Geometrization of heat conduction in perturbative space–times

2019 ◽  
Vol 97 (2) ◽  
pp. 187-191 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Space Time ◽  
Conduction Equation ◽  
Small Perturbations ◽  
First Order ◽  
Geometric Conditions ◽  
Geometric Symmetry

We prove that the problem of symmetry determination linked to first-order perturbations of a metric, can be elegantly expressed using geometric conditions. In particular, an important feature of this study is that for any space–time that contains small perturbations, any equation constructed on such a space will inherit the perturbations. Intrigued by this connection between geometry and perturbations, we take the heat conduction equation and explore how the inherited perturbations affect the geometric symmetry conditions.

The Cattaneo type space-time fractional heat conduction equation

2011 ◽  
Vol 24 (4-6) ◽  
pp. 293-311 ◽  
Author(s):  
Teodor Atanacković ◽  
Sanja Konjik ◽  
Ljubica Oparnica ◽  
Dušan Zorica
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Space Time ◽  
Conduction Equation ◽  
Type Space ◽  
Fractional Heat Conduction

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.

Sign in / Sign up

Export Citation Format

Share Document