Reiterated homogenization applied to heat conduction in heterogeneous media with multiple spatial scales and perfect thermal contact between the phases

2016 ◽  
Vol 38 (4) ◽  
pp. 1333-1343 ◽  
Author(s):  
Ernesto Iglesias Rodríguez ◽  
Manuel Ernani Cruz ◽  
Julián Bravo-Castillero
Keyword(s):  
Heat Conduction ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Thermal Contact ◽  
Multiple Spatial Scales ◽  
Reiterated Homogenization ◽  
Perfect Thermal Contact

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

Effect of a Heat-Conducting Well Casing on Temperature Distribution in an Observation Well

1979 ◽  
Vol 101 (1) ◽  
pp. 20-27
Author(s):  
P. J. Closmann ◽  
E. R. Jones ◽  
E. A. Vogel
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Constant Temperature ◽  
Thermal Contact ◽  
Heat Conducting ◽  
Formation Temperature ◽  
Maximum Difference ◽  
Observation Well ◽  
Perfect Thermal Contact

The effect of heat conduction on temperature along the wall of a well casing has been determined by solution of the equations of heat conduction. The casing was assumed to pass vertically through a planar heat source of constant temperature. The casing and formation were assumed to be in perfect thermal contact. Numerical results were obtained for two sizes of steel casing and one size of aluminum casing. At any given distance from the heat source, the casing temperature differs most at early times from the formation temperature computed in the absence of casing. This difference decreases rapidly with time. Furthermore, the maximum difference occurs at greater distances from the heat source as time increases. In general, after about three months of heating, errors in measured temperatures due to conduction along the casing wall are negligible.

scholarly journals Heat Conduction Through a Flat Punch

1981 ◽  
Vol 48 (4) ◽  
pp. 871-875 ◽  
Author(s):  
Maria Comninou ◽  
J. R. Barber ◽  
John Dundurs
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Half Plane ◽  
Contact Region ◽  
Thermal Contact ◽  
Total Heat Flux ◽  
Flat Punch ◽  
Imperfect Contact ◽  
Perfect Contact ◽  
Perfect Thermal Contact

An elastic half plane is indented by a perfectly conducting rigid flat punch, which is maintained at a different temperature from the half plane. It is found that, depending on the magnitude and direction of the total heat flux, one of the following states occurs: separation at the punch corners, perfect thermal contact throughout the punch face, or an imperfect contact region at the center with adjacent perfect contact regions.

scholarly journals Time-Fractional Heat Conduction in Two Joint Half-Planes

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 800 ◽  
Author(s):  
Yuriy Povstenko ◽  
Joanna Klekot
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Fourier Transforms ◽  
Graphical Representation ◽  
Thermal Contact ◽  
The Cauchy Problem ◽  
The Laplace Transform ◽  
Fourier And Laplace Transforms ◽  
Perfect Thermal Contact ◽  
Fractional Heat Conduction

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.

Finite element computation of the effective thermal conductivity of two-dimensional multi-scale heterogeneous media

2018 ◽  
Vol 35 (5) ◽  
pp. 2107-2123 ◽  
Author(s):  
Lucas Prado Mattos ◽  
Manuel Ernani Cruz ◽  
Julián Bravo-Castillero
Keyword(s):  
Thermal Conductivity ◽  
Finite Element ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Heterogeneous Media ◽  
Volume Fraction ◽  
Maximum Heat ◽  
Content Type ◽  
Multi Scale ◽  
Reiterated Homogenization

Purpose The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium. Design/methodology/approach The methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm. Findings The effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain. Research limitations/implications The present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization. Practical implications It is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media. Originality/value The novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.

Inhibition of coral settlement at multiple spatial scales by a pervasive algal competitor

2019 ◽  
Vol 612 ◽  
pp. 29-42 ◽  
Author(s):  
NR Evensen ◽  
C Doropoulos ◽  
KM Morrow ◽  
CA Motti ◽  
PJ Mumby
Keyword(s):  
Spatial Scales ◽  
Coral Settlement ◽  
Multiple Spatial Scales

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
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