With the global fossil fuels scarcity and environmental pollution problem becoming much severe in recent decades, novel energy resources are under evaluation. Nuclear energy is one of the most promising energy resources with advantages such as high energy density, zero carbon dioxides emission and less space. Nevertheless, safe operation and the issue of nuclear waste are problems in the nuclear industry. Multiphase ceramic material is an approach for immobilization of nuclear waste and potentially for nuclear fuel design. A composite material with 8mol% Yttria Stabilized Zirconia (8YSZ), Aluminum Oxides (Al2O3) and Spinel (MgAl2O4) was investigated due to potentially high thermal conductivity, good mechanical performance and radiation tolerance. OOF2 simulation work was performed based on SEM images. This thesis introduces the equipment build and standard operating procedures for a new type of thermal measurement, the 3ω method. Thermal conductivity measurement on an 8YSZ benchmark sample as well as several 3-phase large grain (>1μm) and fine grain (~500nm) samples were performed using 3ω method. Comparison between 3ω and laser flash methods as well as simulation results from OOF2, MOOSE and Bruggeman modeling is discussed in this thesis.