Calculation of the external thermal resistance of buried cables through conformal transformation

The calculation of the outside thermal resistance of a buried cable system related to uniform, nonuniform and temperature-dependent resistivity of soil can be made, if a suitable transformation of the thermal field is automatically drawn and the resistance is computed on the transformed field. A suitable conformal transformation is analysed giving rise to maps of the transformed field. On the maps, the calculation of resistances involves simple operations even when the soil is nonuniform and of temperature-dependent resistivity, provided some approximations are introduced. The errors incurred by such approximations are slight and can be checked, when necessary, by direct computation of the thermal field. The calculation of resistances on the maps can also be carried out by means of automatic design programs.