INDUSTRIAL AND ENGtNEERING CHEMISTRY
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Dividing the original physical case into pieces or increments will introduce errors, the magnitude depending on the degree of subdivision. Other errors will come in when the run must be broken into time increments. Still others will come from inaccuracies present in heat transfer and other constants. However, assuming constants to be known (as must be assumed no matter how a problem is solved) and assuming that enough increments are used largely to eliminate errors from this type of approximation, the apparatus should be made to yield very satisfactory results in a large variety of applications. * * *
VOL. 28, NO. 6
A single large Hydrocal, with but eighteen usable standpipe positions, would apply only to the simpler types of threedimensional problems. However, the design can be such that Hydrocal units may be placed side by side and interconnected without limit. Present plans call for gaining some experience in operating the large Hydrocal before attempting to redesign it. It is practically a hand-built job, and some changes will have to be made before production by some instrument maker can be arranged. RECEIVED February 11, 1936
Temperature in
INDUSTRIAL FURNACES Interpretation and Use to Measure Radiant Heat Flux H. C. HOTTEL, F. W. MEYER, AND I. STEWART Massachusetts Institute of Technology, Cambridge, Mass.
C
OMMON to most developments in the design of processing equipment is the transition from a period of satisfaction with the prediction of over-all performance to one of profit from a consideration of the detailed performance of the various elements of the structure. In the field of high-temperature heat transmission the empirical method of building a furnace like one which was found satisfactory has to some extent been replaced by designs influenced by calculations based on an analysis of the mechanism of the heat transmission. Such calculations have, in general, had an objective no more ambitious than the prediction of over-all performance, with no consideration of how the heat is distributed to the various heat-receiving surfaces in the radiant section of the furnace. In the case of furnaces with heat-receiving surfaces a t a relatively low temperature, knowledge of such heat distribution was not essential. The high-pressure processes of chemical industry, however, involve the transmission of heat through surfaces a t elevated temperatures a t rates which must not exceed definite values imposed by considerations of strength of the materials of construction. Hence the spread between average and maximum heat-input rates per unit of surface determines the amount of surface required; and, since the unit cost of such surfaces is high, the need for equalization of heat flow in the various parts of such furnaces becomes evident. The first step in that direction is the development of instrumentation for measurement of heat flow rates in the various parts of furnaces; that is the objective of the work here described. A few sporadic attempts in this direction are recorded in the technical literature. The instrument used was a “thermaprobe,” a metal body whose rate of heat absorption can be measured by observing its rate of rise of temperature. The earliest device was a spherical probe (1). Later a flat plate, protected below and on the sides, was used to determine the heat transfer in a billet-reheating furnace, the instrument being held above and close to the stock (6). Just this year a boiler
furnace was investigated with a short cylindrical probe (5) of the same diameter as a boiler tube; the instrument was held a t various points along a tube axis so that the convection and radiation characteristics should correspond exactly to those of a tube. (Presumably the tubes in the lowest banks were double-spaced and the instrument was inserted in the blank rows.) Finally the A. S. M. E. Committee on Absorption of
The significance of temperature measurements in industrial furnaces is discussed. The true gas temperature has less utility, except in making heat balances, than the uncorrected reading ordinarily obtained with a protected couple: the latter measures the rate at which heat would be transferred if the couple were replaced by a surface at the temperature of the heat sink. An instrument consisting in principle of a pair of oriented thermocouples is shown to be capable of measuring the actual rate of heat flow across any plane in a furnace. The instrument was tested at rates of radiant heat flow across a plane of from 5000 to 18,000 B. t . u . per square foot per hour, with an average error of 4 per cent in eight tests. Its application to a study of uniformity of heat distribution in furnaces is discussed.
JUNE, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
Radiant Heat in Boiler Furnaces reported this year that they had considered, for the determination of heat distribution to the water walls of a boiler furnace, the use of a water-cooled probe, in which the rise of temperature and the rate of flow of the water would give data for the calculation of the incident radiation (7). The instrument was discarded because of unwieldiness and of the disadvantage common to the others that only the radiation towards the tubes or stock is measured; the heat reradiated or reflected must still be determined before the net heat-transfer rate is known.
