Thermomechanical instability of a heat releasing granular layer

A study is made of a homogeneous granular layer of thickness h and porosity in which heat is released uniformly with bulk power q. The heat is taken up by a uniform gas flow through the layer in the transverse direction of the y axis at velocity v ° produced by a given pressure difference across the layer. This scheme corresponds to the simplest model of a gas-cooled nuclear reactor, in which the heat release does not depend on the thermogasdynamic state. The case of a chemical reactor with heat release of Arrhenius type is considered in [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–53, March–April, 1979.     

Studying heat exchange of dispersion-drop gas-liquid flow in granular layer

Conclusions Experimental procedure has been developed for physical modeling of monopropellant decomposition in a catalytic packet upon limiting stage of the process, i.e., during evaporation of a liquid in drop conditions. Heat exchange of liquid drops in a catalyst layer heated to high temperatures has been analyzed. Experimental dependence of a volume heat transfer coefficient on grain diameter, liquid flow rate and catalyst material has been obtained. It has been shown that within parameter variations this coefficient is practically independent of the gas velocity and drop diameter. Evaporation mechanism of drops in a heated granular layer has been discussed and carried out. For a more comprehensive examination of the interaction mechanism between the drops and the catalyst layer, a further experimental investigation is necessary in a wider range of change of the basic parameters of the process and use of mathematical modeling in analyzing experimental data. Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 118–123, July–August, 1994.     

Fine structure of boundary flows in media with diffusion and heat conduction

The influence of the boundary conditions at the surfaces confining multicomponent stratified media on the formation of flows in problems of multicomponent diffusion and thermoconcentration convection is investigated. Exact solutions of these problems are given. Analysis of these solutions shows that several boundary layers (concentration and velocity layers) are formed in the case of multicomponent diffusion, which leads to decomposition of the physical fields and splitting of the characteristic spatial scales. In the case of thermoconcentration convection, a more complicated dynamic structure is formed, which, besides boundary layers, includes injection fronts. The latter have a significant effect on the flow characteristics at distances far exceeding the thickness of the boundary layers. Institute of Mechanics Problems, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 54–63, July–August, 1998.     

Influence of heat conduction on the unlimited shockless compression of a flat gaseous layer

A numerical investigation is made of the influence of heat conduction on the compression of a flat gaseous layer in which, in the case of an ideal adiabatic gas, shockless compression occurs with unlimited cumulation of density and energy. Approximate formulas are obtained that characterize the asymptotic behavior of the cumulation of energy and density and of the energy expended on compression. It is shown that the phenomenon of density and energy cumulation is preserved when heat conduction is taken into account. Institute of Technical Physics, Snezhinsk 456770. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 25–32, July–August, 1998.     

Formulas for the heat and diffusion fluxes to a catalytic surface in a chemically nonequilibrium multicomponent boundary layer

On the basis of an asymptotic expansion of the solution of the equations of a multicomponent chemically nonequilibrium boundary layer for large Schmidt numbers, formulas are obtained for the heat flux and the diffusion fluxes of the reaction products and chemical elements on a surface with arbitrary catalytic activity. The results are compared with well-known analytic and numerical solutions. The comparison reveals the high accuracy of the formulas proposed. The results of calculating the diffusional separation of the mixture due to the selectivity of the catalytic properties of the surface with respect to recombination of oxygen and nitrogen atoms are presented. Values of the reduction of the convective heat fluxes due to the catalytic properties of the surface are obtained over a wide range of conditions in the free stream.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–176, March–April, 1996.     

Transverse vibrations of a piezoelectric layer of class 622

The exact frequency equation for the transverse vibrations of a piezolelectric layer of crystal class 622 is obtained and analyzed numerically. The problem is also solved by using an asymptotic method, the results of which are compared with those obtained from the exact frequency equation.     

Stationary heat conduction in a macro- and microperiodically layered solid

Summary This paper deals with the stationary heat conduction in a solid consisting of planar, isotropic or transversely isotropic layers. The following cases are considered: (1) arbitrarily layered solid, (2) macroperiodically layered solid, consisting of equal pairs of different basic layers with finite thicknesses, (3) microperiodically layered solid, consisting of equal layer groups of two or more different basic layers of infinitesimal thicknesses. Assuming a perfect contact between the layers, exact solutions for the plane, the axisymmetric and the general three-dimensional problem of macro- and microperiodically layered semispaces, respectively, are derived using integral transforms and the transfer-matrix method. It is proved that the microperiodically layered solid with isotropic or transversely isotropic basic layers is equivalent to a homogeneous transversely isotropic solid. Received 31 March 1999; accepted for publication 21 May 1999     

Stationary and transient heat conduction in a non homogeneous material

An apparent thermal conductivity for inhomogeneous materials is widely used. In this paper it is demonstrated that the apparent thermal conductivity for stationary heat conduction is not sufficient to describe the transient heat response of an inhomogeneous medium. In the geometry we used the heat transfer is estimated too high when the stationary thermal conductivity is employed. A numerical solution of the equation of thermal diffusion has been used to check several approximations. For short and for long times a separate approximate analytic expression can be used.

