456
INDUSTRIAL AND ENGINEERING CHEMISTRY
anhydrous ether. After removal of the ether, the product was placed without delay in a vacuum desiccator over solid potassium hydroxide. Benzene and ether which separated overnight were later drawn off. The product was highly hygroscopic, but by handling i t rapidly while i t was in the air it was obtained as a dry, pulverable solid. The yield (41 grams) agreed satisfactorily with that expected for the maleamic acid. Heptaethyleneoctamine. This was prepared as described by Jones, Langsjoen, Neumann, and Zomlefer (19), who followed the general procedure of van Alphen (1). I n the first place a sample of technical triethylenetetramine was fractionally distilled to obtain a purer sample of the amine. The fractions collected were: 129" to 154' C., 18 mm., 15.2%; and 154" to 158.5" C., 18 mm., 71.8%, ng 1.4963. Fraction 2 was used in preparing the octamine. To triethylenetetramine (59.8 grams, 0.5 mole plus 16.8 grams excess) in 25 ml. of absolute alcohol in a three-necked, 500-ml. flask fitted with a stirrer, condenser, and dropping funnel, ethylene dibromide (47 grams, 0.25 mole) in 25 ml. of absolute alcohol was added over a period of 1 hour, the temperature being prevented from rising above 55" C. The mixture was then refluxed for 1 hour. Potassium hydroxide (36 grams in 200 ml. of absolute alcohol) was added and the mixture refluxed for a further period of 1 hour. Potassium bromide was removed by filtration and alcohol by distillation, after which the product was fractionally distilled in an allglass apparatus comprising a 6-inch T'igreaux-type column: fraction 1, 101.5" to 117" C., 3 mm., was 51.9 grams, of a faint yellow liquid, representing recovered, unreacted tetramine, ng 1.4965; fraction 2, 117" to 129" C., 3 mm., 2.5 grams; and fraction 3, 230" C., 3 mm., to 228" C., 2 mm., 14.1 grams of This fraction represents an amber-colored liquid, ~ 2 %1.5132. ~ the octamine. Still residue was 13.5 grams. The figure for the refractive index of the octamine-% 1.4986-which is given by Jones et al. (IQ),not only disagrees with the figure found in the present work, but also seems to be out of line with their other figures for the refractive indexes of members of the polyethylene polyamine series. Nonaethylenedecamine. This was prepared similarly from tetraethylenepentamine (141.2 grams, 0.6 mole plus 27.7 grams excess) and ethylene dibromide (56 grams, 0.3 mole). The pentamine used consisted of a blend of the main fractions obtained by distilling two samples of technical pentamine. These fractions were: boiling point 174" to 178" C., 5 mm., n y 1.5058; and boiling point 178' to 185" C., 6 mm., ng 1.5060. Fractional distillation of the product of reaction with ethylene dibromide gave: (1) a first fraction, up to 162' C., 2 mm., con-
Vol. 42, No. 3
sisting of recovered, unreacted pentamine (79 grams, 72%5 1.5045); (2) a small intermediate fraction; (3) the decamine, at 282" to 284" C., 9 mm. (36.7 grams, nZ,51.5161); and (4) a still residue (24.1 grams). LITERATURE CITED
(1) Alphen, J. van, Rec. true. chim., 55, 412 (1936). (2) Ibid.. a. 835: 56. 343 (1937).
(6) Campbell, K. K'., Armiger, H. S.,and Campbell, B. K., Ibid., 66. 82 (1944). (7) Falk; report t o I. G. Farbenindustrie (Nov. 27, 1941) [Compare Ital. Patent 370,482 (Feb. 2, 1939); French Patent 850,210 (Dec. 11, 1939)l. (8) Firestone Research Laboratories, private communication t o Office of Rubber Reserve (May 15, 1949). (9) Gabriel, S., Berichte, 22, 1137 (1899). (10) Gambarjan, S.,Ibid., 58B, 1775 (1925). (11) Gambarjan, S., and Cialtician, O., Ibid., 60B, 390 (1927) (12) Gambarjan, S., Cialtician, O., and Babajan, A . , BzdZ. ~ n s t . sei. R.S.S. Armhie, No. 1, 265 (1931). (13) Gambarjan, S., and Kaaarian, L., J . Gen. Chem. (U.S.S.R.), 3, 222 (1933). (14) Graf, R., U. 8. Patent 2,317,757 (April 27, 1943). (15) Hobson, R. W., and D'Ianni, J. D., 1x-n. ENG.CHERI.,to be (16) (17) (18) (19)
aublished. Hurdis, E. C., U. S. Patent 2,449,299 (Sept. 14, 1948).
