Application of combined BEM-FEM algorithms in numerical modelling of diffusion problems

  • E. Majchrzak
Conference paper

Abstract

A thermal diffusion process proceedings in heterogeneous domain Ω = Ω1
$$ X \in \Omega :\quad {C_1}\partial {}_t{T_1}(X,t) = div[{\lambda_1}grad{T_1}(X,t)] + q{}_{{v1}}(X,t) $$
(1)
$$ X \in \Omega :\quad {C_2}{\partial_t}{T_2}(X,t) = div[{\lambda_2}gard\,{T_2}(X,t)] + {q_{{v2}}}(X,t) $$
(2)
and the following boundary-initial conditions
$$ X \in {\Gamma_{{12}}}:\quad - {\lambda_1}{\partial_n}{T_1}(X,t) = \frac{{{T_1}(X,t) - {T_2}(X,t)}}{{R(X,t)}} = {\lambda_2}\partial {}_n{T_2}(X,t) $$
(3)
$$ X \in {\Gamma_{{10}}}:\quad \Phi [{T_1},{\partial_n}{T_1}(X,t)] = 0,\quad X \in {\Gamma_{{20}}}:\quad \Phi [{T_2},{\partial_n}{T_2}(X,t)] = 0 $$
(4)
$$ t = 0:\quad T{}_1(X,0) = {T_{{10}}}(X)\quad \quad {T_2}(X,0) = {T_{{20}}}(X) $$
(5)
where C e , λ e , q Ve , e=1, 2 are the thermophysical parameters and capacities of internal heat sources, t T=∂T/∂t, ∂ n T is a normal derivative at the point X∈Γ, R(X, t) is a thermal resistance between sub-domains considered, Γ10, Γ20 form the outer surface of the system. In the case R(X, t)=0 the heat flux continuity condition resolves itself into the condition additionally determining a continuity of temperature field. The domain considered is shown in Fig. 1.

Keywords

Enthalpy Assure 

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References

  1. [1]
    B. Mochnacki and J. Suchy, Modelling and Simulation of Casting, PWN, Warsaw, (1993).Google Scholar
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    C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques, Springer-Verlag, Berlin, New York (1984).MATHCrossRefGoogle Scholar
  3. [3]
    E. Majchrzak, Application of the BEM in Thermal Theory of Foundry, Mechanics, No 102, Gliwice, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • E. Majchrzak
    • 1
  1. 1.Silesian Technical UniversityGliwicePoland

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