Solving heat conduction and diffusion problems

2014 ◽  
pp. 289-318
Keyword(s):  
Heat Conduction ◽  
And Diffusion ◽  
Diffusion Problems

On the correctness of a model for phase transitions in binary alloys

1990 ◽  
Vol 1 (4) ◽  
pp. 327-338 ◽  
Author(s):  
I. G. Götz
Keyword(s):  
Phase Transitions ◽  
Heat Conduction ◽  
Stability Criterion ◽  
Binary Alloys ◽  
The Self ◽  
Self Similar Solution ◽  
Self Similar ◽  
The Stability ◽  
Similar Solutions ◽  
And Diffusion

The main result of this paper is a non-uniqueness theorem for the self-similar solutions of a model for phase transitions in binary alloys. The reason for this non-uniqueness is the discontinuity in the coefficients of heat conduction and diffusion at the inter-phase. Also the existence of a self-similar solution and the stability criterion are discussed.

Asymptotic state lumping in transport and diffusion problems on networks with applications to population problems

2015 ◽  
Vol 26 (02) ◽  
pp. 215-247 ◽  
Author(s):  
Jacek Banasiak ◽  
Aleksandra Falkiewicz ◽  
Proscovia Namayanja
Keyword(s):  
Differential Equations ◽  
Asymptotic State ◽  
Fast Diffusion ◽  
Interface Conditions ◽  
Macro Model ◽  
Structure And Dynamics ◽  
Fast Transport ◽  
Transport And Diffusion ◽  
And Diffusion ◽  
Diffusion Problems

In this paper we consider a general macro-model describing a metapopulation consisting of several interacting with each other subpopulations connected through a network, with the rules of interactions given by a system of ordinary differential equations. For such a model we construct two different micro-models in which each subpopulation has its own structure and dynamics. Precisely, each subpopulation occupies an edge of a graph and its dynamics is driven, respectively, by diffusion or transport along the edge. The interactions between the subpopulations are described by interface conditions at the nodes which the edges are incident to. We prove that with an appropriate scaling, roughly speaking with, respectively, fast diffusion or fast transport combined with slow exchange at the nodes, the solutions of the micro-models can be approximated by the solution to the macro-model.

Contribution of segregation and diffusion to refractory-material heat conduction

1978 ◽  
Vol 35 (5) ◽  
pp. 1367-1369
Author(s):  
E. Ya. Litovskii ◽  
A. V. Klimovich
Keyword(s):  
Heat Conduction ◽  
Refractory Material ◽  
And Diffusion
Sign in / Sign up

Export Citation Format

Share Document