Two-Dimensional Coupled Conduction-Convection Problem for an Underground Circular Duct Containing an Insulating Cable

The coupled heat conduction/convection problem for an insulating cable resting on a circular duct filled with air, and buried underground is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The temperature distribution in the insulating layer, and in the surrounding air and soil, together with the convective flow pattern are obtained. Prom the profile of the local Nusselt number, which is strongly dependent on the thermal conductivity ratios and weakly dependent on the Rayleigh number, it is concluded that most of the heat transfer takes place in the lower half of the cable through a conductive mode.