Heat transfer through annular enclosures has received considerable attention due to number of engineering applications that include thermal energy storage systems, nuclear reactors, solar energy collectors and some others. Based on the literature review, it seems that the exact solutions for heat conduction in the eccentric enclosure (that formed between two eccentric circular tubes) with internal heat generation have not been available so far.

Therefore, in the present study, exact solution for heat conduction equation in annular enclosures with uniform internal heat generation is obtained. The annular enclosure formed between two eccentric circular tubes are considered. The heat conduction process within the enclosure is mainly influenced by the enclosure geometry and internal heat generation. The solutions are obtained in terms of the temperature and local heat flux distributions along inner and outer walls of the enclosure. The solutions for dimensionless total heat transfer rates from inner and outer walls of the enclosure are also considered.