Creator:H.M. Strong, F.P. Bundy, and H.P. Bovenkerk Date Created:June 8, 1959 Place Created:Schenectady, New York Keywords:flat panel vacuum thermal insulation Context:article reprinted from Journal of Applied Physics ************************************************** RES. LAB. FfEPRINT 3421 GENERAL (A) ELECTRIC FLAT PANEL VACUUM THERMAL INSULATION BY H. M. STRONG, F. P. BUNDY, and H. P. BOVENKERK SCHENECTADY, NEW YORK Reprinted from Journal of Applied Physics, Vol. 31, No. 1, 39-50, January, 1960 Copyright 1960 by the American Institute of Physics Printed in U. S. A. Flat Panel Vacuum Thermal Insulation H. M. Strong, F. P. Bundy, akd H. P. Bovenkerk General Electric Research Laboratory, Schenectady, New York (Received June 8, 1959) Evacuated mats of glass fiber made up of fibers of proper size and orientation are capable of supporting a compressive mechanical loading of at least one atmosphere and yet maintain a thermal conductivity of less than 10 microcalories/cm°C sec. The use of such a glass fiber mat as a filler makes possible an evacuated flat-panel thermal insulation which is comparable to a Dewar flask in insulation efficiency. The rate of heat transfer through a Dewar flask wall was reduced several-fold at liquid nitrogen temperatures and below by adding a 2-cm-thick layer of orientated and evacuated glass fiber mat to the outer surface. This investigation showed that in evacuated glass fiber mats, supporting external atmospheric loading, the fiber to fiber contact area is less than 10-4 the mat area, making the contact pressure about 15 000 kg/cm2. The effective length of the thermal conduction paths along the fibers is about four times the mat thickness. The mean pore size for gas molecule motion in the mat was found to be about 54X10-4 cm and 2X10-4 cm for mean fiber sizes of 14X10^* cm and 0.2 X10-4 cm, respectively. The radiation mean free paths for the same fiber sizes were found to be 150X10-4 cm and 52X10"4 cm, respectively. The thermal diffusivity is about 10 4 cm2/sec, which is much smaller than any other insulating material. I. INTRODUCTION ONE of the most effective types of thermal insulation known is a wall space evacuated to less than one micron pressure and having surfaces highly reflective to thermal radiation. In the form of the familiar Dewar flask, this type of insulation has been in use for over sixty years. However Dewar-type insulation is limited to cylindrical and spherical shaped vessels because of the necessity of supporting the atmospheric load by the inner and outer walls without any mechanical support in the evacuated space between. No insulation has appeared in flat panel form that approaches the vacuum type wall in insulation efficiency. Almost all of the other familiar insulations contain air, and regardless of their makeup have the conductivity of still air as their lower limit of conductivity. Few of them reach this lower limit and only the finest particle insulations such as the silica aero-gel of Kistler1 have conductivities equivalent to, or slightly lower than that of still air. The lowest thermal conductivities can be reached only by removal of air. A variation of the highly evacuated empty wall space is the moderately evacuated wall space containing lightly packed powders proposed by Smolukowski,2 1 S. S. Kistler, Nature 127, 741 (1931); J. Phys. Chem. 39, 79-85 (1935). 2 M. Von Smolukowski, Krakauer Anz., 129(A) (1910); Max Jakob, Ileal Transfer (John Wiley & Sons, Inc., New York, 1949), p. 90. Langmuir,3" and Stanley4 for cylindrical and spherical containers. While such a heat barrier is roughly equivalent to a Dewar-type wall, attempts to use powders to support flat evacuated walls3 6,6 were not as successful because of the high thermal conductivity of the same powders when compacted by the atmospheric pressure load. The possibility of discovering a supporting structure for flat evacuated walls that has great stress bearing capacity and exceedingly low thermal conductivity is very intriguing. The present report describes the authors' study of this and associated problems. References of further interest in connection with this subject are text books on the kinetic theory of gases,7'8 the early work of Smolukowski9 and Knudsen10 on the application of the kinetic theory of gases to explain 3 Unpublished work of (a) I. Langmuir and (b) A. W. Hull, made available to authors. 4 W. Stanley, powder filled vacuum wall flask, U. S. Patent 1,071,817 (1913). 