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For irregular geometries, the distance from the surface to the thermal centre is not uniform. This makes the calculation of freezing time impossible. The difficulty can be overcome by defining a ‘mean conducting path’ D m /2, which can then be used to calculate Biot numbers. D m /2 is considered to be the mean length of heat conducting paths from the surface of the body to the thermal centre. For rectangular blocks, experimental data suggest that D m is proportional to the geometric mean of the two shorter sides. An equation for calculating the effective Biot number is presented, which incorporates one empirical coefficient. For squat-shaped bodies a good estimate of D m can be obtained by averaging the shortest and longest dimensions. Pham's freezing time prediction method applied to brick-shaped blocks yields about the same accuracy as for the basic shapes (infinite slabs, infinite cylinders and spheres), and is more accurate than previous methods, including finite-different methods.

In this paper, we have considered the thermal instability of a rotating, heat conducting, micropolar fluid layer heated from below and confined between two rigid boundaries. The onset of thermal instability is governed by a linear eigenvalue problem. The solution of the eigenvalue problem is obtained by using finite difference method and Wilkinson's iteration technique. The effects of rotation and micropolar parameters on the critical Rayleigh number and the wave number at the threshold of instability are discussed in detail.

According to theoretical predictions, a heat conducting gas of polar molecules can become birefringent in the presence of an electric field. No effect could be detected, however, within the experimental uncertainties. An upper limit for the relevant production cross sections is presented.

The existence of global classical solutions to initial boundary value problems in the dynamics of a one-dimensional, viscous, heat-conducting gas is established. The nonlinear dissipative effects turn out to be sufficiently strong to prevent the development of singularities.

The radiant efflux from a cylindrical cavity having nonisothermal bounding surfaces is determined by solving a problem of combined radiation and conduction. The cavity may be visualized as a circular hole machined into the exposed face of a solid, with the solid being heated uniformly from behind. A two-dimensional temperature distribution is set up in the solid owing to radiative heat losses from the cavity and from the exposed face of the solid. A solution method is employed whereby the radiation and conduction problems are dealt with successively. Results are obtained for parametric values of the cavity emittance and depth-radius ratio and of a group which fixes the axial temperature variation. The results indicate that the radiant efflux from the cavity increases with increasing values of the aforementioned parameters. The effect of the presence of the cavity is confined to a region of the solid whose depth and radius are, respectively, twice and four times the depth and radius of the cavity.

Asymptotic solutions are presented which describe the formation of one-dimensional flows of a viscous heat conducting gas at short and long times. Comparison of them with numerical calculations made in the study for the system of Navier-Stokes equations in conjunction with an estimate of the ratio of each term in the asymptotic expansion to the preceding term leads to dimensionless-number dependences that determine the limits of applicability of the obtained solutions.

It is shown that for sufficiently large values of the thermal conductivity of the condensed phaseλ' as compared with the thermal conductivity of the vaporλ (λ/λ' ∼ Kn) the effects associated with the presence of a Knudsen layer on the evaporating surface must be taken into account in order to obtain a solution of the problem of a spherical particle in a slow (Re∞, ≪ 1) continuum (Knudsen number Kn ≪ 1) flow of its own vapor. The drag is calculated for various types of boundary conditions on the particle surface.

We outline an approach to irreversible thermodynamics leading to a set of covariant equations describing the evolution, along the world-line, of dissipative variables characterizing a relativistic heat-conducting viscous fluid.

A scheme for the relativistic magnetohydrodynamics for a heat conducting fluid, of infinite conductivity, is proposed, together with a generalized thermodynamical differential equation. Its main consequences, as far as the wave propagation is concerned, are examined under suitable compressibility hypotheses.

A closed set of CGL equations, modified to include heat flux correction, is used to study the firehose and mirror instabilities in a rarefied plasma. A significant feature which has been noticed is that some of the terms contributed by the higher-order moments are of the same order as the terms in the unmodified CGL equations. We study the effect on the firehose and mirror instabilities of those terms which persist in the limit of vanishing heat flux vector. It is found that these terms lead to a new criterion for mirror instability. The criterion for hose instability, however, remains unaffected.

A build-up scheme of the second order of approximation for calculating the stationary flows of a viscous gas is proposed. The stability of the scheme is proved, and the resules of cest calculations are given.

The diffraction of cylindrical and plane stationary sound waves by a cylinder in a viscous heat-conducting medium is analyzed. A solution of this problem is given in [1] without regard for heat conduction.

It ist shown that the ordinary non-linear second order differential equation of the phenomenological theory of the one-dimensional steady shock wave in heat conducting viscous gases can be transformed into the Abelian differential equation of the second class. Among the known special solutions of Abel's equation is one applicable to the shock wave and leads to a hitherto unknown closed form solution. Es wird gezeigt, das die gewohnliche, nichtlineare Differentialgleichung zweiter Ordnung der phanomenologischen Theorie der eindimensionalen, stationaren Stoswelle in warmeleitenden, viscosen, idealen Gasen sich in die Abelsche Differentialgleichung zweiter Art transformieren last. Von den bekannten, speziellen Losungen der Abelschen Gleichung ist eine auf die Stoswelle anwendbar und fuhrt zu einer bisher nicht bekannten Losung in geschlosssener Form.

The question of stability of propagation of acoustic waves within a continuum of compressible viscous heat‐conducting fluid has been investigated. A bounded solution (i.e., a stable solution) is assured if either of the following two conditions is satified: γ = 1 (i) or 3(2 − γ)4[1 + (3/4)(υ/η)]P⩽ 1 (for γ> 1), where P is the Prandtl number, γ the ratio of specific heats, and υ and η the bulk and shear viscosities, respectively. According to the theory, the above inequality must be obeyed for all passive fluids with γ> 1. Using experimental values for many different fluids, it appears to be generally obeyed except for the molten metals including mercury and, possibly, the superfluids.

