An analytical model of steady state heat conduction in multiple cylindrical domains is presented and discussed. The domains are axisymmetric, contiguous, and coaxial. Three domains are considered in the current study. The thermal conductivities, thicknesses, and radii of the domains may be different. The entire geometry composed of the three connected domains is considered as adiabatic on its lateral surfaces and is subjected to uniform convective cooling at one end. The other end of the geometry is subjected to a constant heat flux, while uniform heat generation is imposed in one of the domains. The analytical solution of the model is found and special cases of it are shown to be in agreement with known solutions for simpler geometries. One application of this model relates to the thermal management of computer chips that are attached to a heat sink or a heat spreader. The three layers could simulate the chip, the thermal adhesive and the heat sink. Another application is the simulation of a nanotube or nanocylinder connecting a region of the chip to a region of the heat sink. Many other potential applications may be simulated using the different possible configurations for the solution presented.