Green Functions of Thermal-Wave Fields in Spherical Coordinates
Spherical coordinate boundary-value problems in diffusion-wave fields arise in isotropic geometries especially at spatial locations which lie far away from the source compared to characteristic lengths of the problem, such as the diffusion length in thermal-wave fields. The chapter begins with general considerations regarding the derivation of thermal-wave Green functions in spherical coordinates, so as to introduce the special functions that are germane to the geometry. Point sources in infinite space and inside spheres of finite radius are then examined. The special geometry of spherical thin-shell sources concentrically located inside a larger sphere is given much attention because it leads to a useful theorem (Theorem 7.1) which links one-dimensional Cartesian geometries for multilayer structures and spherical radial thermal-wave Green functions. Theorem 7.1 describes the transformation method between Cartesian and spherical coordinates and is used to derive proper and improper Green functions for spherical geometries under Dirichlet, Neumann, third-kind, or field and flux continuity boundary conditions in isotropic multilayer structures. The chapter ends with azimuthally isotropic Green function derivations in full spheres and spherical cones.
KeywordsHeat Transfer Coefficient Green Function Hollow Sphere Spherical Geometry Homogeneous Boundary Condition
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