6C. G. Munters, U. S. Patent 2,164,143 (1939). 6 Blat, Bresler, and Ryabinin, J. Tech. Phys. (USSR) 15, 916-23 (1945). Yu N. Ryabinin (thesis) from Kislorod (1944), No. 3, pp. 39-43. 1 Saul Dushman, Vacuum Technique (John Wiley & Sons, Inc., New York, 1949). 8 E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill Book Company, Inc., New York, 1938). 9 M. Von Smolukowski, Akad. Wiss. Wien. 107, 304 (1898); 108, 5 (1899). 10 M. Knudsen, Ann. Physik 34, 593 (1911). 40 STRONG, BUND Y, AN D BOVENKERK Table I. Comparison of approximate thermal conductivities in the temperature range 0° to 100°C. Coefficient of thermal conduction, k in micro- Substance calories/cm°C sec 1. Structural materials Metals Organic polymers Ceramic and refractory materials Glass 2. Insulations Air filled fibers, foams, etc., in common use Still air 65°C Finest powders 65 °C (silica aero-gel) Dewar flask (66°C inner T) (65 °C outer T) Flat vacuum wall structure (max. value desired) gaseous conduction, Smolukowski's2 early experiments on gaseous conduction at reduced pressure in fine powders, papers by Kistler1 on the properties of his silica aero-gel, tests on evacuated silica aero-gel for liquid air storage by Blat et al.,6 and studies on mechanisms of conduction in air-filled, evacuated and heavy-gas-filled insulations by Verschoor and Greebler.11 II. PHYSICAL REQUIREMENTS To be comparable with a Dewar flask in insulation quality, the mechanical supporting structure between the walls of a flat vacuum panel should have an effective thermal conductivity not exceeding 10 microcalories/ cm°C sec.* Thus, the supporting structure must have very small contact areas and devious heat flow paths of high thermal resistance. Small contact areas imply high contact stresses attainable only with hard, strong materials which can maintain their properties under conditions of vacuum bake-out and long service life without creep. It is also desirable that the geometry of the supporting structure provide radiation baffling, and that it divide the space into cells small enough that gaseous thermal conduction would be negligible up ,to gas pressures of a few hundred microns. In choosing a material to support flat walls against an atmospheric pressure load it is helpful to compare the approximate thermal conductivities of a variety of substances with the desired conductivity of the supporting structure. The values are noted in Table I. Most glass, ceramic, and refractory materials are hard stable substances suitable for use in permanently evacu- 11 J. D. Verschoor and P. Greebler, Trans. Am. Soc. Mech. Engrs. 74, 961 (1952). * The unit of thermal conductivity used throughout this report is the microcalorie/cm°C sec. This unit will not be repeated except where necessary for clarity. Thermal conductivity values given apply for an average temperature of the insulation within the range 0° to 100°C, usually about 70°C. Where there are exceptions or where the exact temperature is important to the discussion, the temperature will be given, otherwise not. ated containers and are the most favored choice for use in devising a vacuum wall support structure. It is clear from their thermal conductivity values that a suitably low thermal conductivity in these materials must be achieved through proper geometric distribution of the support material. It was found that a pad made of glass fibers oriented randomly in planes parallel to the pad (perpendicular to the temperature gradient) fulfilled all requirements. The thermal conduction characteristic of a number of granular and fibrous substances taken from the authors' test results are shown in Table II. The tests were all made in a one to 10 micron vacuum with a tempearture range across the sample of about 20° to 110° or at an average temperature of 65°C. In some tests the sample supported the load of the atmospheric pressure; in others the atmospheric pressure load was not applied to the sample. From the numbers in the table it is readily seen that granular materials are sensitive to applied pressure while fibrous materials are not. A glass column structure was proposed by Hull:!b of this laboratory which has a solid thermal conductivity very close to 10. Each column consisted of two 3^-in.