Theoretical determination of anisotropic effective thermal conductivity in transformer windings

A two-dimensional region representing a typical transformer winding cross-section is studied analytically and numerically. The winding region is characterized by layers of round or flattened conductors separated in one direction by insulating paper. The voids within the windings are filled with transformer oil. The theoretical limits of the effective thermal conductivity in two directions are determined using both the parallel isotherms and the parallel adiabats approaches. A steady state conduction analysis in the composite region is performed using standard commercial finite element analysis software. The conductor, curvature radius and contact widths were varied relative to the paper thickness for a typical value of oil thermal conductivity and for aluminum and copper conductors. It was found that the effective thermal conductivity was strongly affected by the paper and that there was negligible difference between results for aluminum and copper conductors. It was observed that the ratio of the effective thermal conductivities in the two directions could be 300 in some cases. (C) 2003 Elsevier Science Ltd.