In relativistic mechanics the forces acting on a body have the following two properties: (i) their sum is equal to the rate of change of momentum of the body, and (ii) they have certain prescribed transformation properties under Lorentz transformations. It is pointed out that not both of these properties can be taken over to relativistic thermodynamics: they lead to different interpretations of the energy-momentum tensor and its divergence for a heat conducting continuum. Postulating the first of them gives the thermostatics of Planck and others, whereas postulating the second one gives that of Ott, Kibble, M?ller, and others. The work differential of Kibble and M?ller is generalized to include changes of velocity. The equilibrium of rotating systems is also discussed.

Approximation equations for gas flows considering viscosity and heat conductivitys and with partial consideration for the non-linear componcnts were developed in order to solve certain problems. The equations can be used in calculations of diffusors, losses in gas pipe flows etc. (R.V.J.)

The Navier–Stokes hypersonic weak-interaction theory is presented for the flow of a viscous, heat-conducting, compressible fluid past a very slender axisymmetric body, when the ratio of the radius of the body to the radial thickness of the viscous region, produced and supported by the body, is much less than unity. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Solutions are studied for the free-stream Mach number, the free-stream Reynolds number based on the axial length of the body, and the reciprocal of the weak-interaction parameter much greater than unity.It is shown that, for the viscosity-temperature exponent ω less than 1, seven distinct layers span the region between the shock wave and the body, which is of arbitrary shape. The leading approximations for the behaviour of the flow in these seven layers are analyzed, and the restrictions imposed on the theory are obtained.

This paper discusses the gravitational instability of a non-uniformly rotating, infinite, axisymmetric cylinder of a homogeneous, heat conducting medium. It is found that the Bel and Schatzman criterion of gravitational instability remains unaffected, even when the medium is heat conducting.

The general theory of a Gibbs ensemble representing a system in contact with its surroundings is applied to several concrete situations of interest. By an appropriate choice of heat reservoirs a simply modified Liouville equation is found to describe a heat conducting system. The stationary nonequlibrium $\ensuremath{\Gamma}$-space ensembles which describe such a system are found explicitly for some cases. In the simplest cases these ensembles turn out to be canonical with a temperature that is a weighted average of the reservoir temperatures. For other systems, such as Brownian particles inside a fluid whose temperature is not uniform, we find the stationary ensemble to terms linear in the temperature gradient. From this we are led to discuss ensembles that will approximately represent an arbitrary heat conducting fluid. A more general proof than previously given for the asymptotic approach of the $\ensuremath{\Gamma}$-space distribution to its stationary value is also presented.

In this paper heat-conducting micropolar fluids are introduced as an extension of the theory of micropolar fluids. Constitutive equations appropriate to describe the thermal and mechanical response of micropolar fluids are constructed. The heat conduction equation is derived and the field equations are obtained. The solution to the problem ofPoiseuille flow through a channel with flat walls is given.

(1872). LIX. On the heat-conducting power of iron and German silver. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 44, Supplement, pp. 481-500.

A new mathematical model and the resulting computer code ZOCO V are described, which allows to calculate the time- and space-dependent pressure and temperature distribution in containments of water-cooled nuclear power reactors following a loss-of-coolant accident, which is caused by the rupture of a main recirculation or steam pipe (MCA). With this computer code, subdivided full pressure containments as well as pressure suppression systems can be treated primarily for the short term behaviour (within the first seconds from the beginning of the accident until the end of the blow-down when pressure equilibrium between primary system and containment is reached) and also for the following long term behaviour. This model is a multi-pressure node one whereby the number of the pressure nodes, that of the connections between them and that of the heat conducting solid structures can be arbitrarily chosen. Calculated pressure time histories have been compared with corresponding experimental results for full pressure containments and pressure suppression systems showing good agreement between theory and experiment.

A technique is presented for the numerical solution of quasi-one-dimensional, viscous, heat conducting, compressible Laval nozzle flows. A time-dependent finite difference scheme is used to integrate the unsteady flow equations yielding second-order accurate steady-state solutions. Several features of the shock wave solution are shown and discussed.

Mit der Warmeleitsonde nach Hensel wurden Warmeleitzahl- und Durchblutungsmessungen in der Leber durchgefuhrt. Die Warmeleitzahl der undurchbluteten Menschenleber, im Durchschnitt 11,3 · 10−4 cal × cm−1 · s−1 · °C−1, wird durch pathologische Gewebsveranderungen wie Stauungsleber, verschiedene Formen der Atrophie, carcinomatose und cirrhotische Veranderungen nicht mesbar beeinflust. Lediglich bei Leberverfettung erfahrt sie eine merkliche Verminderung. Bei isolierter Durchstromung von Hundelebern fand sich eine nicht lineare Abhangigkeit der Warmeleitzahl vom Stromzeitvolumen. Die mittlere Warmeleitzahl der undurchbluteten Hundeleber betragt 11,0 · 10−4, die Warmeleitzahlerhohung bei Durchblutung im Mittel 3,9 · 10−4. Die Streuung der Werte bei durchbluteter Leber ist erheblich. Unterschiedliche Blutfulle beeinflust die Warmeleitfahigkeit der Leber nicht. Mit einem besonders konstruierten flexiblen Typ der Warmeleitsonde ist die fortlaufende Registrierung relativer Durchblutungsanderungen auch am wachen Tier und am wachen Menschen moglich.