Question

The thermal conductivity values of glass fiber and epoxy resin are 1.05 W \(m^{-1} \text{K}^{-1} \) and 0.25 W \(m^{-1} \text{K}^{-1}\), respectively. The thermal conductivity of a glass fiber reinforced epoxy composite with a fiber content of 60% by volume along the fiber direction is _________ \(\text{ W m}^{-1} \text{K}^{-1}\) . (Round off to two decimal places).

Hint:

For composites, the thermal conductivity is typically calculated using the rule of mixtures. This assumes parallel heat flow along the fiber direction.

Answer 1

Correct Answer: 0.71

The thermal conductivity of the composite, \( k_c \), is given by the rule of mixtures for thermal conductivity: 
\[ k_c = k_f V_f + k_m V_m \] Where: 
- \( k_f = 1.05\ \text{W/mK} \) (thermal conductivity of fiber) 
- \( k_m = 0.25\ \text{W/K} \) (thermal conductivity of matrix) 
- \( V_f = 0.60 \) (volume fraction of fiber) 
- \( V_m = 1 - V_f = 0.40 \) (volume fraction of matrix)
Substituting the values: 
\[ k_c = (1.05)(0.60) + (0.25)(0.40) \] \[ k_c = 0.63 + 0.10 = 0.73\ \text{W/mK} \]