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CHAPTER V

HEAT TRANSMISSION

Nature of Heat.-At one time heat and light were looked upon as being two different substances or conditions; now it is universally admitted that they are identical, the only difference being an objective one, and depending solely on the incapability of our optic nerves to perceive heat rays. Our other nerves make no distinction between the two, and the back of the hand will as readily feel the radiation from a blackened stove as from an electric arc, the one emitting only heat and the other chiefly light.

By those who believe in the existence of a universal ether, light and heat are thought to be vibrations of this medium. Every known experiment on the subject points to the conclusion that these vibrations. are of a transverse nature, like waves on the surface of fluids, and no relation seems to exist between these and the longitudinal vibrations called sound. The lengths of the waves of visible heat (light) range from 30,000 to 60,000 per inch. The non-luminous heat waves are longer, and the ultra-violet light, invisible to our eye but very active in photographic reactions and in vegetable life, consists of very much smaller waves. The speed with which heat and light travel through space is at the rate of about 187,000 miles per second, so that the number of vibrations per second has to be counted by hundreds of billions.

Radiant Heat of Gases and Solids.-Heat being invisible, many of the phenomena connected with radiation will be more readily understood if exemplified by the action of light, though Prof. Langley ('C. E.,' vol. c. p. 469) has done a good deal to confirm, by direct experiment, the conclusions which naturally suggest themselves when comparing light and heat.

It has been found that solids, when heated to incandescence, radiate heat and light of every colour, which is very clearly shown in the spectroscope by the fact that the spectrum of a luminous solid is a continuous one, light being visible continuously from the red end to the violet, and perceptible beyond both ends. Luminous gases do not radiate light of every colour, and some are even monochromatic. Thus the vapour of the metal cæsium has a spectrum consisting of only one green line. Indium shows three lines, chiefly blue; hydrogen shows four lines, placed in various parts of the entire spectrum. Arsenic and sodium show several lines near the yellow; potassium also shows comparatively few lines. For further information see W. M. Watts, 1872. Naturally all these gases also radiate definite colours of heat, if one may use this term; but the important point is that for the same intensity of colour of light or heat the heat thus radiated is very small

as compared with the heat radiated by a solid which shows the same intensity of light and heat over the entire spectrum; so that it will take much longer to cool a gas than a solid. An idea of the enormous disparity existing between the two will be obtained by examining the spectrum lines of sodium with a good instrument. They will appear to be no wider than very fine inked lines. The full spectrum from red to violet, measured by yards, represents the amount of radiation from a solid of the same temperature as the gas, whereas the breadth of the lines represents the entire heat radiation of sodium vapour.

The radiating power of solids also varies considerably, as will be seen from the following table. The values for a carbon film were obtained from experiments kindly made for the author by Messrs. Slingo and Brooker on an incandescent lamp, and with an optical pyrometer by MM. Mesuré and Noël, which unfortunately is only graduated up to about 2,000° F. The experimenters found no appreciable differences in the results on immersing the glow lamp either in cold or in boiling water. The values for other substances are deduced from W. H. Preece's experiments ('Proceedings,' 1884 and 1887) on the heating effects of electric currents (see also p. 125):—

Evaporative Units of Heat Radiated per Square Foot of Exposed Surface per Hour per Degree (F.) of Difference of Temperature

J. T. Bottomly (Proceedings,' 1884, Transactions,' 1887, 1893, vol. clxxxiv. a) gives the amount of radiation from bright and black copper in air and in vacuo.

Absorption of Heat.-Gases absorb only such light as they can emit, but experiments as to the influence of temperature on this phenomenon are still wanting. According to present views it would appear that gaseous flames are only luminous at their outer surfaces, which is contrary to what one sees.

It may, therefore, be assumed that flames, unless they are quite luminous, radiate and absorb little heat, and none at all when they have grown cold and transparent. The heat which radiates from a glowing coke fire is not absorbed by the non-luminous flame over it. It also follows that when the gases are cooled below the point of luminosity they cannot transmit any of their heat to the boiler plates, except by actual contact, or-and this is of great importance-by contact with the suspended particles of soot and ashes, which, as they are solids, are capable of radiating heat even at low temperatures. It would therefore appear probable that a little smoke is a good admixture to the products of combustion. It is also probable that luminous flames, such as are produced from North-country coal, will be more efficient radiators in the furnace than those which are produced from coke, anthracite, &c. In the former case the radiating surface,

i.e. the outer part of the flame, is very much larger than the exposed incandescent surface of the fuel on the grate.

