DECEMBER 27, 1889.]

ON THE HEATING OF CONDUCTORS BY ELECTRIC CURRENTS.

By A. E. KENNELLY.

III.

On the Heating of Bare Copper Wires and Strips
Suspended in Air within Doors.

IT has been shown by Prof. Forbes and others that for pare cylindrical wires suspended in air, the temperature elevation produced in them by a current will be proporional directly to the square of the current and inversely so the cube of the diameter, provided that the loss of energy per unit surface of wire per second, known as the emissivity, be itself directly proportional to the temperature elevation. This assumption, though frequently made, is recognised to be untrue, and consequently this law cannot apply rigorously to suspended bare wires, just as it has been shown to be only approximately true for empanelled wires. Experiment shows that the emissivity rises rapidly with the rise of temperature, being in some cases nearly twice as great per degree Centigrade at 100° as it is at 20° Centigrade of temperature elevation.

Hitherto in calculating the limiting temperature of a bare wire suspended in air the emissivity has been generally taken from the data supplied by the careful experiments of Messrs. McFarlane and Nichols, who observed the rate of cooling of large metal spheres in special inclosures, conditions which are not fairly applicable to the cooling of wires, and which cannot, as Prof. Forbes himself pointed out, be strictly depended upon for that purpose.

He suggested that the effect of convection was not proportional to the surface, while radiation was; and experiments have verified this belief. Thus the emissivity for a polished copper surface in the experiments of MacFarlane and Nichols was about 0·000168 therm per degree Centigrade between 0° and 60° Centigrade. With this value Forbes and others have been led to greatly under-estimate the carrying capacity of bare suspended wires. In the table accompanying his paper already mentioned, the calculated currents to raise the temperature of bright copper wires of 0.040 inch and 0120 inch diameter 49° Centigrade are 65 and 335 ampères, respectively; while experiment shows that about twice as much current is needed in each case. In fact, the emissivity per degree Centigrade has been found to vary from 0.00019 therm, with a thin flat bright copper strip to 0001364 therm with a bright copper wire 0-0356 inch (0·0904) centimetre) diameter, at about 50° Centigrade temperature elevation, or in the latter case some eight times as great an emissivity as that quoted from the previous data.

A hot wire suspended in air parts with its heat both by convection and radiation. These two processes are essentially distinct, and are governed by different laws, so that the complete treatment of the subject can only be attained by dealing with each separately and summing their effects. The experiments to be described have succeeded in determining up to temperature elevations of 100° Centigrade the separate rates of convec tion and radiation, together with the conditions to which they are independently subject. It is true that to determine all these conditions accurately would demand much further investigation, but the results appear to be at least reliable as a good first approximation.

Instead of dealing with the emissivity in therms, as has been customary, it will be more simple and direct to give all the results in watts.

Fig. 6 represents the temperature elevation measured with different current strengths passing through uninsulated copper conductors suspended in air within doors. Five different conductors were tested, and of these four were copper wires of diameters from 0 0356 inch (0-0904 cm.) to 0 1345 inch (0341 cm.). The fifth was a strip of bright brush copper, 1 inch (2:54 cme.) wide and 00065 inch (0-0165 cm.) thick. Curves I., II., III., IV., V., VI., and VII. are the traces of the bservations made upon them. Their surfaces were all

725

Bright wire 011010.879 cm) diam

bhu wwe 0.0356 10 0904cm) diam. Bright Bright wired 058/10/14/13cm diam.

20° 30 40 50° 60 70 80° 90 100° 110' Elevation of temp degrees Cent.

B
CONVECTION

Curves representing to two different
scales the energy parted with by convec

tion in Watts per centimetre length of cof -nductor at various temperature elevations 0.120 The upper set of curves are to right hand scale. The lower set of curves are to left hand scale.

0.110

0.1000

0.090

0.080

0.070

0.060

0.050

0.040

0.030

0.020

0.010

0.600

0.550

0.500

0450

0400

0.350

0.300

a250

0200

O 0.150

10 20 30° 40 50 60°

Elevation of temp degrees Cent.

RADIATION.

