Solution of heat-conduction problems in heterogeneous media by the integral relations method

1981 ◽  
Vol 40 (4) ◽  
pp. 455-461
Author(s):  
Yu. V. Kalinovskii
Keyword(s):  
Heat Conduction ◽  
Heterogeneous Media ◽  
Integral Relations

Integral Transformation of Multidimensional Heat Conduction Problems in Heterogeneous Media

2017 ◽  
Author(s):  
Carolina Palma Naveira Cotta ◽  
Renato Machado Cotta ◽  
Anderson Pereira de Almeida
Keyword(s):  
Heat Conduction ◽  
Heterogeneous Media ◽  
Integral Transformation

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2016 ◽  
Vol 15 (1) ◽  
pp. 96
Author(s):  
E. Iglesias-Rodríguez ◽  
M. E. Cruz ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
R. Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Small Parameter ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Small Scale ◽  
Multiple Spatial Scales ◽  
Effective Coefficients ◽  
Reiterated Homogenization

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 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 ε . 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.

FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2015 ◽  
Author(s):  
Ernesto Iglesias Rodríguez ◽  
Manuel Ernani Cruz ◽  
Julián Bravo-Castillero ◽  
Raúl Guinovart-Díaz ◽  
Reinaldo Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Multiple Spatial Scales ◽  
Reiterated Homogenization

Numerical Green’s Function for Steady-State Heat Conduction in Heterogeneous Media

1998 ◽  
Vol 120 (4) ◽  
pp. 284-286 ◽  
Author(s):  
Deok-Kee Choi ◽  
Seiichi Nomura
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Homogeneous Boundary Condition ◽  
State Heat ◽  
The Matrix ◽  
Steady State Heat ◽  
The Galerkin Method

Numerical Green's function for steady-state heat conduction problems is derived in a finite-sized medium that may contain inclusions (fibers) in the matrix phase. Green's function is approximated by employing the Galerkin method that uses permissible functions which satisfy the homogeneous boundary condition for the given geometry. The present approach allows physical fields in a medium that contain multiple inclusions to be expressed through isolated integrals semi-analytically while retaining all the relevant material parameters.

A generalized BIE for transient heat conduction in heterogeneous media

1997 ◽  
Author(s):  
Eduardo Divo ◽  
Alain Kassab ◽  
Eduardo Divo ◽  
Alain Kassab
Keyword(s):  
Heat Conduction ◽  
Heterogeneous Media ◽  
Transient Heat Conduction
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