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

Image based modeling is now commonly used to compute the effective thermal conductivity of TBCs. In these works, high resolution cross-sectional images captured by SEM are used to form a mesh and perform suitable thermal calculations. The coating materials and pores are well distinguished due to the high degree of contrast between them. Unlike that of the material, the thermal conductivity of the pores varies in a certain range due to the Knudsen effect (i.e. decrease of the gas thermal conductivity in thin pores). However, the quantification of the Knudsen effect might be unresolved yet because it was difficult to measure the dimension of every fine pore in images. In the present work, image analysis was considered to resolve the problem. The thicknesses of the pores were determined by the combination of Scion image package and a new in-house algorithm coded in C language. The Knudsen effect was quantified from computations performed with both binary images and grey scaled images. Furthermore, the Knudsen effect was also taken into account for 3D computations performed on an artificial coating model. In all cases, a decrease of the computed thermal conductivity was observed while considering the Knudsen effect.