Developments in Ceramic Materials Research

Modeling of Thermal Transport in Ceramics Matrix Composites 189
The thermal properties determined using one model is included in subsequent models. It
is in this way that the synergy between different classes of porosity is assessed. Figure 15
shows the flow chart for thermal transport modelling of this DLR-XT CMC material using
sub-models shown in Figure 14 and incorporating porosity type D, shown in Figure 9.
3.4.1. Thermal Properties
Thermal conductivity is one of the driving forces in designing materials for thermal
applications. In a material, heat flow is proportional to the temperature gradient with the
constant of proportionality being the thermal conductivity. Its general form is
q = − k
i
ij
d T
d x
j
where qi is the heat flux and kij is the thermal conductivity. This is a second-order tensor
and in most cases a symmetric one. Another important parameter for controlling thermal
transport is thermal diffusivity α . It is defined as the ratio of a material’s capacity to conduct
heat versus its capacity to store it. It is related to thermal conductivity k , specific heat C p
and density ρ as:
k = α ρ C
(10)
p
Relevant thermal properties of CMC constituents, shown in Table 3, along with air for
the pores or cracks are employed for the thermal transport models.
Table 3. Standard thermal property values of constituent materials
Material k (W m -1 K -1 ) ρ (kg m -3 ) C p (x10 -6 )(J kg -1 K -1 )
Carbon Fibre Transverse 4 1928 921
Carbon Fibre Longitudinal 40 1928 921
Carbon Matrix 10 1800 717
SiC Matrix 70 3200 1422
Air 0.001 1 1
Finite-element methods for determining the thermal transport properties of solids are
based on the two thermal analyses; Steady State and Transient. The steady state thermal
(9)