Gas motion and heat transfer in a hollow cylinder with applications to arc welding

The problem of the steady heat transfer in a hollow cylinder subject to intense heating on its walls is studied and solved analytically. The heat supplied to the inner cylinder wall is supposed to be generated by the action of a laser beam on a gas circulating inside the hollow cylinder, acting as the cathode of an arc-welding device. The inverse problem is also solved and analysed for a variety of heat flux profiles. The analytical solution is compared with former numerical approaches of the inverse problem.