External thermal resistance of buried cables and troughs

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. LIST OF SYMBOLSc = cable circumference D = cable diameter g = thermal resistivity hj = constant proportional to power loss of source i = general numerical suffix kj, l n j = lengths read on transformed maps m ' = number of source pairs p = vertical distance of cable centre from x axis q = horizontal distance of cable centre from y axis R = thermal resistance r = modulus of co-ordinate z Ru R 3 = thermal resistance for lateral cables R 2 = thermal resistance for centre cable 5 = position of cable centre (q -jp) T = temperature T c = isotherm at which soil resistivity changes (normally 50°C) T Q = ambient temperature Ti = cable surface temperature W = cable power loss Y o = earth surface in transformed plane Yj_ = cable surface in transformed plane z = complex co-ordinate (x + jy) in original plane Z = complex co-ordinate (X + jY) in transformed plane zj, zi = co-ordinates of point sources in original plane 6 = displacement of point source 6 = argument of co-ordinate z

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“…When m > 1, each source pair is developed following eqns 13. and 14, and so we obtain Conformal transformation for two source pairs PR OC.…”

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confidence: 99%