Abstract: Vacuum Insulation Panel (VIP) can achieve very low
thermal conductivity by evacuating its inner space. Heat transfer in the
core materials of highly-evacuated VIP occurs by conduction through
the solid structure and radiation through the pore. The effect of various
scattering modes in combined conduction-radiation in VIP is
investigated through numerical analysis. The discrete ordinates
interpolation method (DOIM) incorporated with the commercial code
FLUENT® is employed. It is found that backward scattering is more
effective in reducing the total heat transfer while isotropic scattering is
almost identical with pure absorbing/emitting case of the same optical
thickness. For a purely scattering medium, the results agrees well with
additive solution with diffusion approximation, while a modified term
is added in the effect of optical thickness to backward scattering is
employed. For other scattering phase functions, it is also confirmed
that backwardly scattering phase function gives a lower effective
thermal conductivity. Thus the materials with backward scattering
properties, with radiation shields are desirable to lower the thermal
conductivity of VIPs.
Abstract: The paper is devoted to stochastic analysis of finite
dimensional difference equation with dependent on ergodic Markov
chain increments, which are proportional to small parameter ". A
point-form solution of this difference equation may be represented
as vertexes of a time-dependent continuous broken line given on the
segment [0,1] with "-dependent scaling of intervals between vertexes.
Tending " to zero one may apply stochastic averaging and diffusion
approximation procedures and construct continuous approximation of
the initial stochastic iterations as an ordinary or stochastic Ito differential
equation. The paper proves that for sufficiently small " these
equations may be successfully applied not only to approximate finite
number of iterations but also for asymptotic analysis of iterations,
when number of iterations tends to infinity.