Bright strip flat

0 100

Watts per

linear cm

050

726

brightened with fine emery paper, except that of the strip, which needed no polishing. The wires were suspended about 8 feet (250 cms.) above the floor, between opposite walls of the laboratory, in the still air with the windows closed. These precautions were taken because it was found that a comparatively small disturbance of the air exercised a decided cooling influence on the wire. Thus a fan gently waved beneath and at right angles to one of these 25-foot lengths of wire under test produced a diminution in its resistance that was plainly discernible, and arrangements were therefore made to keep the air as free from disturbance as possible. For the same reason all the observations, though they reached their practical maxima much more quickly than had been the case with the paneled wires, were more variable and never remained quite steady. The readings had consequently to be repeated several times and means taken to obtain fair results.

The emissivity of the strip (in its upright position, to be later described) proved to be 0.24 watt per linear centimetre, at 50° Cent. temperature elevation, its surface per centimetre being 5.11 sq. cms., while the emissivity of the smallest wire was 0.08 watts per linear centimetre at the same temperature elevation, its surface per centimetre being 0-284 sq. cms. Both these measurements being referred to the unit surface instead of unit length, give, respectively, 0·047 and 0.28 watts per sq. cm., thus making the emissivity of the small wire about six times as great as that of the strip for the same temperature elevation. From this great discrepancy it appeared probable that the convection, instead of being proportional to the surface, like radiation, was equal in both cases, or nearly so; for if the convection had been proportional to the surface the mere difference in the form of the two conductors, whose surfaces were of similar appearance, could hardly account for so large a discrepancy. By assuming the convection to be equal for both wire and strip a pair of simultaneous equations was supplied by each pair of corresponding elevation points in the observation curves, thus giving radiation and convection independently for each such pair. The results for the radiation obtained in this way are :Radiation for both wire and strip

where

h = c (1·0077)o { (1·0077)' —1 };

is the quantity of heat lost by radiation from a hot body per square centimetre per second; c, a constant depending on the nature of the radiating surfaces; 0, the temperature of surrounding bodies, and t the temperature elevation of the hot body in degrees Centigrade.

Taking this formula as representing the best existing knowledge of the rate of radiation with temperature, the test of the above assumption is in the accordance of the above series of calculated radiations with a similar series obtained from Dulong & Petit's equation,

[DECEMBER 27, 1889.

The radiation in watts per square centimetre from surface of bright copper may therefore be accepted a 0.0687 (1.0077' 1) under the condition of these ex periments. But Dulong and Petit's law requires that this factor 0-0687 should itself be a function of the temperature of surrounding bodies, or, in other words, that the radiation loss from a hot wire for a given tempera ture elevation increases with the absolute temperature. It may therefore be assumed that

0.06866 = c(1·0077);

and in these experiments e, the temperature of the sur rounding air, was about 26° Centigrade, so that

Whence the complete expression for the radiation from a bright copper wire in watts per square centimetre is :

0-05625 (1·0077) [ (1·0077)' — 1].

It is to be observed, however, that this factor (10077) is a deduction only, as yet not verified by experiment. It is difficult to decide this point in the summer season, but it is hoped to determine the question of its existence experimentally during the ensuing winter by observing whether the radiation does vary to such a degree for given temperature elevations when the temperature of surrounding bodies is changed. Should this factor's existence be verified it would conpletely establish the application of Dulong and Petit's law. If, on the other hand, the variation is not to be detected, while it would certainly weaken the position. the general evidence, apart from Dulong and Petit's law, is sufficient to maintain the use of the term [ (1·0077) - 1], while the factor 0.06866 would neces sarily be regarded as independent of 0. With this reservation the retention of the factor is probably justi fied, especially as for most practical purposes the question is not a vital one.

728

The radiation is thus roughly 0.0006 watt or 0.00014 therm per square centimetre per degree Centigrade, increasing in geometrical ratio; and one square metre of bright copper at 100° Centigrade elevation would radiate about 800 watts.