Ibid., 2,450,552 (Oct. 5, 1948). Ibid., 2,467,033 (April 12, 1949). Jones, G. D., Langsjoen, A., Neumann, M. M. C., and Zomlefer. J.,J . Org. Chem., 9,125 (1944). (20) Kern, W., Die Xakromol. Chem., B1, 209 (1948). (21) Levine, M. M., U. S. Patent 2,452,669 (Nov. 2, 1948). (22) Mann, F. G., and Pope, W.J., J. Chem. Soc., 1926,p. 489. (23) Maim, F. G., and Pope, W.J.,Proc. Rov. Soe. (London),109A, 448 (1925). (24) Mann, F. G., and Watson, J., J . Org. Chem., 13, 502 (1948). (25) Nozaki, K., and Bartlett, P.D., J . Am. Chem. Soc., 68, 1686 (1946). RBCEIVED October 14, 1949. Presented before the Division of Rubber Chemistry, AMERICANCHEMICAL SOCIETY, AtIantic City, September 22, 1949.
This work was sponsored by the Office of Rubber Reserve, and the authors w e indebted to t h a t office for permission t o publish it.
INFRARE RADIANT HEATING HAROLD J . GARBER University of Tennessee, Knoxville, Tenn.
AND
In a previous paper the theory of radiant heating of thin metallic panels was established. As a result of recent theoretical and experimental investigations, the scope has been widened and generalized to include the radiant heating of thick objects possessing low thermal conductivities, in which the temperature distribution is nonuniform during the transient and steady-state periods. In this article the use of radiation in the heating of materials of low thermal conductivity, with charts for calculating the variation of temperature with time, is discussed. In a third paper the detailed mathematical analysis of radiant heating of thick solids with low thermal conductivities will be presented. The equations derived in the third paper are summarized in the form of Fourier series in the present paper. Simplified graphical solutions are presented for the temperature us. time at the top, center, and bottom of the slab subjected to radiation. With high radiant intensities, it is possible to heat the surface of a thick material having a low thermal conductivity to a high temperature in a short period of time without greatly elevating the subsurface temperatures. The production
F. & TILLER !I. Vanderbilt Unicersity, h7ash2;ille,Tenn.
of this "skin effect" opens up the possibility of baking high temperature finishes on the surface of wood and related materials without undue dissipation of heat or warping and buckling. In addition to the discussion of wood heating, a review of metal heating is presented.
I
SFRARED radiant heating is nom extensively employed in many industries. It has found use in metal heating for baking enamels ( I ) , in vaporization processes including the drying of textiles and explosives (9), as an auxiliary to hot air heating in overloaded installations (e),in mirroring (5), and in localized directional heating (6). Primary emphasis has been placed on paint baking on metals, and the use of radiation for heating mood and similar materials having low thermal conductivities has not attained corresponding prominence. This has been due largely to the existence of certain inherent difficulties which frequently were not overcome in early installations. Nonuniformity of radiant beams directed upon materials possessing low thermal conductivities prevented the use of infrared radiation in many cases. Attempts to use radiation for drying finishes on soft woods met with failure be-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
March 1950
457
the rate of heat transfer is limited by conduction through the stagnant thermal resistant films adhering to the surfaces being heated. This limitation is eliminated in radiant heat transfer. Infrared heating is partially limited by lack of complete uniformity of the beam (largely overcome in better designed ovens) and by the necessity of the radiation having to “see” all surfaces equally. If the radiation pattern is not designed properly, some surfaces of three-dimensional objects will be underheated. However, the same difficulty is encountered in forced convection heating, where the coefficient of heat transfer for surfaces oriented in different ways varies considerably from one surface to another. Infrared or drying lamps are used industrially in preference to the less expensive incandescent lamps b e cause the former are more ruggedly constructed and are better adapted for use under severe temperature conditions. In addition, the filament of the infrared lamp operates at a lower temperature and has a much longer hourly rating than the incandescent lamp. Actually, there is little difference in the radiation characteristics of the two types of lamps, the incandescent lamp itself producing from 80 to 90% of its radiation in the infrared region. K0