-diam glass beads in series, one on top of the other in the direction of heat flow. The columns were positioned three or four inches apart by a plate structure lying perpendicular to the direction of heat flow. In an open structure of this sort the wall surfaces are made reflecting and the air pressure kept below about 1 /x of mercury. To the authors' knowledge, this is the only structure for Table II. Thermal conductivity of granular and fibrous materials in a 1 to 10 ju vacuum; average temperature approximately 65°C. Thermal conductivity, k. microcalories. /cm°C sec 1 atmos Loosely Compressive Material packed load 80 mesh foundry sand 8.7 86 Glass beads A-in. diam 27 98 Glass beads, 0.002-in. diam 50 Crushed Pyrex glass 20 mesh 7.1 23 Carborundum 150 mesh 220 Alumina 100-250 mesh 196 Diatomaceous earth and 51 carbon black 3:1 mixture Silica aero-gel 22 Duck feathers (eider down) 8.3 Asbestos lint 30 Cotton fibers 19 Stainless steel wool (fine) 26 Glass needles 125 n diam 39 Glass fibers 14 m diam 9.6a 6 to 8 (good orientation) Glass fibers 4 /x diam 4 to 5 3.9 to 5.2 (good orientation) Glass fibers 2 ^ diam 5.4 (good orientation) Glass fibers 0.2 n diam 4.6 (good orientation) a Sample thickness under no load increased without much change in heat transfer, making the loosely packed k larger than the k under a compressive load. (See Sec. VI for description of test methods and definition of k.) 100 000 400 10 000 3 000 80 69 60 7 microcalories/ cm2 sec 10 FLAT PANEL VACUUM THERMAL INSULATION 41 flat wall evacuated insulations other than a glass fiber mat approaching 10 in conductivity. To account for the exceptionally low thermal conductivity of evacuated glass fiber structures, the mechanism of heat flow by gaseous, solid, and radiative conduction will be examined briefly in the sections that follow. III. SOLID CONDUCTION IN GLASS FIBER SUPPORTS An exact analysis of heat conduction along the solid paths in a random arrangement of fibers would be a very difficult task. It would be complicated by the existence of radiant heat transfer through the fibers, and at any point there may be an exchange between solid and radiative heat transfer. However, one can visualize an idealized structure consisting of a symmetrical array of uniform fibers like that shown in Fig. 1(a) in which the general heat flow is perpendicular to the fibers. An analysis of a structure of this sort helps to show how glass fiber mat can have so high a thermal resistance, and indicates approximate values of the areas of contact, contact pressures, and path lengths for heat flow. At the points of intersection of the fibers there will be a tiny circular contact area whose radius b, is given by the Hertz formula12 d>=1.13 (£/?/£)*, in which S is the load per contact, R is radius of fiber, E is modulus of elasticity. The heat must pass through these tiny contact areas and along the fiber to the next contact as shown in Fig. 1(b). The heat flow is assumed to be evenly divided to the right and left. Focusing attention on the flow to the right only, the symmetry of the flow lines is closely equivalent to the geometry for flow shown in Fig. 1 (c) in which the ends of the fibers are pictured as being hemispherical and in contact end to end. The actual contact area between the two fibers is shared equally by the flow to the right and the flow to the left. Hence, the thermal resistance of one contact unit [Figs. 1(b) and l(c)3 is made up of the hemispherical end, with contact area one-half the actual contact area, and a length of fiber, /, equal to one-half the distance between successive fiber junctions. Since the heat leaving each contact point has the opportunity of flowing in two directions, the thermal resistance of each layer is that of two parallel paths, each path consisting of two contact units in series. In Fig. 1(b), the area of contact due to the pressure flattening is given by the expression \ivb1= (tt/2)1.28(57?/£)*. (1) This corresponds to a compression of the radius of the equivalent hemispherical end [see Fig. 1(c)] of an 12 See S. Timoshenko, Strength of Materials (D. Van Nostrand Company, Inc., New York, 1945), Part II, Chap. VII. ONE CONTACT UNIT ONE LAYER" ) [:r:][":a i "O KJ ( b) ONE CONTACT UNIT I ATs R-AR- TEMPERATURE DISTANCE (C) Fig. 1. Ideal glass fiber lattice, (a) A symmetrical lattice of glass fibers; (b) detail of a series of two fiber junctions showing the heat flow path; (c) an idealized fiber junction which is approximately equivalent thermally to the junction shown in (b). amount given by AR= (area of contact/2ir/?), = (1.28/4) (S/E) iR~i. (2) The thermal resistance of one contact unit [Fig. 1 (c)] was taken to be the sum of the thermal resistances of the hemispherical end (AT,/q) and the cylindrical