Part 45 (2/2)

The conductivities of air, carbonic acid gas and superheated stealish units, are:

Conductivity of air 0122 (1 + 00132 T) Conductivity of carbonic acid gas 0076 (1 + 00229 T) Conductivity of superheated steam 0119 (1 + 00261 T)

where T is the terees Fahrenheit

Nusselt's formulae can be taken as typical of the nulish writers[85] Physical properties, in addition to the density, are introduced in the form of coefficients from a consideration of the physical dimensions of the various units and of the theoretical foras and the transfer of heat All assu the heat transfer rate is by the use of one term, which seems to be unwarranted and probably has been adopted on account of the convenience in working up the results by plotting thearithmically This was thehis equation for the loss in head in fluids flowing through cylindrical pipes and it is non that the derived equation cannot be considered as anything more than an empirical for this subject to understand at the outset that the formulae discussed are only of an ees of temperature under the conditions approxi the experiments from which the constants of the formula were determined

It is not probable that the subject of heat transfer in boilers will ever be on any other than an experi the quantity of fluid which will flow through a channel of any section under a given head has been found and so the simplest possible section, namely, a circle, it is found that at low velocities the loss of head is directly proportional to the velocity and the fluid flows in straight stream lines or the motion is direct This motion is in exact accordance with the theoretical equations of the motion of a viscous fluid and constitutes almost a direct proof that the fundamental assumptions on which these equations are based are correct When, however, the velocity exceeds a value which is determinable for any size of tube, the direct or strea flow In this flow the head loss by friction is approxih not exactly, proportional to the square of the velocity No explanation of this has ever been found in spite of the fact that the subject has been treated by the best mathematicians and physicists for years back It is to be assu floould be at a her rate than with the direct or stream line flow, and Professors Croker and Clement[86] have demonstrated that this is true, the increase in the transfer being so marked as to enable the the rise in teh a tube surrounded by a stea flow and inasmuch as, from what has just been stated, this form of motion does not exist from zero velocity upward, it follows that any expression for the heat transfer rate that would make its value zero when the velocity is zero, can hardly be correct Below the critical velocity, the transfer rate seee in velocity and Nusselt,[87] in another paper which mathematically treats the direct or stream line flow, concludes that, while it is approximately constant as far as the velocity is concerned in a straight cylindrical tube, it would vary fro less as the surface passed over increased

It should further be noted that no account in any of this experias Since the coases absorb very little radiant heat at ordinary temperatures, it has been assumed that they radiate very little at any temperature This may or may not be true, but certainly a visible flame must radiate as well as absorb heat However this radiation may occur, since it would be a volume phenomenon rather than a surface phenomenon it would be considered soht apply as increasing the conductivity of the gas which, however independent of radiation, is known to increase with the teh tereater than at low temperatures The experih te is known concerning the heat radiation froh tee proportion of the heat absorbed by a boiler is received direct as radiation from the furnace Experiments show that the lower row of tubes of a Babcock & Wilcox boiler absorb heat at an average rate per square foot of surface between the first baffle and the front headers equivalent to the evaporation of frorees Fahrenheit per hour Inasmuch as in these experiments no separation could be made between the heat absorbed by the bottoe includes both maximum and minimum rates for those particular tubes and it is fair to assume that the portion of the tubes actually exposed to the furnace radiations absorb heat at a higher rate Part of this heat was, of course absorbed by actual contact between the hot gases and the boiler heating surface

