A comprehensive discussion of heat transfer by thermal radiation is presented, including the radiative behavior of materials, radiation between surfaces, and gas radiation. Among the topics considered are property prediction by electromagnetic theory, the observed properties of solid materials, radiation in the presence of other modes of energy transfer, the equations of transfer for an absorbing-emitting gas, and radiative transfer in scattering and absorbing media. Also considered are radiation exchange between black isothermal surfaces, radiation exchange in enclosures composed of diffuse gray surfaces and in enclosures having some specularly reflecting surfaces, and radiation exchange between nondiffuse nongray surfaces. The use of the Monte Carlo technique in solving radiant-exchange problems and problems of radiative transfer through absorbing-emitting media is explained.

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Thermal Radiation Heat Transfer

This overview of diffusion and separation processes brings unsurpassed, engaging clarity to this complex topic. Diffusion is a key part of the undergraduate chemical engineering curriculum and at the core of understanding chemical purification and reaction engineering. This spontaneous mixing process is also central to our daily lives, with importance in phenomena as diverse as the dispersal of pollutants to digestion in the small intestine. For students, Diffusion goes from the basics of mass transfer and diffusion itself, with strong support through worked examples and a range of student questions. It also takes the reader right through to the cutting edge of our understanding, and the new examples in this third edition will appeal to professional scientists and engineers. Retaining the trademark enthusiastic style, the broad coverage now extends to biology and medicine.

Diffusion: Mass Transfer in Fluid Systems

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

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Microfluidics: Fluid physics at the nanoliter scale

* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index

Generalized inverses: theory and applications

Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

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Multiferroics: a magnetic twist for ferroelectricity

Arguably the most influential nineteenth-century scientist for twentieth-century physics, James Clerk Maxwell (1831–1879) demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field. A fellow of Trinity College Cambridge, Maxwell became, in 1871, the first Cavendish Professor of Physics at Cambridge. His famous equations - a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density - first appeared in fully developed form in his 1873 Treatise on Electricity and Magnetism. This two-volume textbook brought together all the experimental and theoretical advances in the field of electricity and magnetism known at the time, and provided a methodical and graduated introduction to electromagnetic theory. Volume 2 covers magnetism and electromagnetism, including the electromagnetic theory of light, the theory of magnetic action on light, and the electric theory of magnetism.

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A Treatise on Electricity and Magnetism

The theory of transport processes in gases—such as diffusion, heat conduction, and viscosity—is developed on the basis of the assumption that the molecules behave like point-centres of force. The method of investigation consists in calculating mean values of various functions of the velocity of all the molecules of a given kind within an element of volume, and the variations of these mean values due, first, to the encounters of the molecules with others of the same or a different kind; second, to the action of external forces such as gravity; and third, to the passage of molecules through the boundary of the element of volume.

On the Dynamical Theory of Gases

1. In this paper I have followed the method given in my paper “On the Dynamical Theory of Gases” (Phil. Trans., 1867, p. 49). I have shown that when inequalities of temperature exist in a gas, the pressure at a given point is not the same in all directions, and that the difference between the maximum and the minimum pressure at a point may be of considerable magnitude when the density of the gas is small enough, and when the inequalities of temperature are produced by small solid bodies at a higher or lower temperature than the vessel containing the gas. 2. The nature of this stress may be thus defined:— Let the distance from a given point, measured in a given direction, be denoted by h; then the space-variation of the temperature for a point moving along this line will be denoted by dθ/dh, and the spaced variation of this quantity along the same line by d2θ/dh2.

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On Stresses in Rarified Gases arising from Inequalities of Temperature

HE proposed Theory seeks for the origin of electromagnetic effects in the medium surrounding the electric or magnetic bodies, and assumes that they act on each other not immediately at a distance, but through the intervention of this medium.

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A Dynamical Theory of the Electromagnetic Field

(1) The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. In this way mathematical theories of statical electricity, of magnetism, of the mechanical action between conductors carrying currents, and of the induction of currents have been formed. In these theories the force acting between the two bodies is treated with reference only to the condition of the bodies and their relative position, and without any express consideration of the surrounding medium.

James Clerk Maxwell

Papers

A Treatise on Electricity and Magnetism

On the Dynamical Theory of Gases

On Stresses in Rarified Gases arising from Inequalities of Temperature

A Dynamical Theory of the Electromagnetic Field

VIII. A dynamical theory of the electromagnetic field