Significance of High-Temperature Measurements Although the described methods of direct measurement have not been entirely satisfactory, they suggest the desirability of investigating the significance of high-temperature measurements as a basis for the development of a satisfactory instrument. The proper method of measuring a temperature i n the gas space of a heat exchanger depends on the use 40 be made of the measurement. It may be of interest either in evaluating the rate of heat transmission to a near-by surface or in determining the heat content of the gas passing the point. If the heat exchanger operates a t low temperature, both of these uses demand the measurement of “true gas temperature” a t the point, free of errors due to interchange of radiant heat between the measuring instrument and its surroundings. If the heat exchanger operates a t a high temperature, the second use still demands the use of true gas temperatine; but the first-i. e., the evaluation of heat transfer rate to a near-by surface-involves the gas temperature only to the unimportant degree to which convection contributes to the total heat transmission in a furnace. Of more importance at furnace temperature levels is the “true radiation temperature” of the point, a temperature defined as that attained by an instrument protected from the possibility of interchange of heat with its surrounding gas by convection or conduction. Since at high temperatures the reading of a protected thermocouple is nearer the true radiation temperature than the true gas temperature, such an instrument is superior to the more complicated high-velocity thermocouple or shielded couple for judging heat equalization. Consider a small gray sphere of area A and emissivity (and absorptivity) p a t some point in a furnace chamber, and let the furnace temperature be high enough to justify neglecting heat transmission to the sphere by convection. The heat absorbed by radiation from the flame, various walls, etc., will be equal to pAE,, where E , is the average emissive power of the surroundings, measured a t the sphere. When the sphere has attained thermal equilibrium a t temperature T, it will be emitting radiation a t the rate pAuT4, which must equal its rate of absorption of heat. Then, E,
=
aT4
!I )
where u is the Stefan-Boltzmann constant. If the sphere, representative of the protected thermocouple, is now replaced by a heat-receiving surface of similar shape but maintained a t some known lower temperature, T,, the net rate a t which this surface will receive heat is given by the expression: Q / A = ap(T4 - Tc4)
(2)
The temperature T measured by the protected thermocouple is a t any point in the furnace; therefore, it is a measure of the potentiality of that point for transferring heat (provided that the net heat withdrawn is insufficient to disturb conditions in the furnace). If, then, a number of protected thermocouples are installed in a furnace close to the tube bank or other “heat sink,” and symmetrically placed with regard to it, the difference between the rates of radiation to the tubes a t the vari-
709
ous points may be calculated from Equation 2. Or, if the duty and method of operation of a furnace remain steady, a thermocouple fixed in any point will show the variations in heat transfer conditions in the furnace from day to day.
Need for Modification of Protected Thermocouple Although the protected thermocouple does provide a basis for estimating variations in heat flow rates, it is desirable that an instrument for surveying the distribution of heat transfer in a furnace should indicate a t any point the actual net radiant heat flow across a plane separating the heat sink (the tube bank, stock surface, etc.) from the rest of the furnace. As an ideal instrument consider a thermocouple in the form of a small plane plate, perfectly insulated on the back and sides. If this instrument is held in the furnace until an equilibrium temperature is reached, then, by analogy to Equation 1, the emissive power E1 of that part of the furnace system “seen” from the plane of the plate will be numerically equal to the emissive power uT14 of a black body a t the equilibrium temperature attained by the plate: i. e., for the calculation of radiation from the furnace in one direction through the plane of the instrument, we may regard the furnace walls, flames, etc., as replaced by a “black-body” enclosure a t the temperature T1 attained by the instrument. If this instrument were placed parallel and close to the plane of the heat sink, the heat transfer across that plane could be calculated from the Stefan-Boltzmann equation, Q/A = a(Ti4 - T S 4 ) p 8 . F ~ (3) where pa, T , = emissivity and temperature of the sink, respectively F A = a geometrical factor t o allow for the shape and arrangement of the sink (8, 4) ( F Ais unity if the heat sink is a continuous plane a t uniform temperature.) To obviate the measurement of p , and T,and the calculation of F A , another instrument may be used in the same plane but facing the sink. It will now be exposed to the radiation reflected or reradiated from the surface of the sink, and will attain an equilibrium temperature T zwhich measures the emissive power of the system on the sink side of the plane of the instrument. Combining the two instrument readings, we obtain the net radiant heat exchange across the plane of the instrument per unit area : q / A = E1 - E2 = u(T14
-
Tz4)
(4)
The net rate of heat transmission from furnace to sink, across the plane of the instruments, is then the same as that between two infinite black parallel planes a t the two respective temperatures measured by the instruments. These temperatures are independent of the emissivities of the surfaces of the thermocouples, provided each of the latter is “gray”-i. e., of uniform emissivity throughout the spectrum. It is also essential that the introduction of the instruments does not disturb the furnace equilibrium. In practice a perfectly insulated instrument cannot be constructed, nor can convection be eliminated, but allowance may be made for both of these divergences from the ideal case. Consider an instrument consisting of two parallel plates, each of emissivity p , separated by an insulating medium of thickness L and conductivity k , and exposed to gas at temperature TG; and assume that the coefficient of convective heat transfer h, is the same for both sides. The average rates of radiation incident on the two sides, per unit area, are E1 and El, and the temperatures in equilibrium, T1 and T2,respectively. Then the equations of heat flow into each of the two side3 are:
INDUSTRIAL AND ENGINEERING CHEMISTRY
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a thermopile and the optical pyrometer; and throughout the tests the temperature wits held constant at this value. The final results are given in Table I. TABLEI. RESULTS OF EXPERIMENTS
Subtracting and dividing by p , we obtain:
--Ten i p . ,‘-Rankine-Hot Cold face, face, DifferTI Tz ence
That is, the radiant heat flux across the plane is numerically equal to the black-body radiation between infinite planes a t temperatures the same as those of the two plates of the instrument, together with a correction term equal to the temperature difference multiplied by an “instrument constant,” K (the bracketed term), which depends on the surface emissivity, the convection coefficient, and the heat conductance
1013 1166 1179 1289 1317 1365 1433 1643
734 781 787 826 843 856 691 992
279 385 392 463 474 509 562 651
Heat FluxQ B . t . u./hr./ SQ. ft. 5,180 6,700 7,170 9,340 9,760 11,020 13,710 17,880
Instrument co! 1stant K (from Col. 4) 13.86 10.81 11.51 11.63 11.61 11.75 13.26 10.76
Heat
Flux& B . t. u . / h r . t sq, ft,
4,636 7,115 7,334 9,480 9,948 11,100 12,960 18,620
Ratio. Kctual’to Calcd. Flux (Col. 4/ Col. 5) 1.118 0.942 0.997 0.984 0.982 0.991 1.058 0.960
a From hot-plate temperature and dimensions. b From instrument temperatures and average K.
