The Experts below are selected from a list of 261 Experts worldwide ranked by ideXlab platform

Yuriy Povstenko - One of the best experts on this subject based on the ideXlab platform.

  • Time-Fractional Heat Conduction in Two Joint Half-Planes
    Symmetry, 2019
    Co-Authors: Yuriy Povstenko, Joanna Klekot
    Abstract:

    The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of Perfect Thermal Contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results.

  • Fractional Heat Conduction and Related Theories of Thermoelasticity
    Solid Mechanics and Its Applications, 2015
    Co-Authors: Yuriy Povstenko
    Abstract:

    This chapter is devoted to time- and space-nonlocal generalizations of the standard Fourier law, the corresponding generalizations of the classical heat conduction equation and formulation of associated theories of fractional thermoelasticity. Different kinds of boundary conditions for the time-fractional heat conduction equation are analyzed including the Dirichlet, mathematical and physical Neumann and Robin conditions, the conditions of Perfect Thermal Contact and the moving interface boundary conditions at the solid-liquid interface. Representations of stresses in terms of the displacement potential, biharmonic Galerkin vector and biharmonic Love function are discussed.

  • Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion
    Entropy, 2013
    Co-Authors: Yuriy Povstenko
    Abstract:

    The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0< r < R) and a matrix (R < r < ∞) being in Perfect Thermal Contact at r = R is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 0 < a ≤ 2 and 0 < β ≤ 2, respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions.

  • Fractional Heat Conduction in Infinite One-Dimensional Composite Medium
    Journal of Thermal Stresses, 2013
    Co-Authors: Yuriy Povstenko
    Abstract:

    The problem of fractional heat conduction in a composite medium consisting of two semi-infinite regions being in Perfect Thermal Contact is considered. The heat conduction in each region is described by the time-fractional heat conduction equations with the Caputo derivative of fractional order α and β, respectively. The solution is obtained using the Laplace transform with respect to time and is expressed in terms of the Mittag–Leffler function and Mainardi function. Numerical results are illustrated graphically.

Julián Bravo-castillero - One of the best experts on this subject based on the ideXlab platform.

  • Calculation of the effective Thermal conductivity of multiscale ordered arrays based on reiterated homogenization theory and analytical formulae
    International Journal of Engineering Science, 2017
    Co-Authors: Eduardo S. Nascimento, Manuel E. Cruz, Julián Bravo-castillero
    Abstract:

    Abstract In this paper the effective Thermal conductivities of multiscale heterogeneous media with ordered microstructures are determined based on the reiterated homogenization method and analytical formulae available in the literature. While conventional homogenization has been extensively applied to Thermal problems in two-scale media, reiterated homogenization appears to have been used, to date, mostly to formulate problems in heterogeneous media with more than two scales, rather than to calculate effective properties. Here, specifically, analytical formulae for the effective conductivities of the 2-D square array of circular cylinders and the 3-D simple cubic array of spheres are used, in conjunction with the appropriate reiterated homogenization expressions, to calculate the effective conductivities of the corresponding three-scale arrays of circular cylinders and spheres. The case with a Perfect Thermal Contact at the interface is considered. The results for the effective Thermal conductivity gain of each three-scale array relative to the two-scale counterpart are given in terms of the problem volume fractions and phase contrast. For each three-scale array the optimal volume fraction at the smallest structural scale that maximizes the conductivity gain is determined, as well as the optimal global volume fraction. In special, gains in excess of 9% may be achieved. The present approach thus allows for the systematic evaluation of conductivity gains solely on the basis of Fourier heat conduction and microstructural information.

  • FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION
    Revista de Engenharia Térmica, 2016
    Co-Authors: E. Iglesias-rodríguez, Manuel Ernani Cruz, Julián Bravo-castillero, Raúl Guinovart-díaz, Reinaldo Rodríguez-ramos, Leslie D. Pérez-fernández
    Abstract:

    Heterogeneous media with multiple spatial scales are finding increased importance in engineering. An example might be a large scale, otherwise homogeneous medium filled with dispersed small-scale particles that form aggregate structures at an intermediate scale. The objective in this paper is to formulate the strong-form Fourier heat conduction equation for such media using the method of reiterated homogenization. The phases are assumed to have a Perfect Thermal Contact at the interface. The ratio of two successive length scales of the medium is a constant small parameter e . The method is an up-scaling procedure that writes the temperature field as an asymptotic multiple-scale expansion in powers of the small parameter e . The technique leads to two pairs of local and homogenized equations, linked by effective coefficients. In this manner the medium behavior at the smallest scales is seen to affect the macroscale behavior, which is the main interest in engineering. To facilitate the physical understanding of the formulation, an analytical solution is obtained for the heat conduction equation in a functionally graded material (FGM). The approach presented here may serve as a basis for future efforts to numerically compute effective properties of heterogeneous media with multiple spatial scales.

