Temperature distribution in a half-space containing spherical inclusion

Description of thermodynamic processes in disperse media placed in containers and tubes becomes more precise if thermodynamic interaction of disperse particles and container walls is taken into account. The paper deals with spherical particle without internal heat sources. This particle is placed near a plane wall and distorts temperature distribution in a medium because of difference in heat conduction coefficients. Authors obtain that it is convenient to use reflection and continue the half-space bounded by the wall, thus replacing system “plane + sphere” by another one: “two symmetric spheres”. To solve Laplace equation in unbounded space authors use multipole expansion; structure of coefficients in this expansion depends on symmetry of particles' configuration and of boundary conditions. The paper also discusses possibility of limit transition from system “a large sphere + a small sphere” to system “plane + sphere” in order to solve a problem about a spherical particle in a half-space.