Figure 1. Temperature Rise (2‘ - To)us. KO for Various Values of T , To= A I / F h To - To
+
-
%a 88’F; Ta=114’F Al=OB Watts/Sq In
cause boiling out of solvents disrupted the film. It was sometimes thought that low radiant intensities were necessary for the successful utilization of radiant heat with wood. One of the purposes of this paper is to demonstrate that high intensity radiation may be used to produce a “skin effect” in which the radiated surface is heated rapidly to a high temperature while the undersurface remains relatively cool. This top surface heating opens a new field for research and investigation in the baking of finishes on wood surfaces. Radiant heating has been employed alone and combined with convection to produce heat transfer rates which are higher than those obtainable with convection alone. In convectional heating,
I
I
I
I
I
I/
I
Distance from Top, Feet
Figure 3. Temperature Distribution in an Oak Block 0.75 Inch Thick at Various Times
METAL HEATING
A: 0.S Ta: 300
t
o
I
I
a2
0.4
I
I 0.8 Minutes
0.s
I 1.0
1
I
1.2
1.4
Figure 2. Comparison of Time-Temperature Curves for Forced and Natural Convection d t h and without Radiation
With thin metallic panels, the heat absorbed from the lampsis rapidly conducted throughout the panel, and the temperature distribution is substantially uniform. With materials having low thermal conductivities, such as pigments, cloth, foods, wood, and plastics, the heat will not be conducted away from the surface rapidly, and scorching and burning may occur. On the other hand, the low thermal conductivity may be converted into an
INDUSTRIAL A N D ENGINEERING CHEMISTRY
458
Vol. 42, No. 3
advantage by using an intense radiant beam for a short period of exposure, thereby producing high surface and low subsurface temperatures simultaneously. This method of heating localizes the energy at the top surface, making for better utilization of the radiation. The temperature attained by a thin material having a high thermal conductivity in a given period of time is determined by the absorption of radiation augmented or dccreased by convectional heat transfer from or to the air. During the period Jvhen thp panel temperature is bdow the air temperature, all the absorbed radiation is rrtairied and is augmented by a gain of convectional heat. IIowever, as soon as the stock temperature exceeds the surrounding air temperature, COURTESY TRUMBUCL ELECTRIC MANVFAOWRINO COMPANY part of the absorbed radiation is lost to the air. Thusl for 1:igure 4. Inside of Commercial Infrared Oven Equipped for Air Circulation maximum utilization of dectrical energy as radiation, the a r tcinperature should remain above the stock temperature. This necessitates sectionalizing the oven. The first part should I J a~ combined radiation and convection section for rapid attainment of the desired temperature, M hile the second portion should cfonsiet of a hot air section for holding the desired temperature for the required time. The maximum temperature, T,, attainable by a thin metallic pmel is given (Y,8) by
\+liere 7', is the air temperature, A the over-all absorptivity, I
the radiant intensity in B.t.u./(hour)(sq. foot), F the surface factor representing the ratio of the area from which convectional heat transfer occurs to the radiated area, and h the convectional cdhcieiit of heat transfer. Increments in the maximum tem-
TABLE *I. RADIATION INTENSITIES
Type of Lamp
Spacing, 60" Centers, Inches
230-watt clear, open reflectors 375-watt clear, open reflectors 260-watt reflector-lamp 376-watt reflector-lamp
TABLE 11. .kBsORPTIVITIES O F
Intensity of Radiation Watts/ B.t.u./ (sq. (hour) inch) (sq. foot)
10.5 10.5 5.5 5.5
hNAMELED
1.80
3.20 3.70 8.65
886 1570 2800 4200
SURFACES
Black enamel 0.87 ( 7 ) 0 . 7Sa Carbon black 0.76b Gray 0.73 Chrome green 0.61 Toluidene red O.5lb Aluminum Chrome yellow 0.50" 0.46b Cream 0.38 Titanium dioxide 0.87 and 0.56 by Ernst and Schumacher (I), apparently in
COURTESY TRUMBULL ELECTRIC MANUFACTURINQ COMPANY
Figure 5 .
Section of Tower Dryer Showing Accessibility of Lamps
a Revolted as error. b Obtained in Chemical Engineering Laboratories at Vanderbilt Univer-
sity.
INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1950
459
perature are directly proportional to increments in the air temperature. Equation 1 shows directly the desirability of high ambient temperatures. Equation 1 can be derived by equating the absorbed radiation to the convection losses at equilibrium. The instantaneous variable temperature, T , is given as a function of the time, 8, by (7, 8)
T
=
T, - (T, - T o ) e - F W / c p L
(2)
where c , p, and L are the specific heat, density, and thickness, respectively, of the stock. Equation 2 can be obtained by integrating a differential heat balance for the system. Equation 2 can be rearranged to give the temperature rise (7' - T o ) as follows
T
- To = (T, -
T o )(1 - e - K e )
(3)
where K = Fh/cpL. A plot of Equation 3 is shown in Figure 1, where (T - T o ) is plotted against KO for different maximum temperature rises (T, - To). In Figure 1, it can be seen that to obtain a given temperature rise, the time required will be shortened as T, is increased. From Equation 1 it is apparent that the maximum temperature can be raised by increasing either the air temperature or the radiant intensity. It has previously been pointed out that the efficiency of utilization of radiation increases as the intensity is raised, pointing to the use of as high intensities as possible (7). A summary of approximate average intensities of radiation obtainable with present-day equipment is given in Table I. The absorptivity is important in determining the effectiveness of radiation, and values aa obtained by Ernst and Schumacher ( 1 ) are given in Table 11. In Figure 2 a comparison of radiation plus forced convection, radiation plus natural convection, and forced convection alone is illustrated. In deciding upon forced or natural convection in conjunction with radiation, the decision will depend upon whether the temperature desired exceeds or eauals the air temperature. In Vigure 2 it can be seen that it is advantageous to use forced convection when the stock temperature is lower than the air temperature, because a shorter time is required to reach a given temperature. Howb ever, higher maximum temperatures are obtained when the convectional coefficient of heat transfer is low, as indicated by Equation 1. Obtaining temperatures above the air temperature is always at the expense of decreasing the effective utilization of the electrical energy.
Figure 6 . Graph of GI us. aBIL1
The oven for the preceding process consisted of a sheet meta! enclosure containing two rows of 250-watt reflector lamps on 90 centers. The flooring passed directly under the lamps and was held together in a tongue and groove arrangement. The finish was a penetrating sealer type, containing a large rosin content, and no continuous film was formed in which pinholing could occur. The heating was sufficient to eva orate the solvents and leave the surface dry enough for appication of the wax. The baking hastened the hardening of the short varnish while complete curing occurred after the flooring was bundled. In processes where continuous films must be formed with conventional varnishes, in contrast to the operation just described, pinholing (due to absorption and reboiling of solvents) may be-
WOOD HEATING
-1 number of successful installations involving the radiant heating of wood are in existence (9). In one of these (4), large quantities of prefinished flooring have been successfully produced during recent years. Oak flooring is sprayed with a thin sealertype varnish containing a filler. Following this operation, the flooring is brushed and rubbed to remove any excess and then passed into an infrared oven where it remains for somewhat A waxing operation less than 2 minutes. follows the heating with immediate bundling of the flooring for shipping; the entire operation takes about 10 minutes.
a8 Le Figure 7 .
Graph of
G2
us.
oc8ILZ
INDUSTRIAL AND ENGINEERING CHEMISTRY
460
with metal panels were sprayed with a second coat, allowed to sit a few minutes, and then baked under a bank of high intensity 375-watt reflector lamps. There was no tendency toward pinholing on the wood or metal. The difficulty with this first method from a commercial standpoint lies in the long setting period required for the escape of the solvents. In order to overcome this objection, a second method was developed in which the blocks werp first sprayed with a thin coat of Polymerin reduced with ethyl acetate. The combination of the thin coat and volatile ethyl acetate permitted the solvents to vaporize easily without disruption of the film during the baking process. Subsequent coats were applied in a normal manner. Sward hardnesses in the neighborhood of 60 were obtained with baking times of 4 to 6 minutes.
6
I
I .
P
I I I I I I I I I rt-Kc a0 -
Figure 8.
