Applicazione della trasformazione conforme alla risoluzione di equazioni differenziali alle derivate parziali di tipo ellittico con metodi numerici

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

“…Of course, a fully automatic definition of the maps by program is not straightforward and can give rise to some programming difficulties, although it is, in principle, possible, and has actually been used, though with caution. 5 CONCLUSIONS It has been shown that the evaluation of the thermal resistances of cables buried in uniform, nonuniform and/or nonlinear soils can be obtained by means of a geometrical transformation involving a reduced amount of computation. This transformation is therefore very suitable for design purposes, and is carried out in two main steps: first the transformed field is worked out, then some details of it are modified in order to simplify the calculations.…”

“…x 2 + (y -y,coth Y) 2 = ---1 sinh 2 Y and the lines of flux, normal to isotherms, are circles of centre -y x cot X + jO and diameter 2y 1 (5) sin X (x + y 1 cotX) 2 sin 2 X (6) Since the soil surface is the isotherm T = 0, when there is only one cable its external surface is identified with an isotherm and the relevant position of the source Z x ;the cable external temperature T x (or direct resistance R 1X ) is obtained from…”