Non-Fourier heat conduction in an exponentially graded slab

The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.     

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.     

Interaction effects on heat conduction and thermal stress in an infinite elastic plane with two circular holes

Numerous researches have focused on the physical behavior of an elastic material in the vicinity of a single hole under the assumption that the interaction effects arising from the introduction of multiple holes remain negligible if the holes are placed sufficiently far from each other. In an effort to understand hole interaction effects on heat conduction and thermal stress, we consider the case when two circular holes are embedded in an infinite elastic material and use complex variable method...     

Nonstationary heat conduction in a half-space with an infinite number of cylindrical heat sources

The problem of nonstationary heat conduction is treated for a half-space containing an infinite number of cylindrical heat sources, and a boundary condition of the first kind at the surfaces. It is assumed that the radii of the sources are small in comparison with their spacing and the ordinate of the center.     

Transient two-dimensional radiative and conductive heat transfer in an axisymmetric medium

This work considers transient conductive and radiative heat transfer in a two-dimensional, cylindrical, scattering medium heated or cooled by internal heat source or boundary surface. A finite difference scheme is employed for handling the energy storage and the heat diffusion by conduction, while a discrete-ordinate method is used to analyze the radiative heat transfer. The effects of various parameters, including the conduction-radiation parameter, the scattering albedo and the emissivity of the boundary surfaces, are investigated. Received on 30 April 1997     

Self-similar axisymmetric thermal in a variable-density medium

A model of a turbulent axisymmetric thermal rising in a medium whose density varies with height is proposed. An analytic solution describing the self-similar stage of ascent of the thermal is constructed. The effect of the density stratification of the atmosphere on the structure of the thermal during its motion is analyzed, and relations describing the characteristic points of the thermal and the smearing of its leading edge are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–53, July–August, 1991.     

Elastic waves in an infinite medium in the case of plane strain

Summary The paper shows the use of integral transformations for solving the equations of motion of an infinite elastic medium in the case of a plane strain. We take into account general body forces depending both on the coordinates x, y and on the time t.     

Composite heat transfer in a variable porosity medium bounded by an infinite flat plate

Heat transfer by simultaneous radiation and convection in a variable porosity medium bounded by an infinite flat plate is determined by solving momentum and energy equations. The problem is investigated for two different cases, viz., presence of porous medium and absence of porous medium. In the presence of porous medium both variable and constant porosity situations are studied. Similarity solutions are obtained for an isothermal and impermeable wall. The Kozeny-Blake expression connecting porosity and permeability is incorporated in the analysis for unified treatment. A parameter survey is made to study the effect of optical thickness, porous parameter, albedo scattering and ratio of conduction to radiation using Runge-Kutta-Gill method. The heating and cooling cases are considered for variable porosity situation. The results show that both convective and radiative components decrease with increase in porous parameter, and the inhomogeneity of the medium enhances heat transfer rate. The increase in optical thickness leads to decrease in both convective and radiative fluxes. For a particular value of wall emissivity ( _w =0.5932116) the radiative flux is reduced to zero.

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Kombinierter Wärmeübergang in einem durch eine unendlich ausgedehnte ebene Platte begrenzten Medium variabler Porosität

