Approximate study of the temperature distribution in a cylindrical shell

Analysis of the temperature distribution in a thin cylindrical shell whose external surface is exposed to a radiant flux that varies according to the angular coordinate. The boundary conditions for the inner and outer shell surfaces are linearized by assuming that the nonuniformity of the temperature field in the shell does not exceed a few tens of degrees. The classical heat conduction equation is integrated in cylindrical coordinates to obtain the temperature distribution in the shell. On the basis of an integral equation for the polyspherical density of radiation incident on an elementary area, the temperature distribution is expressed in terms of a Fourier series. Numerical results show that the temperature drop along the shell depends strongly on the blackness of the inner surface. Formulas are also obtained giving the temperature distribution in a shell with an insulation coating on the outside.