A Simple Analysis Of A Magnetic Refrigerator

The adiabatic demagnetization refrigeration (ADR) concept was conceived in the early 20th century but was not immediately deployed owing to the lack of research and development in other areas of science, such as superconductivity and study of crystal lattice defects.

The ADR makes use of the magnetocaloric effect, which predicts a loss of heat capacity when a paramagnetic material is magnetized and demagnetized, and contextualized the quantization of phonons in the crystal lattice of the specimen. To date, only the alloys of praseodymium and gadolinium, and the paramagnetic compound cerium magnesium nitrate, have been studied extensively as suitable materials that can be employed in large-scale applications concerning the ADR.

In 1880, Emile Warburg first observed the magnetocaloric effect, which is as follows: when a magnetocaloric material, so named because of its obeisance to the observed phenomenon, is exposed to a magnetic field, the electron spins align themselves and the material becomes magnetized. In the process, heat is generated, which is removed by means of a surrounding helium bath maintained at a temperature of approximately 2 K. As the external magnetic field is slowly reduced, thermal agitation begins to arise in the material in terms of phonons (phonons are quasiparticles quantized by lattice vibrations in crystal solids).

In order to refuse any energy remigration into the material, the helium bath acts as a secondary refrigerant that is quickly pumped out in order to isolate the material. The energy of the phonons is then absorbed by the crystals in the solid to realign the electron spins, thereby cooling the material. In cases where cerium magnesium nitrate, or alloys of nickel and gadolinium, is (or, are) used, the material cools down to a temperature of close to 100 K, wherefore it can behave as the primary refrigerant in a low-temperature refrigeration cycle.

The magnetocaloric effect was first proposed as an alternative to liquid refrigerants in a refrigeration cycle by Peter Debye in 1926, and by William Giauque in 1927, and the adiabatic demagnetization refrigerator, which is a heat pump based on this principle, was first demonstrated practically in 1933 by several groups.

From 1999 to 2002, researchers at the University of Wisconsin (UW), together with the Lockheed Martin Solar and Astrophysics Laboratory (LMSAL), built an adiabatic demagnetization refrigerator for the Advanced Technology Solar Spectroscopic Imager (ATSSI), which required a high temperature-stability at close to 100 mK in order to resolve the energy of absorbed X-ray photons emitted by the solar corona, the blueprint of which is shown below.

[caption id="attachment_402" align="aligncenter" width="531" caption="ATSSI"][/caption]

This device demonstrates one of the chief uses of the ADR as well as its performance in conditions that require stability at temperatures close to absolute zero, and illustrates one of the chief safety issues facing the operation of an ADR as a household appliance: the central induction of the solenoid used to magnetize the magnetocaloric material must be completely contained in order to prevent leakages of the magnetic field. Therefore, the material being used to shield the magnetic field must have a saturation induction greater than the central induction of the solenoid, in which case it must be built with a ferromagnetic material.

For greater operational efficiency, it is necessary that a fluid be used rather than a solid or a gas in the ADR. Therefore, two kinds of paramagnetic fluids are of note: ferrofluids and magnetorheological fluids. The latter exhibit the magnetocaloric effect to a greater extent because of the larger particles dispersed in the carrier fluid. The particles are further coated with a surfactant (such as tetramethylammonium hydroxide or sodium citrate) to prevent agglomeration and coagulation of the particles, possible due to Van der Waals forces and gravitational sedimentation.

Magnetorheological fluids exhibit a change in mechanical properties in the presence of a magnetic field, whereupon the dimorphic nature of the fluid is in play: the particles align themselves in the direction of the magnetic flux, leading to an increase of shear stresses in the fluid, summarized by the following equation:

τ = τ_y(H) + η.dv/dz

(τ – shear stress; τ_y – yield stress; H – magnetic flux density; η – coefficient of viscosity; dv/dz – acceleration in the z-direction).

Further, magnetorheological properties such as regulation of the direction of flow can be brought about by manipulating the direction of the imposed magnetic field.

The phenomenon of thermomagnetic convection arises because the cooler fluid, by virtue of possessing an increased magnetic susceptibility, tends to displace the warmer fluid in a region of higher magnetic flux density. This reduces pumping costs by suitably designing a duct that allows “fresh” fluid to flow towards the target space along with a temperature gradient. To model the flow of a fluid under the influence of magnetostatic potential, application of the Navier-Stokes equation gives:

ρ{∂v/∂t + v(∇v)} = -∇p + η∇v + ρg + M∇B

In conclusion, the ADR is a peculiar but strong candidate to replace the bulky and environmentally abrasive ammonia-cooled vapor compression cycles. Some of the chief difficulties standing in the way of a full-scale deployment of the ADR are completely technical and therefore, it would be unwise to speculate that they cannot be overcome. If a suitable MR fluid were to be conceived and produced after focused research on the subject, a magnetic refrigerator would find widespread use in hospitals, space stations and in cooling devices like the LHC or even the upcoming SLHC.