The performance of gas turbine engines may be improved by increasing the tolerance of the turbine blades to hot gases emerging from the combustor. One approach to achieving high operating temperatures involves application of a thermal barrier coating (TBC) to the exterior surface of a blade, while passing cooling air through the blade. Typically, the blade is made from a high-temperature superalloy, such as Inconel $(k \approx 25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$, while a ceramic, such as zirconia $(k \approx 1.3 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$, is used as a TBC.