  • Reiterated homogenization applied to heat conduction in heterogeneous media with multiple spatial scales and Perfect Thermal Contact between the phases
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016
    Co-Authors: Ernesto Iglesias Rodríguez, Manuel Ernani Cruz, Julián Bravo-castillero
    Abstract:

    Several types of heterogeneous media with multiple spatial scales presently offer good potential to improve upon more traditional materials used in heat transfer and other engineering applications. An example might be a large scale, otherwise homogeneous medium filled with dispersed small-scale particles that form aggregate structures at an intermediate scale. In this paper, the strong-form Fourier heat conduction problem in such media is formulated using the method of reiterated homogenization. The constituent phases are assumed to have a Perfect Thermal Contact at the interface. The ratio of two successive length scales of the medium is a constant small parameter $$\varepsilon$$ ε . The method is an up-scaling procedure that writes the temperature field as an asymptotic multiple-scale expansion in powers of the small parameter $$\varepsilon$$ ε . The technique leads to two pairs of local and homogenized problems, linked by effective coefficients. In this manner the phenomenon description at the smallest scale is seen to affect the medium macroscale, or effective, behavior, which is the main interest in engineering. To facilitate the physical understanding of the derived sub-problems, an analytical solution is obtained for the heat conduction problem in a laminated binary composite. The present formulation shall serve as a basis for future efforts to numerically compute effective properties of heterogeneous media with multiple spatial scales.

Urszula Siedlecka - One of the best experts on this subject based on the ideXlab platform.

  • Fractional heat conduction in a sphere under mathematical and physical Robin conditions
    Journal of Theoretical and Applied Mechanics, 2018
    Co-Authors: Stanisław Kukla, Urszula Siedlecka
    Abstract:

    In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in Perfect Thermal Contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.

  • An analytical solution to the problem of time-fractional heat conduction in a composite sphere
    Bulletin of the Polish Academy of Sciences Technical Sciences, 2017
    Co-Authors: Stanisøaw Kukla, Urszula Siedlecka
    Abstract:

    Abstract An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and Perfect Thermal Contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.

  • Green's function for heat conduction problems in a multi-layered hollow cylinder
    Journal of Applied Mathematics and Computational Mechanics, 2014
    Co-Authors: Stanisław Kukla, Urszula Siedlecka
    Abstract:

    In this paper, derivation of the Green's function for the heat conduction problems in a finite multi-layered hollow cylinder is presented. Formulation and solution of the prob- lem includes an arbitrary number of the cylinder layers characterized by various Thermal properties. At the interfaces Perfect Thermal Contact was assumed. The Green's function for the three-dimensional heat conduction problems in the cylindrical coordinate has been presented in the form of a product of two other Green's functions.

Khalid Masood - One of the best experts on this subject based on the ideXlab platform.

  • Recovery and regularization of initial temperature distribution in a two-layer cylinder with Perfect Thermal Contact at the interface.
    Proceedings of the Japan Academy. Series B Physical and biological sciences, 2006
    Co-Authors: Khalid Masood
    Abstract:

    We investigate the inverse problem associated with the heat equation involving recovery of initial temperature distribution in a two-layer cylinder with Perfect Thermal Contact at the interface. The heat equation is solved backward in time to obtain a relationship between the final temperature distribution and the initial temperature profile. An integral representation for the problem is found, from which a formula for initial temperature is derived using Picard’s criterion and the singular system of the associated operators. The known final temperature profile can be used to recover the initial temperature distribution from the formula derived in this paper. A robust method to regularize the outcome by introducing a small parameter in the governing equation is also presented. It is demonstrated with the help of a numerical example that the hyperbolic model gives better results as compared to the parabolic heat conduction model.

Dariusz Golański - One of the best experts on this subject based on the ideXlab platform.

  • Temperature distribution in a cylindrical Al2O3-steel joint during the vacuum brazing cycle
    Journal of Materials Processing Technology, 1996
    Co-Authors: Dariusz Golański
    Abstract:

    Abstract This paper deals with the investigations of temperature distribution during vacuum brazing of cylindric Al 2 O 3 and steel samples, using the AgCuInTi active filler metal. The thermovision system AGA 680S was used to register the temperature field during brazing cycle. Bonded joints were observed by the infrared scanner unit during heating, brazing and cooling. Two types of joints with different shape of steel element were examined during temperature measurements. Additionally, a 2D finite element code “ADINA-T” was used to solve for the problem of nonlinear transient Thermal analysis of temperature distribution in the axisymmetric models of Al 2 O 3 -steel brazed joints. The experimental results revealed the presence of big transient axial temperature drops in the ceramic part. The change of metal shape resulted in a reduction of the transient temperature drops in the ceramic element. The finite element calculations corresponded well with the results of measurements and showed that the Perfect Thermal Contact between adjacent surfaces plays the important role in heat transfer and can be a factor affecting temperature gradients in ceramic.