External thermal resistance of three buried cables in trefoil-touching formation. Restricted application of superposition

An approximate formula, with error bounds, is derived for the thermal resistance between three touching circular cylinders and a plane. The formula is based on a restricted application of the principle of superposition. The distance between the cylinder configuration and the plane is assumed to be much greater than the cylinder radius, which is the case for the evaluation of the external thermal resistance of three equally loaded identical cables laid direct in the ground in trefoil-touching formation. Numerical calculation indicates that formulas now in use for this application may give values that are noticeably on the high side. The method may be used to obtain approximations to the solution of other thermal resistance problems involving a plane as one of the boundaries.