Knudsen Effect on the Estimation of the Effective Thermal Conductivity of Thermal Barrier Coatings

A numerical model based on the use of cross-sectional micrographies and a 3D image of thermal barrier coatings for the estimation of the material effective thermal conductivity is presented. The case of a YSZ thermal spray coating consisting of a 2 phase network, namely, the coating material and pores, is considered. The variation of the thermal conductivity of pores caused by their small size was considered by taking the Knudsen effect into account. The quantification of this effect on the effective thermal conductivity of the coating was achieved with the help of image analysis combined with an in-house program coded in C language. Finite-difference (FD) and finite-element (FE) models were applied using both 2D images and a 3D image. Despite the differences in the computed values obtained with these two numerical methods, the decrease of the computed thermal conductivity caused by the Knudsen effect was found to remain quite moderate for both methods (i.e., about 3-5% for the 3D results).