By James R. Melcher
Designed for use as a graduate-level textual content and as an engineering reference paintings, Continuum Electromechanics offers a finished improvement of its subject—the interplay of electromagnetic forces and ponderable media, the mechanical responses to electromagnetic fields, and the reciprocal results of the cloth motions produced via these fields. The author's method is extremely interdisciplinary, and he introduces primary recommendations from such matters as electrohydrodynamics, magnetohydrodynamics, plasma physics, electron beam engineering, fluid mechanics, warmth move, and actual chemistry.
The purposes of continuum electromechanics also are remarkably assorted, and lots of of them are handled within the booklet, either as a result of their intrinsic engineering significance and as a method of illustrating uncomplicated rules. between those purposes are the layout of rotating machines and synchronous turbines, polymer processing, magnetic melting and pumping in metallurgical operations, the processing of plastics and glass, the manufacture of man-made fibers, inductive and dielectric heating, thermal-to-electrical strength conversion, the keep watch over of pollution, the layout of controlled-fusion units, photograph processing and printing, the magnetic levitation and propulsion of autos, the research of flicks and membranes, and the research of the advanced electrokinetic and physicochemical methods that underlie the sensing and motor features of organic platforms. a lot of those functions are provided within the kind of problems.
The booklet involves 11 chapters, entitled advent to Continuum Electromechanics; Electrodynamic legislation; Approximations, and kin; Electromagnetic Forces, strength Densities, and tension Tensors; Electromechanical Kinematics; Energy-Conversion versions and tactics; cost Migration, Convection, and rest; Magnetic Diffusion and Induction Interactions; legislation, Approximations, and kin of Fluid Mechanics Statics and Dynamics of structures Having a Static Equilibrium; Electromechanical Flows; Electromechanics with Thermal and Molecular Diffusion; and Streaming Interactions.
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And if the particles have a number density n, the polarization density is defined as P • nqit (1) In the most comi:ion dielectrics, the polarization results because of the application of an external electric field. In that case, the internal constraints (represented by the springs in Fig. 1) make the charges essentially coincident in the absence of an electric field, so that, on the average, the material is (macroscopically) neutral. with the application of the electric field 1 there is a separation of the charges in some direction which might be coincident with the applied electric field intensity.
Rame, and the dependent field variables are then fields defined in that reference frame. ) (2) I -J • =~ ot + V,uip The left relations follow by using the chain rule of differentiation and the transformation of Eq. 1, That the spatial derivatives taken with respect to one frame must be the same as those with reape,ct to the other frame physically means that a single "snapshot" of the physical process would be ali required to evaluate the spatial derivatives in either frame, There would be no way of telling which frame was the one from which the snapshot was taken.
Generally, there is a continuous stream of particles through the point (x,y,z). 6 r l I l I I I Computation of the particle acceleration ~akes evident the contrast between Eulerian and Lagrangian representations. By definition, the acceleration is the rate of change of the velocity computed for a given particle of matter. A particle having the position (x,y,z) at time twill be found an il\3tant 6t later at the position (x + vx6t 1 y + vy6t,z + vz6t). tt,t + 6t) - v(x 1 y 1 z 1 t) • (3) 6t Expansion of tte first term in Eq.