## Materials Science and Engineering: An Introduction

$k_{max}= 31.0 W/mK$ $k_{min} =28.71 W/mK$
Required: The maximum and minimum thermal conductivity values for a cermet that contains 90 vol% titanium carbide (TiC) particles in a nickel matrix assuming thermal conductivities of 27 and 67 W/mK for TiC and Ni, respectively Solution: Using the modified form of Equation 16.1, the maximum thermal conductivity is: $k_{max} = k_{m}V_{m} + k_{p}V_{p} = k_{Ni}V_{Ni} + k_{TiC}V_{TiC} = (67 W/m.K)(0.10)+ (27 W/m.K)(0.90) = 31.0 W/mK$ Using the modified form of Equation 16.2, the minimum thermal conductivity is: $k_{min} = \frac{k_{Ni}k_{TiC}}{V_{Ni}k_{TiC} + V_{TiC}k_{Ni}} = \frac{(67 W/m.K)(27 W/m.K)}{(0.10)(27 W/m.K) + (0.90)(67 W/m.K)} = 28.71 W/mK$