Coupled conduction-convection problem for an underground duct containing eight insulated cables

The coupled heat conduction/convection problem for eight insulating and heat-generating cables in an underground circular tunnel filled with air 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 main feature of the solution procedure is that the multi-phases are treated as a single computational domain with unknown interfacial boundary conditions. The temperature distribution in the metal cores, the insulating layers, and in the surrounding air and soil, together with the convective flow pattern are obtained simultaneously. From 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 via the bottom of the enclosure through a conductive mode.