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Franco, V., Blázquez, J.S., Ipus, J.J., Law, J.Y., Moreno-Ramírez, L.M., Conde, A., “Magnetocaloric effect: From materials research to refrigeration devices”, Progress in Materials Science. 93 (2018) 112-232.

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Thermodynamically Consistent Analysis of Magnetocaloric Effects

1The US Army Research Laboratory, Aberdeen Proving Ground, USA

2Department of Mathematics, Drexel University, Philadelphia, USA

Applied Mathematics and Physics. 2020, Vol. 8 No. 1, 14-19
DOI: 10.12691/amp-8-1-3
Copyright © 2020 Science and Education Publishing

Cite this paper:
Michael Grinfeld, Pavel Grinfeld. Thermodynamically Consistent Analysis of Magnetocaloric Effects. Applied Mathematics and Physics. 2020; 8(1):14-19. doi: 10.12691/amp-8-1-3.

Correspondence to: Michael  Grinfeld, The US Army Research Laboratory, Aberdeen Proving Ground, USA. Email:


We suggest a thermodynamically and mathematically consistent analysis of magnetocaloric effect for a plate immersed in a uniform static magnetic field. We ignore deformability of the plate, but make no assumption regarding the amplitude of the magnetic field - it can be arbitrarily large. Traditional presentations of magnetocaloric effect are rather simple and straightforward - they are based on the algebraic manipulations with thermodynamic identities, and no analysis of boundary value problems is required. But they suffer one conceptual drawback - they are dealing with the magnetic field inside the specimen. However, the interior field is, a priori, unknown and depends on the geometry of the specimen. In fact, the meaningful analysis should be based on usage of the experimentally controllable exterior field. The relevant analysis therefore, should be based on the consideration of the boundary value problem for the equations of magnetostatics. We establish the relevant relationships of the magnetocaloric effect for the sample in the shape of a plate.