portion (ATe/q), where q is the rate of heat flow through the fiber. This was found to be 47? I ATa+ATc AT 1 q 2trkR A R rrkR- -=—=-ln- (3) The first term on the right applies to the hemispherical end and the second term to the cylindrical portion. AT is the temperature drop across one contact unit. The total rate of heat flow, Q, through a one square centimeter area of panel for a temperature difference AT across each contact unit will be 2nq, where n is the number of fiber junctions in one square centimeter and the factor 2 accounts for the two parallel paths of heat flow entering and leaving each fiber junction. From Eq. (3), the value of Q is given by Q—2nq = 4ir R-k R ln(4/?/Ai?)+2/ nAT. (4) 42 STRONG, BUNDY AND BOVENKERK 1 , INITIAL THICKNESS y INCH DENSITY .354 q /c c AVG. FIBER DIA. 0005 INCH I 10 100 1000 10,000 TIME UNDER COMPRESSIVE LOAD-HOURS Fig. 2. Decrease in thickness of a glass fiber mat with time under an atmospheric pressure load. Typical glass fiber mats having fibers with an average diameter of 0.00036 cm and occupying 10% of the space (density about 0.25 g/cm3) when supporting an atmospheric pressure load, had solid conductivities ranging between 4.5 and 5.2. For calculating the effective solid conductivity of such a mat, it must be assumed that all fibers have exactly the same diameter and are laid in a symmetrical lattice array as shown in Fig. 1 (a). From the density of packing and the fiber diameter it can be determined that there are 2.78X 103 layers of fibers in a mat one centimeter thick, and that the fibers in a single layer are spaced four fiber diameters apart so that 1=4R. In each layer the fibers are laid parallel with 360 fibers to each centimeter. The number of fiber junctions between layers is therefore (360)2 or 13X104. Each contact in supporting the atmospheric pressure must carry a burden of 103/13X104 g or 7.5 d.f The value of AR was obtained through the use of Eq. (2). The value of E used was 7X1011 d/cm2. Assuming a temperature difference of 1CC across the 1-cm-thick mat, the temperature difference across one contact unit, AT, will be 1.8X10~4°C. Substitution of all the data in Eq. (4) gives for Q the value 10 microcalories/ sec. Since the conditions chosen for calculating Q were a 1°C temperature difference across a 1-cm cube, this value of Q is also the value for the effective coefficient of solid conduction in microcalories/cm°C sec. The value 10 is to be compared with the values 4.5 to 5.2 obtained experimentally. Tests on mats of fibers averaging 13 X 10~4 cm in diam gave "solid" conductivity values between 6 and 8 as compared to the theoretical value of 24. Fibers of 125X10-4 cm average diameter gave "solid" conductivity values around 18 contrasted to the theoretical value of about 300. The variation between the theoretical and experimental values is in the direction to be expected due to deviation from the perfect lattice assumed. Variation of diameters of the fibers and randomness of orientation in planes causes a smaller f The area of each contact was about 5X10~10 cm2 and the pressure about 15 000 kg/cm2. number of contacts than was assumed in the ideal lattice. The greater lateral stiffness of the larger fibers would be expected to enhance this effect still more. The possibility of fiber breakage and eventual loss of insulating effect over a long period of use has been investigated for 3.6-ix- and 13-/x-diam fibers. Upon first loading the fibers a great many of them can be heard snapping if the ear is placed close to the fibers. The fiber snapping may continue for several hours but with steadily diminishing frequency until it eventually stops. The breakage continues longer for coarse fibers than for fine ones. After the initial adjustment period, the load distribution stabilizes. Evidently the fiber contacts are stressed nearly to their ultimate strengths even in the final stable state. Measurements of the change in fiber mat thickness as a function of time have been taken and are shown in Fig. 2. Fiber breakage always ceases before any noticeable increase in solid conduction occurs. A number of vacuum insulation panels have been in use for nine years, and have been perfectly stable during this period. Many of them have been subjected to severe mechanical jarring without noticeable change in thickness or insulating value. IV. GASEOUS CONDUCTION IN POROUS MEDIA The mechanism of the thermal conductivities of gases was explained by the kinetic theory of gases largely