Stationary Temperature Fields in Radially Inhomogeneous Hollow Cylinders

A technique for solving two-dimensional steady-state heat-conduction problems for inhomogeneous hollow cylinders is discussed when the temperatures on both inner and outer surfaces exhibit arbitrary variation within the circumferential coordinate. Using the direct integration method, the original boundary value problems are reduced to an integral equation of the second kind. This allows for addressing arbitrary variation profiles of the thermophysical properties within the radial coordinate and deriving a solution in the form of explicit dependences on the applied thermal loadings. A modification of the solution technique allows for constructing a similar solution in the case of multilayer cylinders with perfectly contacting layers whose properties are arbitrary functions of the radial coordinate.