Thermal resistance of circular cylinder cross sections with convective and flux prescribed boundaries

Two-dimensional, steady, zero source strength heat conduction within a domain whose boundaries for part of a circular cylinder coordinate system is considered. One of the constant radius surfaces is convectively coupled to a constant ambient temperature while the opposite face is subjected to a nonzero flux over a portion of its boundary. An analytical solution is performed after transforming the problem to a Cartesian-like frame, wherein convectional solution techniques can be applied. The solution depends on the Biot modulus, a geometric parameter describing the problem slenderness, and the extent and character of the flux distribution. Graphical results are presented over the range of practical interest.