through the efforts of Smolukowski9 and Knudsen10 at the turn of the century. (References 7 and 8 have detailed accounts of this work.) Two different types of gaseous conduction were distinguished, one a pressure independent region of conduction ranging from atmospheric pressure down to fairly low pressures, and the other a pressure dependent region at quite low pressures. The transition from the one type of conduction to the other occurs at pressures where the mean free path for collision between gas molecules is about equal to the mean free path for collisions between gas molecules and the walls of the container, or the particles of the porous structure inside the walled container. The familiar expression giving the coefficient of thermal conductivity of a still gas, k, is ApCVVaLg, (5) where p is the gas density, Cv the specific heat at constant volume, t'a the average molecular velocity, Lg the mean free path of gas molecules and A a numerical constant. Over a wide range of pressures, k is independent of pressure because La varies inversely with the pressure while p varies directly with the pressure. When the pressure is reduced below the point where L„~d, the distance between the walls or particles against which molecules strike, k becomes proportional to the pressure. At these pressures the mean free path, L, of the molecules, taking into account both collisions between gas molecules and between gas molecules and solid barriers, FLAT PANEL VACUUM THERMAL INSULATION 43 GAS PRESSURE MICRONS OF MERCURY » Fig. 3. Thermal conductivity as a function of residual air pressure in insulations of different fiber diameters. Theoretical curves obtained from Eq. (6). becomes L=L0[_d/{d+La)']. At pressures such that La<£d, L~La. Thus, Eq. (5) taking into account the full range of pressure from atmospheric down may be written k=ApCvvalLgd/(d+L0)J (6) In writing Eq. (6), it is assumed that the accommodation coefficient between gas molecules and the particles is unity. If this coefficient is less than unity, the k calculated from Eq. (6) will be too large. Equation (6) is useful for predicting the gaseous conduction in a porous medium as a function of pressure provided the pore dimension, d, is known. Conversely, it is useful for determining the size of pores in a finely-divided material if one knows how its thermal conductivity varies with the gas pressure. Kistler1 made use of this relation to determine that the size of the pores in his silica aero-gel was about 5X10-6 cm. For the glass fiber mats used in this work, it was possible to calculate the pore size d in the direction of heat flow and to predict the gas conduction within the mat for various pressures. With the optimum fiber arrangement as described in the previous section, the distance, d, a gas molecule can travel on the average in the direction of heat flow between collisions with glass fibers is given by d=wR/2s, in which R is the fiber diameter and s the' fraction of space occupied by fibers. Fibers 14X 10~4 cm in average diameter and packed to a space factor, s, of about 14% had a d value of 54X 10~4 cm. Fibers that had an average diameter of 0.2X10"4 cm packed to a volume density of 9% had a d value of 2X10~4 cm. The predicted and experimental values of the thermal conductivity at different pressures are shown in Fig. 3. At pressures of 1 to 10 n of mercury in a glass fiber mat, the gas conduction is negligible and only the re- sidual solid conduction and radiative heat transfer remain. Together these account for 5 to 9 units of heat transfer. This residual heat conduction must be included with the gas conduction computed for a particular pressure to obtain the estimated total conductivity of the glass fiber mat at that pressure. It is evident from the calculated and experimental data that a space with glass fiber mats supporting an atmospheric pressure load need not be reduced in pressure below about 100 n of mercury, depending on fiber size, to obtain negligibly low gas conductivity. This is a distinct advantage because pressures between 10 and 100 /li are rather easy to maintain in a vacuum insulation panel whereas to establish a permanent pressure of 1 n or less would be more troublesome. Equation (6) suggests the possibility of finding a material whose d value is so small that the gas conduction k at one atmosphere pressure might be reduced to yjth its normal value. If this could be done, then there would hardly be need for making a vacuum type insulation in