not moderated as they are for AMRR, so AARR has higher within-year fluctuations.
For both AMRR and AARR, construction of the variables was based on a data set commencing in 1957.
In 10 cases where it produced models with a higher [R.sup.2] (most of which were shallow bores), AARR was substituted for AMRR in the regression model.
This paper uses a physics-based, numerical model to predict the practical limits of the efficiency of a magnetic cooling cycle and compares the AMRR cycle to current technology.
Practical residential AMRR systems will likely use permanent magnets to produce a magnetic field and achieve variations in applied field by physically moving the magnetic regenerator relative to the magnetic field, either linearly as demonstrated by Rowe and Barclay (2002), Hirano et al.
A detailed model of the AMRR system has been developed (Engelbrecht 2005).