Vol. 42, No. 3
Graph of GB us. ab'IL2
come so serious as to preclude the use of infrared radiant heating. However, if the wood surface can be made impermeable to thinner absorption, there will be no more tendency for pinholing on the wood than is normally expected on metal surfaces. Two methods for making an impermeable wood surface were developed by the authors. In the first method, blocks of beech and oak were sprayed with a synthetic polymerizing varnish or enamel commercially known as Polymerin (the trade name for a product of the Ault and Wiborg Corporation). The samples were allowed to set overnight, so that the solvents would vaporize completely. A continuous film was thus formed, through which solvent from a subsequent spray application could not readily pass. These blocks along
No attempt Tyas made in the experiments described to test types of finishes or methods of application exhaustively. While enamels were successfullj- baked on numerous small wood blocks, a developmental program would be necessary to carry the work forward to large scale operation. It is the chief purpose of this paper to present methods for making time-temperature calculations. Radiant baking Pith electric lamps is well adapted for surfaces having a low thermal conductivity. As is demonstrated in the section on temperature calculations, the use of a high intensity radiation 2500 to 3600 B.t.u./(hour)(sq. foot) results in the surface accumulation of heat which is not rapidly conducted away during the initial period of from 1 to 5 minutes. With intensities of from 2000 to 3000 B.t.u./(hour)(sq. foot) [4 to 6 natts per square inch], from 1 to 3 minutes are required to reach 300' F. surface temperature on 0.75-inch oak flooring with an initial temperature of 80" F. and an air temperature of 140" F. Thus, high-quality, hard, and durable synthetic enamels can1be:baked on nood in a short period of time. Table tops, pianos, baseboards, and numerous other items which present flat surfaces should lend themselves to finishing operations as described. Qualitatively the considerations concerning air temperature, intensity, absorptlvity, etc., which !yere discussed under metal heating are equally applicable to wood heating. Nom ever, because of warping, it is not possible to subject the wood to the radiation for too long a period of time. TIME-TEMPERATURE DISTRIBCTIOY FOR THICK LOR -CONDUCTIVITY MATERIALS
In the third of the series of papers on infrared radiant heating, the theoretical derivations and experimental verification of the temperature equations are to be presented. h summary of the results and simplified methods for making the calculations are illustrated in this section. In most cases of radiant heating of wood, the radiation is directed tomard one side only, whereas convected heat flows through all surfaces.
I
ae L!
Figure 9.
Graph of G1 us. orOfL2
In summary, the problem reduces itself to the radiation of a block of low thermal conductivity nith a beam having a substantially uniform intensity of I B.t.u./(hout-)(sq. foot). The block is surrounded by air at a constant temperature T,, and the assumption is made that convection losses from the edges are negligible. This is tantamount to assuming t h a t the temperature is the same a t all points In planes a t given depths belOR the top surface and that the heat transfer is unidirectional. The final results mill
The results of the third paper of this series are
INDUSTRIAL AND ENGINEERING CHEMISTRY
462
Vol. 42, No. 3
temperature at the top, center, or bottom as a function of the time.
EXAMPLE 1. I t is desired to know the top surface temperature us. time variation for a fiber insulating board, 0.'5 inch thick, coated with a chrome green enamel and radiated with an intensity of 3000 B.t.u./(hour)(sq. foot) in an oven with an air temperature of 150" F. The board is initially at 80" F . The specific heat of the board is. 0.35 B.t.u./(pound)( F. j, the thermal conductivlty is 0.028 B.t.u./(hour)(foot)( F.), and the density is 15 pounds per cubic foot. The convectional coefficient of heat transfer, h, is taken to be 2.0 B.t.u / (hour)(,sq. foot)(' F.). From Table I1 the absorptivity IS found to be 0.73. Equation 5 and the graphs for GI and Gz will be employed. The following quantities are needed: j" = hL/k = (2.0)(0.5/12)/(0.028) = 2.97
a / L , = F;/cpL, = (0.028)/(0.35) (15) (0.5/12)2 = 3 072
AZ/h = (0.73) (3000)/(2) = 1095 AZL/k = (0.73)(3000)(0.5/12)/0.028
='
3259
Equation 5 becomes
Tr = 150
=
cot En =
;[$ - f]
:61
+ 1095 [E
1024
- 3259G1
-
-
(2)(2.97)(150 - 80)Gz
- 3259 GI - 416 G2
It now remains to obtain the groups, GI and Gz, for various values of aO/L2 = 3.072 0 where 8 is in hours. The values of Table 111can be obtained from Figures 6 and 7. Because the coefficient of heat transfer would increase and the thermal conductivity would change with temperature, the results would be only approximate after the first 2 or 3 minutes. GRAPHICAL CALCULATIQN OE TIME
The mid-plane temperature is given by
Tc
=
Ta
+ AZ/2h - [AZL/L+ 2J( 1', - To)]Gs
where
The bottom temperature is given by
The GI and Gz us. Fourier number plots employed for the previous example do not lend themselves readily for direct determination of the time required to reach a specified temperature. In order to obtain this time with the G charts, it is necessary to make trial and error computations, because the G; and G, groups cannot be evaluated until a0/L2 is known. However, the top temperature-time relationships can be graphed by another procedure which will permit direct determination of time as well as temperature.