A large portion of it, however, must have been due to radiation Whether this radiant heat cah the gases in the furnace with little or no absorption, or whether, on the other hand, the radiation were absorbed by the furnace gases and the heat received by the boiler was a secondary radiation fro to the actual gas temperature, is a question If the radiations are direct, then the term ”furnace te, for obviously the teas in the furnace would be entirely different from the radiation tenificance to the term ”radiation temperature”, and it is not possible to do this unless the radiations are what are known as ”full radiations” from a so-called ”black body” If furnace radiation takes place in this manner, the indications of a pyrometer placed in a furnace are hard to interpret and such temperature ases absorb the radiations from the fire and from the brickwork of the side walls and in their turn radiate heat to the boiler surface, it is scientifically correct to assuas would be measured by a pyrometer and the amount of radiation could be calculated from this temperature by Stefan's lahich is to the effect that the rate of radiation is proportional to the fourth power of the absolute te formula that has been determined from direct experi of the matter, the radiations absorbed by a boiler can be taken as equal to that absorbed by a flat surface, covering the portion of the boiler tubes exposed to the furnace and at the temperature of the tube surface, when completely exposed on one side to the radiations from an atmosphere at the temperature in the furnace With this assumption, if S{1} is the area of the surface, T the absolute teases, t the absolute temperature of the tube surface of the boiler, the heat absorbed per hour measured in B t u's is equal to

_ _ | / T / t | 1600 | |----|{4} - |----|{4}| S{1} |_1000/ 1000/ _|

In using this formula, or in any work connected with heat transfer, the external te surface can be taken as that of saturated stea, with an alible error, since experiments have shown that with a surface clean internally, the external surface is only a few degrees hotter than the water in contact with the inner surface, even at the highest rates of evaporation Further than this, it is not conceivable that in a modern boiler there can be much difference in the temperature of the boiler in the different parts, or much difference between the temperature of the water and the temperature of the steam in the drums which is in contact with it

If the total evaporation of a boiler measured in B t u's per hour is represented by E, the furnace te the boiler by T_{2}, the weight of gas leaving the furnace and passing through the setting per hour by W, the specific heat of the gas by C, it follows from the fact that the total amount of heat absorbed is equal to the heat received fro from the temperature T_{1} to the temperature T_{2}, that

_ _ | / T / t | E = 1600 | |----|{4} - |----|{4}| S{1} + WC(T_{1} - T_{2}) |_1000/ 1000/ _|

This for the furnace temperature when E, t and T_{2} are known but it must be remembered that an assumption which is probably, in part at least, incorrect is i any similar formula Expressed in this way, however, it seeo by Dr Nicholson[88]

where, in place of the surface exposed to radiation, he uses the grate surface and assuas temperature as equal to the fire temperature

If the heat transfer rate is taken as independent of the gas temperature and the heat absorbed by an eleiven out frole integration gives

Rs (T - t) = (T_{1} - t) e{- --} WC

where s is the area of surface passed over by the gases froas temperature T is measured, and the rate of heat transfer is R As written, this foras at any point in the boiler setting Gas temperatures, however, calculated in this way are not to be depended upon as it is known that the transfer rate is not independent of the te directly with the weight of the gases passing, which is Reynolds'

suggestion, it is seen that the weight of the gases entirely disappears from the for as the te the surface frohout the setting would be the same

This is known also to be incorrect If, however, in place of T is written T_{2} and in place of s is written S, the entire surface of the boiler, and the fored, it beco[89]| --------- | S |_ T_{2} - t _|

This for an average transfer rate It has been used in this way for calculating the average transfer rate from boiler tests in which the capacity has varied from an evaporation of a little over 3 pounds per square foot of surface up to 15 pounds When plotted against the gas weights, it was found that the points were almost exactly on a line This line, however, did not pass through the zero point but started at a point corresponding to approxiainst enerally and this is true even thoughthe furnace temperature The inclination of the line, however, varied inversely as the average area for the passage of the gas through the boiler If A is the average area between all the passes of the boiler, the heat transfer rate in Babcock & Wilcox type boilers with ordinary clean surfaces can be determined to a rather close approximation from the formula:

W R = 200 + 0014 - A

The manner in which A appears in this formula is the same as it would appear in any for upon the product of the velocity and the density of the gas jointly, since this product, as pointed out above, is equivalent to W/A

Nusselt's experiments, as well as those of others, indicate that the ratio appears in the proper way