Heat Insulation on
Cvlindrical Surfaces J
CHANNING TURNER Alfol Insulation Company, Inc., New York, N. Y.
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N THE design of insulation for pipes and cylindrical surfaces, it is not only necessary to consider the conductivity of the insulating material for the mean temperature of service, but also the relative effectiveness of the covering due to its individual proportions. This effectiveness decreases with decreased radius of curvature and increased thickness of insulation. On high-temperature equipment of relatively small diameter, the effect of curvature or shape of insulation is often important. Except on piping, it is usually neglected in calculating heat transfer because it is impractical to cover all possible conditions by tables, and the exact heat transfer is somewhat cumbersome to figure. The purpose of this paper is to lay out a table or chart by which the approximately true insulating effect of coverings on piping or other cylindrical vessels can be determined quickly. I t is obvious that a given thickness of insulation, placed around a cylinder, is not so effective in resisting the passage of heat as the same thickness of the same insulation applied on a flat surface. In the case of the flat surface, the insulation offers the same area in resisting the flow of heat all the way from the warmer side to the cooler side. In the case of cylindrical insulation, as the heat flows outward, the area of resisting insulation increases and therefore offers less resistance per unit thickness per unit area of heated surface. It can be shown mathematically that the logarithmic-mean area is the proper average value for area of insulation', and that the heat flow through cylindrical insulation is greater than the heat 1.00
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A graph is presented for the rapid calculation of heat transfer by correlation of the relative effectiveness of insulation with its thickness and radius of curvature, as defined by the ratio of diameter of cylinder to diameter of insulation.
flow through flat insulation in the same ratio as the logarithmic-mean area of the insulation is greater than the surface area of the cylinder. The logarithmic-mean area of insulation on a cylinder is:
area of surface of insulation - area of surface of cylinder area of surface of insulation log area of surface of cylinder Since the areas for a given length are in proportion to the respective diameters, logarithmic-mean area =
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where D
=
Dc =
L
i FIGURE1. CORRECTION FACTOR BY WHICH THERMAL RESISTANCE OF FLAT INSULATION SHOULDBE MULTIPLIED TO FIND THERMAL RESISTANCE OF CYLINDRICAL INSULATION 904
=
Di - DC log * Di A
+ 2L = outside diameter of insulation outside diameter of cylinder thickness of insulation Dc
The correction factor for increased conductance is:
The correction factor for decreased resistance is the reciprocal of the above:
1 MoAdams, W. H.. "Heat Transmission", 1st ed., p. 10, New York, MoGraw-Hill Book Co.. 1933.
JULY, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
Total resistance
905
9.27
INDUSTRIAL AND ENGINEERING CHEMISTRY
906
Corresponding rate of heat loss (1/9.27) is 0.108 per square foot of surface of cylinder per hour per O F . temperature difference. Heat loss (0.108 X 830) is 90 B. t. u. per square foot per hour. To figure effective surface resistance of cylindrical insulation per square foot of heated surface, it is necessary to multiply the coefficient of resistance per square foot of insulation surface for given temperature and air conditions by the ratio of diameter of vessel to diameter of insulation. Since this ratio must always be used in this part of a heat loss computation, it is convenient to relate the graph to this same ratio. The above example calculated on the assumption of flat insulation would be: Resistance of insulation, (1/0.50) X 5 Resistance of surface Total resistnnoe
10.00 0.57 10.57
Corresponding heat loss is (1/10.57) X 830 or 79 B. t. u. per square foot per hour. The true value is 90 B. t. u. or 14 per cent more, which illustrates that for high-temperature vessels it is often worth while to figure heat losses more accurately than the flat surface assumption allows. This chart is also useful in working out
VOL. 32, NO. 7
combinations of pipe insulation for which heat losses are not given in tables. TABLEI. EFFECTIVENESS OF PIPE INSULATION OF VARIOUS PROPORTIONS
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Di 600 500 400 350 300 260 233 220 200 190 180 175 167 150 140 133 125 120 116 108 104 102
101
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Di 0.167 0.200 0,250 0.286 0.333 0,385 0.429 0.455 0.500 0.526 0.556 0.571 0.600 0,667 0.714 0.750 0.800 0.833 0,862 0.926 0.962 0,980 0.990
[Dc 100) -Correction Resistance, formula 2 0.358 0 402 0 462 0 501 0 549 0 597 0 635 0 657 0 693 0 713 0 735 0 746 0 766 0 811 0 841 0 863 0 892 0 912 0 928 0 962 0 981 0 990 0.895
FactorsConductance, formula 1 2.790 2.485 2.164 1.996 1.821 1,675 1.574 1,522 1.443 1.402 1.301 1.341 1,305 1.233 1.189 1.159 1.121 1.097 1.078 1.040 1.020 1.010 1.005
MAKING CASEIN FIBER E. 0. WHITTIER AND S. P. GOULDl Bureau of Dairy Industry, U. S. Department of Agriculture, Washington, D. C. ASEIN fiber has been of In making casein fiber, alkalies are required lems of making fiber from the considerable popular inproteins of the soybean, of the to dissolve the casein; salts of metals such terestsinceitscommercial as calcium, and barium to inpeanut, of silk waste, of fish production was announced in waste, and of slaughterhouse crease strength; fat acids to increase flexiItaly in 1936. Its characteristics waste. have been discussed in many bility; acids to coagulate the fiber; and articles in textile and dairy substances such as sugars and salts to deThe Casein journals, but, with a few excepThe method used in the manuhydrate it. Formaldehyde, or other aldehydes, are used to increase further the facture of the casein affects the tions, details of the manufacturing processes have been pubfiber made from it. As stated strength of the fiber, and oil emulsions to lished only in patents (1-6). by Ferretti exposure of Since patents covering the increase further the softness and flexibility* casein to acidities greater than novel features of our researches The effectiveness of compounds used for those ordinarily employed in these specific purposes is discussed in this commercial casein manufacture have either been issued or are pending, and since our work is has the effect of causing the paper. done in the public interest, we fiber made from it to be much are publishing our results for softer than that made from the information of any who may wish to develop further the commercial casein. This softness is obtained a t the sacrifice manufacture of casein fiber. of some strength. Caseins prepared by the use of sulfuric or In barest outline, the process of converting a protein into a lactic acids give stronger fibers than those prepared by the use fiber consists of dissolving the protein in an alkaline solvent of hydrochloric acid. “Cooked-curd” caseins appear to give and extruding the solution through fine openings into a prestronger fibers than do those made a t lower temperatures. However, solutions of cooked-curd caseins are somewhat more cipitating bath that is strongly acid in reaction. Such a simple procedure produces a fiber, but a number of characteristics viscous than those of other caseins and, consequently, must be necessary for its use in textiles, such as strength, flexibility, diluted to smaller concentrations before extrusion. Thus the softness, and insolubility, are lacking. The supplying of strength advantage of cooked-curd casein is offset by the these characteristics constitutes the problems of casein fiber necessarily greater dilution required to extrude it. Other research. The chemical attack can be made a t four pointsfactors being equal, we have found fibers spun from solutions the protein, the protein solution, the precipitating bath, and of greater concentrations of casein to be stronger than those the solutions for aftertreatment. spun from solutions of less concentration. We have obtained The only protein considered here is casein; it is probable satisfactory fibers from 8 and 12 per cent casein solutions, but that most of the factors discussed apply as well to the proba t a working temperature of 50” C., the most practical percentage appears to be 10. 1 D r Gould died September 12, 1939.
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