Zusammenfassung Der Wärmeübergang bei gleichzeitigem Einfluß von Strahlung und Konvektion in einem Medium variabler Porosität, das durch eine unendlich ausgedehnte ebene Platte begrenzt ist, wird durch Lösung der Impuls- und Energiegleichung bestimmt (den Sonderfall, daß nur Fluid, aber kein poröses Medium vorliegt, eingeschlossen). Im allgemeinen Fall — mit porösem Medium — wird sowohl variable, wie auch konstante Porosität unterstellt. Für die isotherme und stoffundurchlässige Wand existieren Ähnlichkeitslösungen. Um eine einheitliche mathematische Behandlung zu ermöglichen, wird die (Porosität und Permeabilität verknüpfende) Beziehung nach Kozeny-Blake eingeführt. Eine Parameterstudie, durchgeführt unter Verwendung der Runge-Kutta-Gill-Methode, zeigt den Einfluß der optischen Dicke, des Porositätsparameters, der Albedo-Streuung und des Verhältnises von Leitung zu Strahlung. Die Fälle Heizung und Kühlung wurden bei variabler Porosität untersucht. Aus den Ergebnissen geht hervor, daß die Konvektions- und Strahlungsanteile mit zunehmenden Porositätsparameter abnehmen und daß der Wärmeübergang durch Inhomogenität des Mediums verbessert wird. Zunehmende optische Dicke verusacht eine Abnahme sowohl des Konvektions- wie des Strahlungsflusses. Beim Wert _w =0.5932116 des Wandemissionsverhältnisses fällt der Strahlungsfluß auf Null ab.

     

Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.     

Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation

The problem of reactive blast waves in a combustible gas mixture, where the heat release at the detonation front decays exponentially with the distance from the center, is analyzed. The central theme of the paper is on the propagation of reactive blast into a uniform, quiescent, counterpressure atmosphere of a perfect gas with constant specific heats. The limiting cases of Chapman-Jouguet detonation waves are considered in the phenomenon of point explosion. In order to deal with this problem, the governing equations including thermal radiation and heat conduction were solved by the method of characteristics using a problem-specific grid and a series expansion as start solution. Numerical results for the distribution of the gas-dynamic parameters inside the flow field are shown and discussed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

Contribution to the heat conduction in composite infinite solids

Summary Comparatively little attention has been paid to problems on heat conduction in a homogeneous and isotropic infinite solid bounded internally by a circular cylinder. And it is almost impossible to find some results on composite media of this kind. The present paper brings new facts on the subject.     

Free convective heat and mass transfer flow induced by an instantaneous point source in an infinite porous medium

A simple mathematical theory is proposed for the analysis of the buoyancy-driven heat and mass transfer flow induced by an instantaneous point source in an unbounded fluid-saturated porous medium of uniform porosity, assuming the validity of the Brinkman model. The theory consists of retaining only the leading terms of the series expansions of the dependent variables in terms of the thermal Rayleigh number and is valid within the limit of small Rayleigh numbers only. The heat generating rate is assumed to be not excessive, so that the induced flow is slow. The evolution of the flow field is demonstrated by drawing the streamlines at various times, and the results are delineated by comparing them with those of the Darcy flow model. The significance of the impact of species concentration gradients upon the thermally driven flow has been highlighted. Even though heat was specified to be one of the two diffusion mechanisms, the results apply as well to the case where the source simultaneously generates two different chemical components.     

Freezing around a finite heat sink immersed in an infinite phase change medium

Freezing around a spherical heat sink immersed in an infinite phase change medium — a free boundary problem involving growth and decay of the free boundary — is analysed here. A one-dimensional conduction model is formulated and the resulting partial differential equations are solved by finite difference methods. The energy discharged from the phase change medium during the heat transfer process is analysed for latent heat thermal energy storage applications. Results are presented for a wide range of parameters that are encountered in energy storage devices. The cases of slab/cylindrical heat sink are reexamined for a range of parameters not covered by the earlier investigators     

On some diffusive waves in non-linear heat conduction

We address the non-linear heat conduction in the presence of absorption for the case of spherical symmetry geometry. The non-linear model is based on both a temperature-dependent thermal conductivity and a non-linear generalization of the Fourier law. The governing equation belongs to a class of degenerate parabolic equations. We obtain similarity solutions in closed form for the Cauchy problem corresponding to an instantaneous point source problem. We investigate the non-linear effects on the propagation of the temperature distrubances. We find that in certain cases the temperature distribution displays travelling wave characteristics. The solution for the Cauchy problem is recovered by considering a suitable first boundary value problem.     

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.