The same series of simultaneous equations which gave the radiation values furnish also the convection for wire and strip and its rate of change. Fig. 6 gives the result of the analysis. Curves Nos. I., II., IV. and V., in the left-hand section (A) represent the total emission in watts per linear centimetre as actually measured, and as composed of both radiation and convection. In the right-hand section (c) the total radiation obtained in the above manner is represented in the corresponding curves I., II., IV. and V., drawn to the same scale. The difference at each pair of corresponding points between the total emission and the total radiation represents the convection loss, and this is given by the lower set of curves, I., II., IV. and V., in the central section (B) to the same scale, and also in the upper curves to this scale magnified five times for the benefit of clearer comparison. It will be observed that the convection was nearly the same in each case, the effect of increasing the diameter of the wire from 0.0356 inch (0-0904 centimetre) to 0.1345 inch (03476 centimetre), that is, nearly four times, only appearing to increase the convection 20 per cent. ; thus corroborating the results arrived at by the test of agreement with Dulong and Petit's law. The convection appears to increase rather more rapidly than the temperature elevation, except in the case of the smallest wire. This result is not in accordance with those of Dulong and Petit, who found the convection in their experiments with cooling spheres to increase as the power 1.233 of the temperature elevation, or according to the factor 11.233. It is quite possible, however, that the convection for spheres may not be the counterpart of that for long wires, and it is to be observed that not only are the laws of convection a branch of hydrodynamics more complex than those of radiation, which does not appear to vary with the form of surface, but the number and precision of these particular experiments scarcely warrant any more definite deductions to be made in this direction.

For practical purposes, therefore, it will be sufficient to take a mean value of the convection, and to assume it to be proportional to the temperature elevation, until further investigation may afford more precise information. We may, therefore, take the loss of heat by convection from any wire at the mean value of 0.00175 watt per linear centimetre in still air for each degree Cent. of temperature elevation; that is, 1 kilowatt for ever 114 metres at 50° Cent. temperature rise.

[DECEMBER 27, 1889

Fig. 6 (a) also shows that the total emission of a witt per centimetre may rise faster or slower than the temperature elevation, or may even trace a straight line proportional to the elevation for a certain distance according to the dimensions of the wire and the rela tive proportions of convection and radiation in is cooling. The smaller the wire the greater the likeli hood appears to be of the rate of emission falling behind the rate of rise in temperature.

Experiments were next made to determine the amount of variation that a difference in quality of surface could effect in the rate of radiation. Fr this purpose five wires of the same dimensions and material—that is to say, five lengths of the same wirewere suspended parallel and their surfaces coated with different substances. On another occasion five length of the same strip were treated and experimented upon in a similar manner. The results showed that in still air a black coating of sulphide of copper, produced by painting the bright surface with a solution of sulphide of sodium, reduced the temperature elevation corre sponding to any given current nearly 30 per cent both for wires and strips; while a coating of lampblac and shellac (dead black carpenter's varnish) similarly reduced the temperature of the strips nearly 50 per cent. This has a useful bearing upon bare coppe conductors within doors, say in an illuminating centra station, for if their surfaces are so large that the heat loss takes place principally by radiation (and for sur faces above 5 square centimetres per linear centimetre convection plays but a small part), the saving of energy produced by painting the conductors with this varnish will, through the lowered temperature and resistance, t amount to per cent., where t is the previous tempera ture elevation. So that if these conductors be maintained at 50 degrees Centigrade elevation in the bright state this will fall to about 27 degrees Centigrade afte painting, with a resultant saving of about 8 per cent. of the whole energy previously generated by the current in the painted length. This applies not only to bright copper, but also to copper that has become slightly tarnished by age, but may not apply equally to copper whose surface is encrusted with dust or smoke.

By first determining the radiation and convection for the bright wire and strip, then assuming the convection to be equal for the other coated wires and strips, respectively, the mean ratio of the radiation from each quality of surface to the radiation of bright copper was calculated to be as follows:

For the wires :

Thin coating of brown shellac varnish, 1-6; thick coating of copper sulphide (CaS), 23; thick coating of lampblack made adherent by molasses, 2·0.

