INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1941
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DATABASEDON STEADYTABLE 11. APPARENTCONDUCTIVITY HEATFLOW EXPERIMENTS (POROSITY, 38 PERCENT) Conductivity, B. t. u. Hr.-1 Ft.-’
Wiloox Sand with: Air
Water/Lb. Hr.
Water Oil
73.60 70.90 68.60 98.40 116.10 116.10 80.10 70.10 98.70
Of
70.73 69.97 71.35 69.96 70.89 71.96 72.10 71.61 71.02
Water* F.
’ F.-1
Steedy~nsteady flow flow
82.00 82.30 83.25 102.05 107.76 109.97 92.49 94.18 88.36
0.41 0.40 0.40 2.60 2.61 2.63 0.87 0.85 0.87
Acknowledgment The authors wish to express their appreciation for the help given by G. A. Van Lear and S. B. Townes in the mathematical analysis of the problem, and for the assistance of T. Whelan, J. Cheek, D. Brim, and H. M. Evans in constructing the apparatus and securing the original data.
0.26
Literature Cited Carslaw, “Mathematical Theory of Heat”, pp. 30, 38, New York, Macmillan Company, 1921. Frank and Mises, “Die Differential und Integralgleichungen des Mechanic und Physik”, Tiel 11, pp. 561-3, Braunschweig. Vieweg, 1935. Gurney, H. P., “Heating and Cooling of Solid Shapes”, unpub. monograph, Mass. Inst. Tech. library. Gurney and Lurie, IND.ENQ.CHEM.,15,1173 (1923). McAdams, “Heat Transmission”, Chap. 11, New York, McGrrtwHill Book Co., 1933. McLean, J. D., Proc. Am. wood-Preservers’ Assoc., 1930, 197. Newman, A. B., Trans. Am. I n s t . Chem. Engrs., 24,44 (1930). Bheinman, A. B., et al., Petroleum Engr., Dec., 1938. Shepherd, C. B., Hadlock, C.,and Brewer, R. C., IND. ENG. C H S M . , 30,388 (1938).
2.92 1.03
Obviously the size of the sand grains affected the value of k very little when the pores contained air, as shown by the values for the different size sand grains. The value of k for the marbles is approximate, since at no point do the true curves fit the pure conduction curves. Evidently the convection of the air has produced the peculiar shape.
Three-Dimensional Flow from a Point Source WATER-FILLED SANDBODY. The history of the temperature rise for the first three thermocouples, 1, 2, and 4 inches from the heat source, is shown in Figure 9 for the four direotions of heat flow. The upward vertical flow was more pronounced than it was in the other directions, the rate becoming progressively less toward the downward position. For example, after 240 minutes the temperature 1 inch from the sphere was 141” F. in an upward direction while it was only 128’ F. a t a distance of 1 inch downward. The other thermocouples, however, did not show such pronounced differences for the several directions from the heat source. The original data in Figure 9 are presented in a different manner in Figure 10 in order to give a better idea of the temperature gradient in various directions a t certain time intervals. It is evident that there are slight convection currents which are responsible for the more rapid rise of temperature in the upward direction. One of the water-sand runs was continued for several hours after the temperature rise had reached the thermocouples 8 inches from the heat source, a t which time the flow of heat reached a substantially steady state. SAND-AIR BODY. The original experimental data for the three-dimensional flow of heat through an air-filled sand body are given in Figure 11. Temperature records in each direction proved to be practically identical, which indicated that no appreciable upward convection currents were set up within the porous media as was the case with the water-filled sand body. A cross section of the data from Figure 11 is shown in Figure 12 a t 125 minutes from the start of the run and indicate the uniform flow of heat in each direction from the heat source,
Nomenclature
e
= time variable, hours
p
= density of material, Ib./cu. ft.
T
=
temperature variable,
O
T
An error in presenting data occurred in the article in the June, The table gives the correct values for the saturated liquid and vapor density of propane, and the chart is a correct plot which should supersede Figure 4 in the article as published. 1940, issue, pages 837-8.
TABLE IV. SATURATED LIQUIDAND VAPOR DENSITY OF PROPANE Density, G./Co. Density. G./Cc. Temp., e C.
30 35 40 45 50 65 60 66
Gas 0.0236 0.0270 0.0305 0.0343 0.0385 0.0440 0.0496 0.0562
Liquid
0.4858 0.4785 0.4715 0.4630 0.4543 0.4443 0.4340 0.4220
Temp., O C. 70 75 80 85 90 95 96.85
Gas
Liquid
0.0640 0.4080 0.0730 0.3923 0.0832 0.3760 0,0980 0.3562 0.1180 0.3320 0.1580 0.2930 0.2240
”
c v)
= =
X
P- V-T Relations for Propane-Correction
>.
F.
O F . )
3
TEMPERATURE, DEGREES C
Q = integral heat entering cylinder, B. t. u. a = Ic/c*p E. = vth root of the equation J&) = 0 A, = W R v = number of root of equation J&) = 0 h = water film coefficient, B. t. u,/(” F. X t = average water temperature, F.
PRISIONTED before the meeting of the American Institute of Chemical Engineers, New Orleans, La.
t
initial temperature, O F. radius variable, ft. R = radius of cylinder, ft. cp = specific heat of material, B. t. u./ (lb.)(O F.) k = conductivity (B. t. u. X ft. of thickness)/(hr. X sq. ft.
T
263
FIGURE 4
hr. X sq. ft.)
This error was called to our attention by W. V. Stearns of the Development Division, Sun Oil Company. GEORGE GRANGER BROWN
