Temperature Fields Of Inhomogeneous Solid Sphere Based On Green Function Method

With the development of technologies, the applications of photothermal techniques in the characterization of materials of various shapes with curvature become more and more popular. One of the key issues in quantatitive characterization of curved sample using photothermal method is the theoretical modelling of the temperature field in the sample. In this thesis, we present the results of the temperature field in inhomogeneous layered spherical samples using Greens function method. Firstly, the basic concept about the Greens function is introduced. Then, the Greens function and the corresponding temeprature of a bi-layered spherical sample under illumination of an arbitrary incident beam is derived, the characteristics of the thermal wave field of a AISI1018 based spherical solid with different thin film are discussed using numerical simulation. To obtain the temperature field of a multi-layer spheres, the Greens function and the temparature field of a three-layer and four-layer spherical solids are further derived, respectively. Lastly, the Greens function and the temperature field of a multi-layer spherical solid is obtained based on matrix iteration method. Two methods are used in the derivation of the Greens function and the temperature fields of the multi-layer structures: one is analogous method by comparing the Green-fuctions of single-layer, bi-layer, three-layer and four-layer spherical solids, and finding out the iteration matrix for the multi-layer spheres, the other one is the direct derivation of the Greens function based on the iteration relationship of the multi-layer structures. The relationship of the two methods is established and the consistency is discussed. The results are verified from some special cases in which the multi-layer model can be reduced to the case of the single-layer, bi- layer, three-layer and four-layer spherical solids, respectively. It is found that the results of the Greens fuction of the multi-layer spherical solids is diffirent from single-layer,bi-layer and three-layer spherical solid in the radial portion, but the same dependence in angular portion. The results of the thesis provide a generalized theoretical tool for the quantatitive evaluation of thermo-physical properties (such as case hardened steel balls) of inhomogeneous spherical solids with arbitrary incident beams.