Thermoelastic State of a Magnetocaloric Ferromagnetic Plate Under Constant-Rate Ambient Temperature Rise.

A simply supported rectangular isotropic ferromagnetic plate with magnetocaloric properties subjected to convective heating on its upper surface is considered. The governing equations comprise a system of two-dimensional transient equations for the thickness-averaged temperature characteristics of the plate and the two-dimensional bending equations for isotropic plates expressed in terms of generalized displacements within the framework of first-order shear deformation theory. Closed-form solutions to the governing equations are obtained by expanding all thermal and mechanical field quantities in double Fourier sine series satisfying the prescribed boundary conditions, combined with the Laplace transform in time applied to the thermal quantities. A comparative numerical analysis is carried out for the magnetocaloric ferromagnetic plate and a carbon steel plate under ambient temperature rising at a finite rate to a prescribed value. The dependences of all quantities under investigation on the ambient temperature rise rate, time, convective heat transfer coefficient, thermal conductivity of the ferromagnetic material, and geometric parameters of the plate are analyzed and presented graphically. The results obtained provide a quantitative basis for assessing the thermoelastic state and for optimizing the geometry and operating conditions of active magnetic regenerator plate stacks with a view to enhancing their structural reliability.