A dimensional analysis of the problem yieIds the following dimensionless groups: ( T - T a ) / ( T G- T o ) ,x / L , hL/k, ae/L=, and AZ/h( T , - T o ) . .4t the top x / L = 0, and hence this group will have a constant value and need not be considered as a variable. The group (Tt 7 T G ) / ( T a- T o )where T is replaced by T t can be plotted against aO/L2 for constant values of j' and AZ/h(To - T o ) . To facilitate construction of the new chart, Equation 5 can be rearranged as follows:
where
fG;- 2fG2 ( 13a) GRAPHICAL CALCULATION OF TEMPERATURE
Any determination of temperature by means of the equations presented involves calculations with infinite series. Unfortunately, these series do not converge very rapidly when the period of radiation is short, and a large number of terms are required for obtaining accurate values of temperature. To avoid the difficulties of making these tedious calculations, a series of charts based on Equations 5 to 12 has been constructed. In Figures 6 to 9, the values of GI, Gz,Gatand Gq are plotted against Fourier's number, CuBIL2, for constant values of Biot's modulus, f. Thus with the aid of these graphs, it is possible t o determine the
If s = (Tt - T,)/(T, - T o )and r = AZ/h(T, 13a can be rewritten as
- T o ) ,Equation (1317)
Since GIand G, are functions of aB/L4 and f, Equation l a b can be written in implicit form as s = p(ffe/Lz,f,1.)
(14)
Using the 0 charts, values of s are found for various values of These values may then be replotted T.
ruejL2a t constant f and as shown in Figure 10.
March 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY TABLE 111. VALUES FROM FIGURES 6 AND 7
d/L=
0.00
a 1 a 2
0.268 0.168 0 80
8, min. Ti, a F.
6
0.01 0.179 0.123 1.95 389
0.02 0.153 0.109 3.91 480
0.03 0,136 0.101 5.86 539
0.04 0.123 0.095 7.82 583
0.05 0.113 0.090 9.77 619
0.06 0.104 0.085 11.7 650
EXAMPLE 2. An oak block 0.625 inch thick with a density of 50 pounds per cubic foot, specific heat 0.5 B.t.u./(pdund)( O F.), thermal conductivity 0.1 B.t.u.(hour)(foot)( 'F.)is radiated with a beam having an intensity of 5 watts per square inch (2458 B.t.u./(hour)(sq.foot)). The absorptivity is 0.9 and the convectional coefficient of heat transfer is 1.92 B.t.u./(hour)(sq. foot)(' F.). The air temperature is 200" F. and the initial uniform stock temperature is 75" F. It is desired to know how long it will take for the top surface to reach 300' F. The following quantities are needed: f = hL/k = (1.92)(0.625/12)/(0.1) = 1.0 s = T
- To) (300 - 200)/(200 - 75) 0.8 - T o ) = (0.9)(2458)/(1.92)(125) = 9.217
(Tt - T,)/(Ta = Al/h(T,
a/L2 = k/cpLz = (0.1)/(0.5)(50)(0.625/12)2 = 1.475
Interpolating from Figure 10, the following values are obtained:
Forr = 10 f = 1 s = 0.8
r =8
d / L 2 = 0.0274
f = 1 s = 0.8 & / L 2 = 0.0445
A linear interpolation yields & / L 2 = 0.0341. Thus 0 becomes 0.0341/1.475 = 0.0231 hour or 1.39 minutes. EXAMPLE 3. It is desired to find the effect of intensity on the top and mid-plane temperatures of an oak slab having the same properties as the one described in Example 2. The coefficient of ieat transfer is increased t o 5.76, the initial temperature to 90" F. and the air temperature is decreased to 140" F. Using Figures 6 to 9, temperature us. time calculations can be made for different intensities using the procedures outlined in Example 1. The results are plotted on Figure 11. The curves in Figures 11 and 12 strikingly illustrate the advantages of high intensities. At A I = 6 watts per square inch, the surface temperature has risen to 300" F. before the midplane has reached 100" F. It is apparent that very short heating cycles can be employed for baking enamels on the surface of wood. ACKNOWLEDGMENT
The authors wish to thank A. A. Watson and P. H. Goodell of the Trumbull Electric Manufacturing Company and Carl Egeler of the Sela Park Engineering Station of the General Electric Company for furnishing infrared reflector lamps for this investigation. Under the auspices of the above companies, Marshall Cherry and Brett Rich carried out the experimental work on wood finishing. W. E. Mehnert of the Ault and Wiborg Division of the Interchemical Corporation generously supplied many samples of Polymerin and helpful advice. Malcom Komitor rendered valuable assistance in drawing some of the figures and charts.
