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.

Thermal radiation heat transfer

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Thermal Radiation Heat Transfer

We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

$f(R,T)$ gravity

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion of the role of fundamental constants, their definition and link with metrology, it reviews the various constraints on the variation of the fine-structure constant, the gravitational, weak- and strong-interaction couplings and the electron-to-proton mass ratio. The review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant, and (3) to point out the underlying hypotheses. Such an investigation is of importance in comparing the different results and in understanding the recent claims of the detection of a variation of the fine-structure constant and of the electron-to-proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories, and other alternative theories. Cosmological implications of these results are also discussed. The links with the tests of general relativity are emphasized.

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The fundamental constants and their variation: observational and theoretical status

The striking broad emission line spectroscopic appearance of Wolf-Rayet (WR) stars has long defied analysis, owing to the extreme physical conditions within their line- and continuum-formin...

Physical Properties of Wolf-Rayet Stars

Relativity, gravitation and world-structure

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The Highly Collapsed Configurations of a Stellar Mass

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Newtonian Universes and the Curvature of Space

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The Equilibrium of Distorted Polytropes: (I). The Rotational Problem

1. The phenomenon of the expansion of the universe has usually been discussed by students of relativity by means of the concept of ‘expanding space’. This concept, though mathematically significant, has by itself no physical content; it is merely the choice of a particular mathematical apparatus for describing and analysing phenomena. An alternative procedure is to choose a static space, as in ordinary physics, and analyse the expansion-phenomenon as actual motions in this space. Moving particles in a static space will give the same observable phenomena as stationary particles in ‘expanding’ space. In each case the space is a construct built up by the mathematician out of observations that could in principle be made; it is built up around the matter in motion according to certain rules. The formulation of the relevant laws of nature depends on the rules adopted, and the laws will be quite different if different rules are adopted, as I have elsewhere† explained. The alternative procedures have been tersely described in a recent paper by S. R. Milner.‡ He explained that we can either modify our geometry in order to retain d ∫ ds c 0 as the paths of free particles, or retain Euclidean geometry and Minkowski space-time and modify the variational principle by weighting the elements of path ds with appropriate invariant weighting factors. Einstein’s general relativity adopts the first procedure; in my recent treatment of the cosmological problem I adopted the second procedure. In neither case has the space constructed any physical significance—no content attaches to the phrase ‘the space of nature’—but the second procedure has the advantage that it employs the space commonly used in physics. The equations of motion I obtained for free particles moving in the presence of a certain distribution of matter in motion were derived by the straightforward method of making

Edward Arthur Milne

Papers

Relativity, gravitation and world-structure

The Highly Collapsed Configurations of a Stellar Mass

Newtonian Universes and the Curvature of Space

The Equilibrium of Distorted Polytropes: (I). The Rotational Problem

A newtonian expanding universe