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: Simultaneous transient conduction and radiation heat
transfer with heat generation is investigated. Analysis is carried out
for both steady and unsteady situations. two-dimensional gray
cylindrical enclosure with an absorbing, emitting, and isotropically
scattering medium is considered. Enclosure boundaries are assumed
at specified temperatures. The heat generation rate is considered
uniform and constant throughout the medium. The lattice Boltzmann
method (LBM) was used to solve the energy equation of a transient
conduction-radiation heat transfer problem. The control volume finite
element method (CVFEM) was used to compute the radiative
information. To study the compatibility of the LBM for the energy
equation and the CVFEM for the radiative transfer equation, transient
conduction and radiation heat transfer problems in 2-D cylindrical
geometries were considered. In order to establish the suitability of the
LBM, the energy equation of the present problem was also solved
using the the finite difference method (FDM) of the computational
fluid dynamics. The CVFEM used in the radiative heat transfer was
employed to compute the radiative information required for the
solution of the energy equation using the LBM or the FDM (of the
CFD). To study the compatibility and suitability of the LBM for the
solution of energy equation and the CVFEM for the radiative
information, results were analyzed for the effects of various
parameters such as the boundary emissivity. The results of the LBMCVFEM
combination were found to be in excellent agreement with
the FDM-CVFEM combination. The number of iterations and the
steady state temperature in both of the combinations were found
comparable. Results are found for situations with and without heat
generation. Heat generation is found to have significant bearing on
temperature distribution.