0.07 0.098 0.082 13.7 670
0.08 0.091 0.078 15 6 696
463
F. M. Tiller wishes to express his appreciation to the Carnegie Research Foundation in the Vanderbilt-PeabodyScarritt area for afellowship grant which has enabled him to devote time to this
NONENCLATURE
A
over-all absorptivity, ratio of rate of conversion of radiation to heat per square foot to incident intensity, dimensionless c = specific heat, B.t.u./(pound)( F.) = Biot's modulus, hL/k, dimensionless f F = surface factor, ratio of area from which convectional heat transfer occurs t o radiated area, dimensionless G1,GP,G8,Ga = groups defined by Equations 6, 7, 10, and 12, dimensionless h = convectional coefficient of heat transfer, B.t.u./(hour) (sq. foot)( O F.) I = intensity of radiation, B.t.u./(hour)(sq. foot) k = thermal conductivity, B.t.u./(hour)(foot)( F.) K = Fh/cpL, l/hour L = thickness, feet r = A l / h ( T. - To), dimensionless R = ( T - Ta)/(TaOTo), dimensionless temperature, T = F. T , = air temperature, ' F. Tb = temperature of bottom surfaze not being radiated, F. T, = temperature of center line, F. T,,, = maximum temperature attained by metal panel, a F. T o = initial temperature, F. Tt temperature of top surface being radiated, a F. Ub = steady state temperature of bottom surfye, F. U e = steady state temperature of center line, F. steady state temperature of top surface, F. Ut distance from top surface, feet x = a = thermal diffusivity, k/cp, square feet per hour €n = successive roots of Equation 8 P = density, pounds per cubic foot e = time, hours =
O
O
=I
LITERATURE CITED
(1) Emst, R. C., and Schumacher, E.F., IND. ENQ.CHEM.,36, 1132
(1944) (2) McAdams, W.H., "Heat Transmission," 2nd ed., New York, McGraw-Hill Book Co., 1942. (3) Olsen, Fred (to Western Cartridge Co.), U. 5. Patent 2,349,300 (May 23, 1944). (4) Partee, W. W., and Gray, M. G. (to E. L. Bruce Co.), Ibid., 2,228,585(June 30, 1942)and 2,341,161(Feb. 8, 1944). (5) Piou, H. H., private communication, Burroughs Glass Co., St. Louis, Mo. (6) Tiller, F.M.,Chemical Products (London),8,35 (1945). (7) Tiller, F. M., and Garber, H. J., IND. ENG.CHEM.,34, 773 (1942). (8) Tiller, F. M., Garber, H. J., and Mackey, R., unpublished manuI
script. (9) White, W.F., and White, J. H., 8s. E. L. Bruce Co., Civil Action No.406,U. 9. District Court, Dist. of Delaware, 1945. RECEIVEDFebruary 11, 1949. Results dealing with the heating of lowconductivity materiale included in this paper were presented b y H. J. Garber under the joint sponsorship of the American Society of Mechanical Engineers and the American Institute of Chemical Engineers at the Heat Transfer December 1946. Symposium, New York, N. Y.,
