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Browsing by Author "Frankel, Jay Irwin"

Now showing 1 - 3 of 3
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    Flux formulation of hyperbolic heat conduction
    Frankel, Jay Irwin; Vick, Brian L.; Ozisik, M. Necati (American Institute of Physics, 1985)
    The development of the general flux formulation for heat conduction based on the modified Fourier's law is presented. This new formulation produces a hyperbolic vector equation in heat flux which is more convenient to use for analysis in situations involving specified flux conditions than the standard temperature formulation. The recovery of the temperature distribution is obtained through integration of the energy conservation law with respect to time. The Green's function approach is utilized to develop a general solution for hyperbolic heat conduction in a finite medium. The utility of the flux formulation and the unusual nature of heat conduction based on the hyperbolic formulation are demonstrated by developing analytical expressions for the heat flux and temperature distributions in a finite slab exposed to a pulsed surface heat flux.
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    A theoretical investigation of thermal waves
    Frankel, Jay Irwin (Virginia Polytechnic Institute and State University, 1986)
    A unified and systematic study of one-dimensional heat conduction based on thermal relaxation is presented. Thermal relaxation is introduced through the constitutive equation (modified Fourier's law) which relates this heat flux and temperature. The resulting temperature and flux field equations become hyperbolic rather than the usual classical parabolic equations encountered in heat conduction. In this formulation, heat propagates at a finite speed and removes one of the anomalies associated to parabolic heat conduction, i.e., heat propagating at an infinite speed. In situations involving very short times, high heat fluxes, and cryogenic temperatures, a more exact constitutive relation must be introduced to preserve a finite speed to a thermal disturbance. The general one-dimensional temperature and flux formulations for the three standard orthogonal coordinate systems are presented. The general solution, in the temperature domain, is developed by the finite integral transform technique. The basic physics and mathematics are demonstrated by reviewing Taitel's problem. Then attention is turned to the effects of radially dependent systems, such as the case of a cylinder and sphere. Various thermal disturbances are studied showing the unusual physics associated with dissipative wave equations. The flux formulation is shown to be a viable alternative domain to develop the flux distribution. Once the flux distribution has been established, the temperature distribution may be obtained through the conservation of energy. Linear one-dimensional composite regions are then investigated in detail. The general temperature and flux formulations are developed for the three standard orthogonal coordinate systems. The general solution for the flux and temperature distributions are obtained in the flux domain using a generalized integral transform technique. Additional features associated with hyperbolic heat conduction are displayed through examples with various thermal disturbances. A generalized expression for temperature dependent thermal conductivity is introduced and incorporated into the one-dimensional hyperbolic heat equation. An approximate analytical solution is obtained and compared with a standard numerical method. Finally, recommendations for future analytical and experimental investigations are suggested.
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    A theoretical one-dimensional analysis of both the temperature and stress distributions in a flat semitransparent plate subjected to a high intensity radiative source at arbitrary incidence angles
    Frankel, Jay Irwin (Virginia Polytechnic Institute and State University, 1982)
    The temperature and thermal stress distributions in a semi-transparent solid of flat plate geometry exposed to a collimated radiative source for various angles of incidence is investigated. This plate is convectively insulated on the surface where the radiation is incident while the rear surface is convectively cooled. Tile effective internal heat generation term is rederived so as to take into account the internal specular reflections (diffuse reflections were not considered) in the plate when the source is present. The newly-derived effective internal heat generation term allows for variations in the angle of incidence of the collimated source. This one-dimensional analysis investigates the importance of the incoming radiation wavelength, and the angle of incidence, on the behavior of the temperature and stress distributions. The nature of the concavity of the temperature distribution in relation to the stress distribution is also studied. The heating of the plate by a single pulsed source (laser) for a duration of 0.001 seconds followed by the subsequent cooling of the plate is examined by numerical example using Corning Glass Works #7940 Fused Silica glass as the semitransparent material.