For the strips:

Thick coating of brown shellac varnish, 1-8; rather imperfect and thin coating of copper sulphide, 15: lampblack by deposit from smoky candle, 14; thin coating of varnish, lampblack and shellac, 2-0.

The coating of copper sulphide was not so successful in promoting radiation with the strips as with the wires, partly owing, however, to imperfect coating. The necessity for a compact adherent layer in obtaining active radiation is also shown, for while lampblack deposited from a flame, only added 42 per cent. to bright radiation, lampblack applied with thin shellac varnish doubled it.

We may therefore take the radiation from a properly blackened wire as double that from a bright wire.

Experiments were also made with two strips of brigh: copper to ascertain how far their convection was affected by their plane of suspension. In the above-mentioned tests of strips, they were all secured at their extremities to lie flat; but toward their centre they each dipped to one side or the other out of the horizontal plane, making a dip of about 45°, and the following tests were made to determine whether the convection depended to any extent upon this angle:

These two strips were supported in air at about every thre feet, one of them being fixed in the vertical plane.

DECEMBER 27, 1889.]

while the other rested flat above all the supports. Their perpendicular distance apart was eight inches (21 centimetres). The testing current was sent through hem in series, and the temperature elevations determined for each in the usual way. Curves III. and VI., ig. 6 (a) represents their relative behaviour. In the first trial the temperature elevation of the flat strip reached 120° Centigrade, at 101 ampères, while that of he upright was only 102 5° C. To make certain that this difference was not due to any inequality of radiating power, the strips were exchanged in position, the upright one being now flat, and vice versa. On repeating the test, the temperature elevation of the flat strip reached 130° C. at 100 ampères, while that of the upright strip was 101.3° C., practically the same result, and the only means of accounting for the difference was the plane of the strips. The diagram shows that the emission of the upright strip was greater than that obtained from it in the previous test while unsupported and drooping, and the emission from the flat strip less-a result quite in accordance with expectation.

Fig. 6 (B) gives the calculated values of the convection from the upright and flat strip. The latter is seen to be about 45 per cent. less than the former, a rather surprising difference, for it would indicate that, supposing the upper surface of the flat strip to be equally affected by convection to the same degree as one side of the upright strip, the convection from the lower surface would then be ten times less.

The final results of the experiments on bare wires in still air point to the following means of calculating the current strength necessary to raise any given copper wire to a certain temperature elevation :

Let d be its diameter in centimetres;

729

No. of Test.

Character of Dynamos.

Outgoing Return Wire. Wire.

...

...

300

...

2 3

none

1,020 none 150 60

30

1, 1,000 volts

"

"

...

"The Cardew patent voltmeter was used for this purpose, one terminal being grounded. The instrument contained three resistance coils in series with it, so that the voltage could be read from 30 to 3,600 volts. The coils were wound so as to cancel the effect of self-induction, and the apparatus has recently been tested by two authorities and found correct within 1 volt. A third calibration is now being made.

"This leakage indicates imperfect insulation. A person touching a wire leaking at a defective point would, if a ground connection were made at the same time, receive the amount of leakage indicated in our table. It is our opinion, based upon our own experiments, and authentic records of the experiments of others, that an alternating current of 250 volts is dangerous to the life of any person through whose body such current might pass; also that a continuous current of 700 volts is, in a like manner, an unsafe amount of electrical force to be permitted to be used upon an imperfectly insulated wire.

"We therefore respectfully recommend that proper measures be taken to reduce the electrical pressure upon wires used in the City of New York to less than what we have indicated as unsafe. " (Signed) CYRUS EDSON, M.D., Chief Inspector. EDWARD W. MARTIN, Chemist. Explanation.

"Tests No. 1, No. 3, and No. 5, are upon poorly insulated circuits, which permit a portion of the continuous current to flow to the ground (it was raining a little on that evening).

"Tests No. 4, No. 6, and No. 7, are upon well insulated circuits, which keep the continuous current from leaking to any dangerous extent.

"Tests No. 8, and No. 10 to No. 17 are upon circuits having most excellent insulation and construction, four of them being in subways and the others on poles. It is said that galvanometer