Magnetic and Thermal Diffusion Effects on a Three-Dimensional Free Convective Flow Past a Uniformly Moving Porous Vertical Plate
The problem of a three dimensional free convection flow with mass transfer of an incompressible viscous electrically conducting fluid past a uniformly moving porous vertical plate with transverse sinusoidal suction velocity is considered. A magnetic field of uniform strength is assumed to be applied normal to the plate. The expressions for skin-friction at the plate in the direction of flow, rate of heat transfer in terms of Nusselt number, rate of mass transfer in terms of Sherwood number, velocity field, temperature field and species concentration field are obtained in non-dimensional forms. The effects of Hartmann number, Schmidt number, Soret number, Reynolds number on the skin friction, Nusselt number, Sherwood number, velocity field, temperature field and concentration field are discussed graphically and the results are physically interpreted.
An introduction to magneto-fluid mechanics
ing journals. At the head of each abstract is the name of the author and the title of the paper, although not its date or origin, and also a pair of numbers. The reader is able to find by trial that one of these numbers is the serial number of the same paper as entered in the bibliographical list, the other being a new serial number for the paper in the sequence of abstracts. At the end of the volume are three lists. The first, a short one, is of numbers entitled ‘List of the entries included in bibliography no. 1’; bibliography no. 1 is apparently what this bibliography used to be when it was issued informally by AGARD in February 1960. The second is an index to authors, which presumably serves to identify the number of a paper written by a known author who is one of several joint authors and not the first named, the latter alone being used in the bibliographical list. The last is a subject-index, in which there are seven main divisions, like ‘magnetohydrodynamics ’ and ‘magneto-gas-dynamics ),with afew sub-divisions for each. The value of the subject index will be limited by the fact that the subheading ‘ General’ swallows up about half the entries in four of the main divisions. It is obviously useful to prepare and disseminate an up-to-date and ordered list of papers on this important subject, and the initiative and work contributed by AGARD have been widely appreciated. But why print a second time, publish, and sell at a substantial price, a bibliography which pays little attention to the ordinary principles of fact-gathering and indexing? As well as being rather wasteful, the book does not maintain accepted standards in scientific publications. G. K. BATCHELOR
The quantum particle in a box: what we can learn from classical electrodynamics
The problem of a charged particle enclosed in an infinite square potential well is analysed from the point of view of classical theory with the addition of the electromagnetic zero-point radiation field, with the aim to explore the extent to which such an analysis can contribute to enhance our understanding of the quantum behavior. First a proper treatment is made of the freely moving particle subject to the action of the radiation field, involving a frequency cutoff ωc. The jittering motion and the effective structure of the particle are sustained by the permanent action of the zero-point field. As a result, the particle interacts resonantly with the traveling field modes of frequency ωc in its proper frame of reference, which superpose to give rise to a modulated wave accompanying the particle. This is identified with the de Broglie wave, validating the choice of Compton’s frequency for ωc. For the stationary states of particles confined in the potential well, the Lorentz force produced by the accompanying field is shown to lead to discrete values for the mean speed and to an uneven probability distribution that echoes the corresponding quantum distribution. The relevance of the results obtained and the limitations of the classical approach used, are discussed in the context of present-day stochastic electrodynamics.