While the underlying principles from which the formula for this average transfer rate was determined are questionable and at best only approximately correct, it nevertheless follows that a.s.suming the transfer rate as determined experimentally, the formula can be used in an inverse way for calculating the amount of surface required in a boiler for cooling the gases through a range of temperature covered by the experiments and it has been found that the results bear out this a.s.sumption. The practical application of the theory of heat transfer, as developed at present, seems consequently to rest on these last two formulae, which from their nature are more or less empirical.
Through the range in the production of steam met with in boilers now in service which in the marine type extends to the average evaporation of 12 to 15 pounds of water from and at 212 degrees Fahrenheit per square foot of surface, the constant 2 in the approximate formula for the average heat transfer rate const.i.tutes quite a large proportion of the total. The comparative increase in the transfer rate due to a change in weight of the gases is not as great consequently as it would be if this constant were zero. For this reason, with the same temperature of the gases entering the boiler surface, there will be a gradual increase in the temperature of the gases leaving the surface as the velocity or weight of flow increases and the proportion of the heat contained in the gases entering the boiler which is absorbed by it is gradually reduced.
It is, of course, possible that the weight of the gases could be increased to such an amount or the area for their pa.s.sage through the boiler reduced by additional baffles until the constant term in the heat transfer formula would be relatively unimportant. Under such conditions, as pointed out previously, the final gas temperature would be unaffected by a further increase in the velocity of the flow and the fraction of the heat carried by the gases removed by the boiler would be constant.
Actual tests of waste heat boilers in which the weight of gas per square foot of sectional area for its pa.s.sage is many times more than in ordinary installations show, however, that this condition has not been attained and it will probably never be attained in any practical installation. It is for this reason that the conclusions of Dr.
Nicholson in the paper referred to and of Messrs. Kreisinger and Ray in the pamphlet "The Transmission of Heat into Steam Boilers", published by the Department of the Interior in 1912, are not applicable without modification to boiler design.
In superheaters the heat transfer is effected in two different stages; the first transfer is from the hot gas to the metal of the superheater tube and the second transfer is from the metal of the tube to the steam on the inside. There is, theoretically, an intermediate stage in the transfer of the heat from the outside to the inside surface of the tube.
The conductivity of steel is sufficient, however, to keep the temperatures of the two sides of the tube very nearly equal to each other so that the effect of the transfer in the tube itself can be neglected. The transfer from the hot gas to the metal of the tube takes place in the same way as with the boiler tubes proper, regard being paid to the temperature of the tube which increases as the steam is heated.
The transfer from the inside surface of the tube to the steam is the inverse of the process of the transfer of the heat on the outside and seems to follow the same laws. The transfer rate, therefore, will increase with the velocity of the steam through the tube. For this reason, internal cores are quite often used in superheaters and actually result in an increase in the amount of superheat obtained from a given surface. The average transfer rate in superheaters based on a difference in mean temperature between the gas on the outside of the tubes and the steam on the inside of the tubes is if R is the transfer rate from the gas to the tube and r the rate from the tube to the steam:
Rr ----- R + r
and is always less than either R or r. This rate is usually greater than the average transfer rate for the boiler as computed in the way outlined in the preceding paragraphs. Since, however, steam cannot, under any imagined set of conditions, take up more heat from a tube than would water at the same average temperature, this fact supports the contention made that the actual transfer rate in a boiler must increase quite rapidly with the temperatures. The actual transfer rates in superheaters are affected by so many conditions that it has not so far been possible to evolve any formula of practical value.
[Ill.u.s.tration: Iron City Brewery of the Pittsburgh Brewing Co., Pittsburgh, Pa, Operating in this Plant 2000 Horse Power of Babc.o.c.k & Wilc.o.x Boilers]