Wednesday, July 4, 2012

1207.0565 (A. G. Ramm)

Heat transfer in a medium in which many small particles are embedded    [PDF]

A. G. Ramm
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting field is derived when the characteristic size $a$ of the small bodies tends to zero, their total number $\mathcal{N}(a)$ tends to infinity at a suitable rate, and the distance $d = d(a)$ between neighboring small bodies tends to zero $a << d$. No periodicity is assumed about the distribution of the small bodies.
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