order to achieve greatly increased insulation efficiency. To make d/d-\-Lg=xo, d must be equal to Lj9. At atmospheric pressure, L0 is about 6X 10~6 cm. If 5 is taken to be yj, which experience shows is about as dense as small fibers can be packed, the fiber diameters turn out to be 10-7 cm. The smallest fibers made available to us averaged 200X10"7 cm in diam. Probably the finest pore sizes yet produced in thermal insulation are in Kistler's silica areo-gel in which the pore size is estimated to be 50X10-7 cm. The thermal conductivity of this material is about 60. V. HEAT TRANSFER BY RADIATION THROUGH FIBROUS MEDIA It will be assumed that the insulation is made up of fibers of diameters smaller than the gaps of empty space between fibers. For simplicity it will be assumed that when radiation strikes a fiber a fraction e (absorptivity or emissivity) is absorbed and later re-radiated as thermal radiation characteristic of the temperature of the fiber in which it was absorbed. The projected sidewise area of the fibers in a volume element of thickness dr and unit area is 2sdr/wR. Hence, the probability of radiation being absorbed while traveling across the element in the dr direction is 2stdr/rR, and the probability of its penetrating a distance r is P(r) — exp (— 2s er/irR). (7) Any preferred orientation of the fibers relative to the axis of the volume element will affect the probability of penetration at different angles d to the axis. Thus, in general P(r,e) = exp[-2strf{e)/wR^ (8) where f(6) is a function characteristic of the fiber orientation. Now consider a spherical element of an extensive 44 STRONG, BUNDY, AND BOVENKERK Fig. 4. Radiation through an element of area in an isothermal plane. uniform volume of insulation which is conducting heat from left to right as shown in Fig. 4. Let the element of area dA at the center of the sphere lie in a plane of equal temperature T. It is assumed that there is a uniform temperature gradient G and that the radiation which passes through the element dA originates and is absorbed within the insulation itself. The radiation which passes to the right through dA may be obtained by integrating the contributions of all the elements of volume in the half-space to the left. This comes out to be 4sae r*12 -> dFr,A = dA- I I sin0cos0/(0) 7T R ^ 0 X exp[ - r—f(6) 1 [T+ j Gr cosd | Jdrdd. (9) L Tri? J The radiation which passes from right to left is given by a similar expression except that the temperature term is \_T— | Gr cos01 J4. The net radiation transfer is the difference of the two integrals. Neglecting some of the small higher order terms this is found to be 8ttR(tGTs c^2 sin0 cos20 dFlad=dA- -dd. (10) se Jo f(e) If the fibers are randomly oriented in all three dimensions f(0) = 1, and dFra,d=dA (8/3) (tRctGT3/se). (11) If the fibers are oriented randomly in planes parallel to dA, then /(0) = cos20+(2/x) sin20 (12) and dFr:li=dA • 3.24- (ttRaGTt/st). (13) If dA = 1 and G= 1 the expressions given in Eqs. (11) and (13) are just the thermal conductivities by radiation. Thus, ^rad = H • (ttRctTS/Se), (14) in which H= 2.67 for complete three dimensional random orientation of the fibers and #=3.24 for the case in which the fibers are randomly oriented in planes perpendicular to the temperature gradient. Heat transfer by radiation in this case may also be considered as a diffusion of the radiation photons due to a temperature gradient in a space containing a uniform dispersion of radiation baffles. According to general diffusion theory the net flow in the direction of the gradient per unit time and unit of area normal to the gradient is FtaA=(c\/3)(dPl!ii/dx), (15) where c is the velocity of the photons (velocity of light), X is the mean free path between absorbing collisions of photons with fibers, and prad is the radiation density. From radiation theory, pr!ld = 4 -=- I exp( — Ti—To \/% J0 F)dP=m, (20) 0 40 80 120 160 200 240 ME ON T'C Fig. 9. Thermal conductivity of two types of fiber pads as a function of temperature. "B" fiber although its gross density is less than that of the TWF fiber. IX. THERMAL DIFFUSIVITY EFFECTS The rate at which a wave of temperature change propagates through a medium is determined largely by the thermal diffusivity, a=k/cp, of the medium, where c is the specific heat and p the density. The relatively high heat capacity and unusually low thermal conductivity of the evacuated fiber pad insulations described in this report cause them to have values of thermal