External Thermal Resistance Research Articles

External thermal resistance of buried cables and troughs

The paper describes how an integral-equation method of potential theory may be used to compute the external thermal resistance of an arbitrary configuration of buried cables or of a buried trough. It is assumed, following Goldenberg, that the outer surface of each cable or cable group is isothermal, this being approximately true when the layer of serving is very thin around the metallic sheath of each cable. With this assumption, numerical results have been obtained for a number of examples. Results for pairs of cables and for three cables in trefoil-touching formation confirm Goldenberg's theoretical estimates for large depths of burial. Results for three touching cables at the same depth and for a rectangular trough appear to be new. The method adopted here is valid for any depth of burial and is also applicable to cables whose shapes are markedly noncircular.

External thermal resistance of two buried cables

External thermal resistance of two buried cables

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.

External thermal resistance of air-installed power cables

Calculations of the external thermal resistance of power cables installed in free air have so far been based on the heat-emission coefficient h, introduced by Whitehead and Hutchings in the form of empirical curves derived from experimental work. This paper gives new formulas for h for the most important cases of cables installed in air.

Procedures for calculating the temperature rise of pipe cable and buried cables for sinusoidal and rectangular loss cycles [includes discussion

It has been customary in calculating the temperature rise of cables in duct to take account of the nature of the load cycle, since this has the effect of reducing the temperature rise from that which would result if the load were maintained continuously at a constant value. With the advent of pipe-cable systems and the increased use of directly buried cables in the United States, the problem naturally arises as to how to calculate the effect of the load cycle in these cases as well. This matter is discussed at some length in an AlEE conunittee report (ibid., vol. 70, pt. I, 1951, pages 45-52). While this report presents the results of many calculations of the effect of various loss cycles on a number of typical cable systems, it does not offer a simplified procedure for making such calculations. This paper presents such a procedure. The procedure involves merely the determination of the internal thermal resistance of the cable system in conventional manner, and adding to it the effective external thermal resistance as given in a table as a function of cable diameter and loss factor. By the use of simple nomographs, the procedure is made to include the effects of changing the earth constants, depth of burial, or frequency of the loss cycle. A rigorous straightforward method of solution of the temperature rise under sinusoidal loss cycles is also given for use where additional accuracy is required.