# 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

Heat Flux Iron Casting Thermophysical Parameter Zero Initial Condition Thermal Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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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).
3. [3]
E. Majchrzak, Application of the BEM in Thermal Theory of Foundry, Mechanics, No 102, Gliwice, 1991.Google Scholar