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Stationäre und Übergangswärmeleitung in nichthomogenen Materialien

Zusammenfassung Oft wird eine scheinbare Wärmeleitfähigkeit für inhomogene Materialien verwendet. In diesem Artikel wird gezeigt, daß es im allgemeinen nicht genügt, die instationäre Übergangswärmeleitung mit der stationären Wärmeleitfähigkeit zu beschreiben. In unserer Geometrie gibt dies eine Überschätzung der Wärmeleitung. Ein numerisches Modell für die Wärmediffusions-gleichung ist entwickelt worden, um mehrere Schätzungen der scheinbaren Wärmeleitfähigkeit zu kontrollieren. Für kurze und lange Zeiten stehen unterschiedliche analytische Beziehungen zur Verfügung.

     

Transient heat conduction in a torus: theory and application

 In production processes of the packaging and plastic industry cooling-problems of ring-like blanks can arise. In this paper, a simple mathematical model for such bodies consisting of foam materials with small heat conductivities is presented using toroidal co-ordinates. The corresponding Biot numbers are very high because the initial heated blanks are exposed to an efficient cooling stage based on forced convection. Thus, from a mathematically point of view the transient heat conduction in a torus with an isothermal surface is present. The fundamental eigenvalues of the problem, i.e. the thermal time constants, are obtained using the Rayleigh–Ritz-method with series of toroidal functions as trial functions for a wide range of the ratio between the inner and the outer radius of the torus. The analytical results are successfully compared with direct numerical simulations based on the method of finite differences. It is found that even for a comparable thick torus a simple correlation arising from the infinite cylinder idealisation leads to a satisfying expression for the thermal toroidal behaviour. This enables a suitable estimation formula for the cooling times required in the considered production process. Received on 17 May 2000     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

Anisotropic conduction of heat in a flowing polymeric material

In this paper a theory is presented which relates the thermal conductivity tensor of an amorphous polymeric material to the history of deformation of the material. The basis of the theory is formed by the network theory for polymeric materials. It will be shown that the results obtained here are in good agreement with experimental results on rubber. The effect of anisotropic heat conduction on the flow of a polymeric material will be demonstrated by the simple example of viscous heating in shear flow.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Analysis of heat conduction in a disk brake system

In this paper, the governing heat equations for the disk and the pad are extracted in the form of transient heat equations with heat generation that is dependant to time and space. In the derivation of the heat equations, parameters such as the duration of braking, vehicle velocity, geometries and the dimensions of the brake components, materials of the disk brake rotor and the pad and contact pressure distribution have been taken into account. The problem is solved analytically using Green’s function approach. It is concluded that the heat generated due to friction between the disk and the pad should be ideally dissipated to the environment to avoid decreasing the friction coefficient between the disk and the pad and to avoid the temperature rise of various brake components and brake fluid vaporization due to excessive heating.     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.     

Hyperbolic heat conduction in the semi-infinite body with a time-dependent laser heat source

 The Cattaneo hyperbolic and classical parabolic models of heat conduction in the laser irradiated materials are compared. Laser heating is modelled as an internal heat source, whose capacity is given by g(x,t)= I(t)(1−R)μexp(−μx). Analytical solution for the one-dimensional, semi-infinite body with the insulated boundary is obtained using Laplace transforms and the discussion of solutions for different time characteristics of the heat source capacity (constant, instantaneous, exponential, pulsed and periodic) is presented. Received on 18 May 1999     

Time-fractional radial heat conduction in a cylinder and associated thermal stresses

The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 < α ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated graphically.     

Transient heat conduction in a solid slab using multiple-scale analysis

In this paper we study the unsteady heat conduction due to a sudden temperature step in the external surfaces of a solid slab. In order to estimate the temperature profile in the solid, we applied the multiple-scale perturbation technique by identifying the “early” and “late” transient regimes for small values of the Biot number, Bi. In this sense, we have re-visited the classical lumped method, incorporating this particular case as an asymptotic limit, which is fully described by the “late” regime for small values of Bi. Once the temperature distribution is analytically predicted, this solution is compared against the exact solution and with other analytical results obtained by using regular perturbation techniques, for different values of the Biot number Bi. Observing a good agreement between the corresponding comparisons, we obtain a very simple and useful formula to predict the nondimensional temperature of the solid slab.