Thermal Analysis of a Magnetic Brake Using Infrared Techniques and 3D Cell Method with a New Convective Constitutive Matrix

Abstract

In this work we analyse the temperature distribution in a conductor disk in transitory regime. The disk is in motion in a stationary magnetic field generated by a permanent magnet and so, the electric currents induced inside it generate heat. The system acts as a magnetic brake and is analysed using infrared sensor techniques. In addition, for the simulation and analysis of the magnetic brake, a new thermal convective matrix for the 3D Cell Method (CM) is proposed. The results of the simulation have been verified by comparing the numerical results with those obtained by the Finite Element Method (FEM) and with experimental data obtained by infrared technology. The difference between the experimental results obtained by infrared sensors and those obtained in the simulations is less than 0.0459%.

New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

“…In the present section, we obtain the analytical formulation of the matrix [M τ ] that has been developed to improve the results obtained with [M λ ]. In a steady state, and without internal heat sources, the equation of energy balance without mass transfer [10][11][12][13] is in the CM,…”

“…In this methodology, we work with the global magnitudes associated with space-oriented elements such as volumes, surfaces, lines, and points of the discretized space, as well as to temporal elements, instead of the field magnitudes associated with independent variables with spatial and temporal coordinates [16][17][18][19][20]. In addition, the equations of constitutive type (equations of the medium) are clearly differentiated from the topological type (equations of balance) [10]. In FF, the physical laws that govern the thermal laws of heat transfer associated with electrical devices are expressed in their integral form.…”

“…Three methodologies have been formulated previously in order to obtain the constitutive thermal matrix. These methods are those by Tonti [16], Bullo [21][22], and the method proposed by Specogna [14], for problems of electrical conduction, which we have adapted to thermal conduction [10][11][12][13].…”

“…Dual barycentric cell complexes are used for both space and time domains, the latter inducing a Crank-Nicolson time integration scheme. In the present work, we propose the finite formulation (FF) [10][11][12][13][14][15], as well as the Cell Method (CM), [16,17] as an associated numerical method to analyze the numerical models proposed. In this methodology, we work with the global magnitudes associated with space-oriented elements such as volumes, surfaces, lines, and points of the discretized space, as well as to temporal elements, instead of the field magnitudes associated with independent variables with spatial and temporal coordinates [16][17][18][19][20].…”

“…In addition, the equations of constitutive type (equations of the medium) are clearly differentiated from the topological type (equations of balance) [10]. In FF, the physical laws that govern the thermal laws of heat transfer associated with electrical devices are expressed in their integral form.…”