Simplified Model for Heat Transport for Cables in Pipes

This paper addresses challenges with modeling of heat transfer phenomenon for cables in duct or pipes when applying a numerical solution. Heat transport mechanisms between the cable and pipe surfaces are conduction, convection and radiation. Numerical calculation of convection when applying a finite element analysis (FEA), or other numerical tools requires heavy computation power and great skills of the program operator. In general, this is the most difficult part when modeling the heat transfer between the cable and the pipe surfaces and practitioners are often forced to use simplifications or approximate models. This paper introduces a simplified model where the contribution from convection is replaced by a heat source at the pipe wall and a corresponding heat sink at the cable. The phenomenon of air rising vertically in the tube resulting in the upper half of the pipe being heated more by convection than the lower half is also modelled. The simplified model is compared to both known models from thermodynamics, FEA including convection and laboratory as well as the full-scale field measurements. The simplified model shows good correspondence to both simulations and measurements, with the temperatures deviating by less than 1oC.