New Constitutive Matrix in the 3D Cell Method to Obtain a Lorentz Electric Field in a Magnetic Brake

Abstract

In this work, we have obtained a new constitutive matrix to calculate the induced Lorentz electric current of in a conductive disk in movement within a magnetic field using the cell method in 3D. This disk and a permanent magnet act as a magnetic brake. The results obtained are compared with those obtained with the finite element method (FEM) using the computer applications Getdp and femm. The error observed is less than 0.1173%. Likewise, a second verification has been made in the laboratory using Hall sensors to measure the magnetic field in the proximity of the magnetic brake.

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

“…These are obtained by solving the electromagnetic Equations (1) that are explained in detail in [13]:[CtMvC−MσVLoC+jWMσMσG−GtMσjW+GtMσVLoC−GtMσG][aϕ]=[CtFe0]…”

“…In this way, we obtain the heat sources in the disk, which are calculated as follows:trueW˜=1σtrueJ→·trueJ→dtrueV˜,where Jfalse→ is calculated, by the following equation:trueJ→=σ(−truegrad→ϕ+truev→×trueB→), being σ the electrical conductivity, ϕ the electric scalar potential, truev→ the velocity of each point and Bfalse→ is the magnetic induction. See [13].…”

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,…”

“…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].…”