Abstract

This thesis presents a combined numerical and experimental study of the heat transfer modes that take place in cavities embedded within solid bodies. The motivation is to develop a practical numerical approach to quantify the role of various regions in the global heat dissipation around underground electrical cable installations, used in electricity transmission and distribution. A detailed numerical solution of the complex heat transfer present; conduction, free convection and radiation, with unknown boundary values at the air-solid interfaces, is first developed. For the convective flows in the cavities, the Navier-Stokes equations are solved, in stream-function vorticity form, using a Newton-Galerkin finite element approach. For the radiation part in these cavities, the shape factors of surface elements of cables and ducts are calculated by a crossed-string technique. A series of simplifications are then made to avoid the solution of the Navier-Stokes equations. First, the cables and their surrounding backfills are discretized in one common mesh, together with the intermediate air gaps, in such a way that only the Fourier partial differential equation is solved. To be able to do so, the air gaps are considered as fictitious solid materials with a specific thermal conductivity and a negligible thermal capacity. The individual thermal conductivity of each air gap is calculated by assuming the convection and radiation heat exchanges as separate thermal resistances acting in parallel between cables and ducts. The convection component is calculated by solving a concentric annuli problem. Results in the form of equivalent conductivity at various Rayleigh number and diameter ratios are then derived to cover the range of interest encountered in underground installations. The same approach is used to analyze the heat transfer in empty ducts by considering such ducts as populated by small fictitious unloaded cables. The demanding resources of cable ampacity finite element conduction code are further alleviated through a new technique dubbed EFECAC (Economic Finite Element for Cable Ampacity Calculation). This technique takes advantage of the fact that the heat dissipation in cables is nearly axisymmetric and hence couples the 2D solution in the surroundings to a 1D axisymmetric grid inside the cable. The Finite Element suite of codes thus developed are used to analyze conventional and non-conventional cable installations. These codes, equipped with an automatic mesh generator, currently enable industrial users to rapidly analyze a variety of complex underground installations.