This article is cited in
7 papers
On the nature of the temperature distribution in a perforated body with given values on the external boundary under conditions of heat transfer by Newton's law on the boundary of the cavities
S. E. Pastukhova Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Abstract:
For
$\varepsilon \in (0,1)$ let $\Omega _\varepsilon =\Omega \cap \varepsilon \omega$, where
$\Omega \subset \mathbb R^d$ is a bounded domain
$\varepsilon \omega$ is the set obtained by an
$\varepsilon ^{-1}$-fold contraction from an unbounded domain
$\omega$ with a
$1$-periodic structure, the set
$\mathbb R^d \setminus \omega$ being dispersible. Then $\partial \Omega _\varepsilon =\Gamma _\varepsilon \cup S_\varepsilon$, where
$\Gamma _\varepsilon$ is the external boundary of
$\Omega _\varepsilon$ and
$S_\varepsilon$ is the boundary of the cavities lying in
$\Omega _\varepsilon$.
We study the effect of the exponentially damping (as
$\varepsilon \to 0$) influence of a non-zero temperature regime established on
$\Gamma _\varepsilon$ on the temperature distribution inside an isotropic body occupying
$\Omega _\varepsilon$ under the condition that the heat exchange on
$S_\varepsilon$ with the medium filling the cavities of the body follows Newton's law with coefficient of proportionality
$a_\varepsilon (x)=a(x/\varepsilon )$, where
$a(y)$ is a
$1$-periodic function defined on
$\partial \omega~$ such that
$\int _S a(y)\,ds>0$, if $S=\partial \omega \cap \bigl \{x\in \mathbb R^d:|x_i|<1/2,\ i=\overline {1,d}\bigr \}$.
UDC:
517.953
MSC: 35J55,
73B30 Received: 27.06.1995
DOI:
10.4213/sm138
Fulltext:
PDF file (245 kB)
