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Magnetocaloric effect
Posted Apr 23, 2015, 3:06 a.m. EDT Low-Frequency Electromagnetics, Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 5.0 1 Reply
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I am currently working on my bachelor project, which involves the numerical analysis of the magnetocaloric effect (MCE). For those of you who are not familiar with this effect: When a suitable material is placed in a magnetic field, a small increase in temperature will occur in this material. Consequently, when the material is removed from the same magnetic field, the temperature of the material will drop. This effect is not built in in the COMSOL (5.0) package, and I probably need to model it using PDEs or ODEs. The governing equations for the MCE are:
or
or
In these equations, T = temperature, t = time, M = magnetisation, H = magnetic field strength, Cp = specific heat, Q = heat and
is the permeability of free space. All these equations describe the same effect, but are rewritten in some kind. My 2d model currently consists of 2 simple permanent magnets, creating the magnetic field. The magnetocaloric material is positioned in the magnetic field created by those two magnets.
I'd like to ask if someone is able to give me a push in the right direction on which equation is best to use and how to model this in COMSOL, in such way that an increase in temperature is seen in the magnetocaloric domain.
Thanks in advance,
Dirk oude Egbrink
Hello Dirk Oude Egbrink
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This issue has been a topic without answers for quite a long time, although simple to solve in theory. The best way to simulate the magnetocaloric effect is by changing the temperature abruptly, i.e. in an adiabatic process, with a value that depends on temperature ∆Tad(T). Note that there is no need to include magnetism in the model.
Numerically, we can stop the numerical calculations in the instant right before the magnetic field application/removal, add/subtract ∆Tad(T) in the solution and use the result as initial condition of a subsequent simulation. Doing this repeatedly, one can compute, e.g., a magnetic refrigerator. But here is the complication: I do not see a way to implement this process: do some manipulation on the temperature at the end of one simulation and use it as initial condition of a next one. Can anyone give a hint to do so? It is quite simple but seems difficult to implement on COMSOL...
Thanks in advance