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  • 1
    Electronic Resource
    Electronic Resource
    Two-dimensional inverse heat conduction problem of estimating the time-varying strength of a line heat source (1992)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 71 (1992), S. 5357-5362 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Inverse analysis utilizing the conjugate gradient method is used to estimate the timewise varying strength of a line heat source placed at a specified location in a rectangular region with insulated boundaries. No prior information was used on the functional form of the source strength with time. Transient temperature recordings taken at the boundaries of the region served as the simulated experimental data needed as input for the inverse analysis. In order to test the accuracy of the inverse analysis under most strict conditions, timewise variation of the source strength is chosen in the form of rectangular, triangular, and sinusoidal functions. Both the regular iterated and modified conjugate gradient method are used for solving the inverse problem. The modified conjugate gradient method often provided the answer with smaller number of iterations when the initial condition for the unknown function was available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.350554
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  • 2
    Electronic Resource
    Electronic Resource
    Inverse problem of simultaneously estimating the timewise-varying strengths of two plane heat sources (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 2132-2137 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used for simultaneously estimating the timewise-varying strengths of two plane surface heat sources located inside a plate with insulated boundaries. No prior information is used for the functional forms of timewise variation of the source strength. Transient temperature recordings taken at the boundaries of the region, modified by addition of random errors, served as the simulated experimental data for the inverse analysis. In order to examine the accuracy of the estimation under most strict conditions, timewise variation of the source strength is chosen in the form of rectangular, triangular, and sinusoidal functions. Several different combinations of pulse shapes and location of the heat sources were studied. For situations in which the two heat sources were located close to each other, difficulty was experienced in the estimation of source strengths.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.353160
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  • 3
    Electronic Resource
    Electronic Resource
    On the decoupling of a system of diffusion equations (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 972-973 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Matrix formalism is used to decouple system of linear diffusion equations of monotype boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.340046
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  • 4
    Electronic Resource
    Electronic Resource
    Unified analysis of solute diffusion with reversible reaction (1987)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 62 (1987), S. 3184-3189 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Generalized three-dimensional time-dependent formal analytic solutions are developed for the problem of solute diffusion with reversible reaction in finite regions, including the important case when zero is also an eigenvalue for the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.339343
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  • 5
    Electronic Resource
    Electronic Resource
    Use of eigenfunctions for solving radiation transfer in anisotropically scattering, plane-parallel media (1986)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 60 (1986), S. 541-551 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Radiation transfer in an absorbing, emitting, gray, anisotropically scattering, plane-parallel medium is solved by using the naturally occurring eigenfunctions, and expressions for the forward and backward radiation intensities, the incident radiation, and forward and backward radiation heat fluxes are presented. To illustrate the method of solution, the situation involving an externally incident isotropic radiation at the boundary surface x=0 and no energy sources in the medium is considered for the cases of four different scattering phase functions. It is shown that the convergence to the exact results is fast, and that lower order approximations are accurate. In addition, the present method of solution has an excellent potential for generalization to problems of plane-parallel media without azimuthal symmetry and to problems in cylindrical and spherical geometries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.337445
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  • 6
    Electronic Resource
    Electronic Resource
    Hyperbolic heat conduction with temperature-dependent thermal conductivity (1986)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 59 (1986), S. 1861-1865 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Hyperbolic heat conduction in a semi-infinite slab with temperature-dependent thermal conductivity is studied numerically, and the results are compared with those obtained from the classical parabolic equation for the following cases: (a) constant applied temperature at x=0.0, (b) constant applied heat flux at x=0.0, and (c) a pulsed heat source released instanteously at t=0.0 in the region 0.0≤x≤Δx adjacent to an insulated boundary. In addition to changing the temperature profiles, the nonlinear thermal conductivity also altered the speed of the thermal front. An increase in the thermal conductivity increased the wave speed, while a decrease in the thermal conductivity decreased the wave speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.336413
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