Developments in Ceramic Materials Research

q
x
=
Modeling of Thermal Transport in Ceramics Matrix Composites 191
N
∑
i=
1
q A
i
i
N
∑
i=
1
A
i
In the case of transient thermal analysis, a heat flux is applied to one face (Figure 17) of
the composite section for a short time and the temperature history is recorded on the opposite
face to simulate the experimental conditions. The temperature profile is obtained by
averaging temperature across the complete rear face. This is obtained from an expression
similar to Equation 12, as here q i is replaced by the nodal temperatures Ti as:
T
av
=
N
∑
i=
1
T A
i
i
N
∑
i=
1
A
i
T av , the average temperature, is calculated for each time step through the transient
analysis and a temperature history is recorded. Assuming 1D uniaxial heat flow, the half rise
time related to this average temperature value is then used in Equation 8 to calculate thermal
diffusivity α and thermal conductivity k is found from Equation 10. The remaining scalar
properties, density ρ and specific heat C p for the composite are determined using the rule
of mixtures in Equation 14 shown in Table 4. It is important to emphasize that two different
volume fractions are involved here. One is 75% Carbon fibre with in the Carbon matrix,
forming the fibre tow. The other is the 65% fibre tow in the composite with remaining being
SiC matrix surrounding it. Using rule of mixtures, specific heat C p and density ρ as
calculated as:
Cp
ρ = ρ V
C
C
f
= Cp
f
f
V
f
+
+
( )
( ) ⎭ ⎬⎫
1− V f ρm
1−
V Cp
f
m
Table 4. C p and ρ for CMC from constituent materials’ property values
Material Property Carbon Fibre Carbon Matrix SiC Matrix Composite
Density ρ (kg m -3 )
Specific Heat p C
(x 10 -6 J kg -1 K -1 )
1928 1800
2310.000
1832 (fibre tow) 3200
921 717.48
1063.278
870.12 (fibre tow) 1422
(12)
(13)
(14)