Another matter which should be mentioned here is the influence of moisture and of carbonic acid on the radiating power of air. Prof. Tyndall (1870, pp. 320, 359) states that carbonic acid absorbs (and therefore also emits) 972 times as much heat as any of the permanent gases, including oxygen and nitrogen, and that humid air (he does not give the percentage of moisture) absorbs 90 times as much heat as dry air. As the products of combustion contain from 10 to 20 % of carbonic acid, this alone would raise the absorbing and radiating power about one or two hundredfold, and the moisture contained in the air and in the fuel would add considerably to this power. As these impurities, including smoke, vary considerably in every trial, it cannot be expected that much uniformity will be obtained in experiments which do not take them into account.

Thermal conductivities. The law which regulates the flow of heat through plates is a very simple one. Let t, and to be the temperatures inside of a plate, measured at two points which are 7 inches t2

apart, then is the temperature gradient, and if c is the thermal

conductivity of the material of the plate, the amount of heat which passes across an area A of the plate in one hour is H = c. A.

tą - t1

The table on p. 118 gives the values of c for various substances.

In this table the values given in the column headed 'Thermal Units' are the number of units of heat which one square foot of heating surface 1 in. thick will transmit per hour, if the difference of temperature of the two surfaces of the plate itself is one degree Fahrenheit. The values in the column Evaporative Units' are found from the last by dividing them by 966, which is the number of thermal units required to evaporate one pound of water from and at 212° F. These values can also be obtained direct from the G.C.S. values by multiplying them by 3.

It should be mentioned that all these experiments have been carried out on rods or rings, and that they are not absolutely reliable, because they are based on an imperfect knowledge of the changes of the specific heat and of the radiating power of the substances. If carried out on a plan similar to the one adopted by A. F. Yarrow for showing the curving of heated plates, these difficulties might be overcome, and, what is of almost greater importance, the coefficients of transmission of heat across the fibre of the material could thus be measured. (See below.)

Surface Resistances. In addition to the resistance which heat meets in its passage through the plates, there is the resistance to its entrance on one side and to its exit on the other side. This differs for different plate materials, perhaps also for different hot gases, and stands in no relation to the thermal conductivity. Thus cast iron, which has a much lower thermal conductivity than copper, is nevertheless a better transmitter of heat for all reasonable thicknesses, because it is the better absorber and emitter of heat. Even earthenware tiles in. thickness are 70% better than copper. (See p. 131.) From various experiments and practical experiences it would appear that when air is in contact with metal the heat transmission is very low.

Some meagre results are to be gleaned from the performances of steamers fitted with Howden's system of hot-air draught, according to which about 2 units of heat are transmitted per hour through one square foot for every degree of difference. The amount would be double for each surface on the assumption that the metal acquires the mean temperature. Plates which are exposed to the direct action of the flame also receive heat by radiation. (See p. 117.)

Considerable light has recently been thrown on this subject by some very careful experiments which were carried out by Miss E. M. Bryant (C. E.,' 1897, vol. clxxxii. p. 274), who measured the temperature gradient in the heated plate of an experimental boiler by electric methods. In the first set of experiments a copper plate was heated by a flame, in four other experiments the heating of steel and copper plates

was done by radiation from a cast-iron hemisphere which was placed, concave side upwards, below the plate, while the heat was applied to the outside of this casting. Its temperature was measured electrically. The heated plates formed the bottoms of dishes filled with water. Comparing the amount of water evaporated with the measured temperature gradient in the plates, it appears that the thermal conductivity of steel (across the grain) is 0.093 G.C.S. This is the mean of 44 experiments, but, as will be seen on comparison with the previous table, it is a rather low value. For copper the average of 25 experiments gave 0 409 thermal conductivity. The ratio of the two conductivities has usually been found to be about 1 to 8; here it is 2 to 9. It is of course well known that impure copper is a very bad conductor of heat, and the experimental plate may have been a bad one.

According to Miss Bryant's summary, the heat radiated from the cast-iron hemisphere to the boiler plate is proportional to the square of the difference of temperature between the two.

H = k. (At)2

in which H is expressed in evaporative units per square foot per hour. The values of k are as follows:

It will be seen that smoked heating surfaces are much more efficient than clean ones, but contrary to expectations, rusted surfaces are very inefficient even if covered with soot. This matter deserves further consideration. It is also a practical experience that the scraping of heating surfaces whereby the tarry film is removed improves a heating surface.

The above experiments do not embrace a sufficiently wide range of temperatures to enable one to say whether Miss Bryant's formula is correct; it would even seem that the amount of radiant heat absorbed is more nearly proportional to the cube than to the square of the difference of temperature; but at any rate the experiments are very conclusive proof that the water side of a plate is from 100 to 200 times as efficient in parting with its heat as the fire side is in absorbing radiant heat. In other words, if the furnace is, say, 1,000° hotter than the fire side of the plate, then the water side of the plate will have to be only about 5° to 10 hotter than the boiling water in order to part with all this heat. If a plate or tube has water on either side, then a difference of from 10° to 20° in the temperatures of the two waters would cause the same amount of heat to be transmitted through one square foot of surface as would be transmitted through a plate