The intensity of radiation falling on the instrument was varied by varying the distance from the plate a t which it was held, and was calculated from the dimensions of the system and the hot plate temperature (2,4). These values for the heat flux are given in Table I, column 4; by substitution in Equation 7 a value for the instrument constant was obtained (column 5 ) . Inspection reveals no trend of variation of K with temperature; therefore the average 11.9 was used to calculate the heat flux as measured by the instrument (column 6). In column 7 the fluxes as calculated from hot plate data and from instrument temperatures are compared, The maximum divergence is 12 per cent and the average only 4 per cent, for rates of heat transfer varying from 5,000 to 18,000B. t. u. per square foot per hour. The instrument constant K was also calculated, assuming
FIGURE I
between the plates of the instrument. It is probable that the instrument constant will vary with temperature, but since both numerator and denominator may be expected to increase with rise of temperature, the variation in the value of the constant should be small. It must be emphasized that this instrument constant affects only an additive term, so that a large error in it will produce but a small error in the calculated heat transfer. The main term in the evaluation of heat flux from the instrument temperatures, a(T14 - T2*),is, .in form, completely independent of the instrument characteristics; but the basic assumptions (that the surfaces of the plates are “gray” radiators, and that heat flow through the instrument is parallel and normal to the plates) must hold.
p , (for a dense oxide layer) = 0.8 (3) h, (vertical plate) = 0.275 (t/H)0.z6= 1.9 B. t. u./sq. ft. X hr. x F. (3) k (kaolin brick at 932’ F.) = 0.15 B.t. u./ft. X hr. X O F. (3)
The value of R so calculated, 11.4, differs from the experimental value of 11.9 by less than the limits of experimental error. The instrument as a t present constructed has a grave disadvantage in that the time taken to reach equilibrium is excessive. At the rate of 5500 B. t. u. per square foot per hour, the hot plate was still 6” F. from equilibrium temperature after an hour. An error of 3 per cent (for these conditions) would be introduced by reading this as the final temperature. A change in design to cut down the heat capacity of the instrument, however, is relatively simple; and the performance of the instrument here described is otherwise so satisfactory that it is to be used in connection with studies of industrial furnace performance.
Description of Instrument
Literature Cited
Such an instrument was built and tested, and is shown in Figure 1:
(1) Hase, R.,Arch. WBrmewirt., 13, 317 (1932). (2) Hottel, H. C., Trans. A m . SOC.Mech. Engrs., Fuels Steam Power, 53 119b). 265 11931): Mech. Em..52. 699 (1932). (3) M c A d k s , ’ W . H.‘, “Heat Transmission,” New York; McGrawHill Book Co., 1933. (4) Ibid.,Chapter 111. Schmidt, T. M., 2. V e r . deut. Ing., 79, 926 (1935); Arch. Wdrme(5) wirt., 14,11 (1933). (6) Stoffregen,H., Arch. Eisenhilttenw., 16, 221 (1933). (7) Wohlenbers, Mulliken, Armacost, and Gordon, Trans. Am. 80c. Mech. Engrs., RP 57 (4), 544 (1935). _
It consists of two stainless-steel disks, 1 inch in diameter and 1/11 inch thick, mounted in an octagonal slab of kaolin brick about 3 inches in diameter and 1 inch thick so that the surface6 are flush. A chromel-alumel couple is eened into a hole in the center of each disk, and the leads areTed along the surface of the disk before bringing them out to the insulating tube, thus minimizing the chance of false temperature readings due to conduction along the wires. Calibration of the instrument was secured using as a source of radiation a vertical hot plate, 5.19 X 5.19 inches of nickel, heated by a nichrome resistance grid immediately behind it. A preliminary survey showed that local variations in emissive power were less than 10 er cent. For the tests the average temperature was determinedy! the use of an optical pyrometer close enough for its field of view to be filled, but with the object purposely out of focus. The emissivity at the test temperature was calculated from simultaneous readings with
r
I
RECEIVED January 8 , 1936.
The paper on “Heat Transfer Coeffioients on Inclined Tubes,” by D. F. Jurgensen, Jr., and G. H. Montillon, IND.ENQ.CHEM.,27, 1466-1475 (Dee., 1935),was also presented as part of this symposium. Other papers appeared in the May, 1936, issue.