diffusivity which are an order of magnitude or more smaller than those of conventional insulations, as shown in Table VI. Preliminary calculations indicated that time intervals of the order of minutes would be required for a temperature shock to penetrate one centimeter of the evacuated insulation. This appeared interesting enough to justify some quantitative tests of this phenomenon. When a semi-infinite piece of homogeneous conducting medium, bounded by a plane face, and initially at a uniform temperature To throughout (see Fig. 10), suddenly has its face temperature changed to Ti and held at that value, a plane wave of temperature change propagates through the medium in a direction perpen- in which /3=x/2(ar)i, x is the distance from the face, a the thermal diffusivity, r the time interval measured from the application of the temperature shock, and T the temperature at a given x and t. A more convenient arrangement of the relationship is Ar/Ar0= 1-/03), (21) where AT0 is the temperature change imposed at the face and AT is the change from the initial temperature at depth x and time r. A convenient way to solve Eq. (21) for a certain ATo is to take a given value of AT and find, by use of tables Table VI. Values of thermal constants for various materials (20°C). k cal cm 1 c p a Material sec-1 °C_1 cal g"i "C"1 g cm 3 cm2 sec-1 Silver 0.974 0.0558 10.5 1.66 Aluminum 0.504 0.214 2.70 0.872 Steel 0.115 0.115 7.90 0.127 Marble 0.008 0.203 2.71 0.0145 Glass 0.0028 0.20 2.6 0.0054 Cork 0.00011 0.40 0.14 0.0020 Refrigerator 0.000086 0.20 0.032 0.013 glass fiber Evacuated glass 0.0000060 0.20 0.25 0.00012 fiber pad to to to 0.0000080 0.40 0.00010 of the /(/3) function, the value of which satisfies the equation. From this /3 and a given x the r is obtained at which the AT occurs. In the experimental tests ATo was about 97°C, x was nearly 1 cm and a for the insulation was approximately 10-J1 cm2 sec-1. The theoretical AT(°C) vs t(sec) curve for this case is shown in Fig. 11. Note that there is practically no change in temperature during the first 360 sec, or 6 min. The experimental results are also shown in Fig. 11. The observed transit time of the thermal shock was closely that predicted by the theory, but the rate of temperature change from that time on was less than indicated by the theory because of the presence of the metal envelope of the insulation panel. The envelope had considerable heat capacity and much greater thermal conductivity than the filler and so decreased the rate of temperature change. This latter effect was verified by running some tests on an electric analog of the thermal system. The results of the analog computer are also shown in Fig. 11. 15 Ingersoll, Zobel, and Ingersoll, Heat Conduction, McGraw-Hill Book Company, Inc., New York, 1948), Chap. 7. FLAT PANEL VACUUM THERMAL INSULATION 49 X. MECHANICAL PROPERTIES OF EVACUATED PANELS The pressure of the atmosphere holding the envelope of an evacuated panel firmly against the filler pad prevents the envelope from buckling easily and thus develops the "skin-strength" of the structure. For this reason evacuated panels having thin metal envelopes have unusual bending and torsional stiffness. Although the envelope supplies most of the strength, the fibrous filler pad also contributes because of the fibers being locked together into a board-like structure by the compression. This is readily demonstrated by placing a pad of fibrous filler material in a flexible rubber envelope, sealing it off, and excuating. Before evacuation the assembly is quite limp and flexible while after evacuation it has about the stiffness and strength of loosely bonded fiber board. Evacuated panels of glass fiber do not have the acoustic absorbing power of similar pads of air-filled insula- Table VII Heat conduction in Dewar flask walls (5-liter Dewars) "Super-Dewar" Standard Standard (2 cm thick Dewar Dewar glass fiber No. 1 No. 2 layer) Liquid nitrogen evaporation rate liter/day cal/sec cal/cm2 sec Liquid hydrogen evaporation rate liter/day cal/sec cal/cm2 sec Liquid He evaporation rate liters/day cal/sec cal/cm2 sec 0.691 0.306 1.91 X10-4 0.672 0.297 1.86X10-" 3.00 0.263 1.64X10- 22.5 0.196 1.23X10" 0.341 0.1515 0.810X10" 0.725 0.0633 0.339X10- 1.75 0.0153 0.082 X10"4 tion. There are two reasons for this: first, there can be no friction damping of the air motion of sound waves relative to the fibers because the fibers are in a vacuum ; and second, the points of contact of the fibers are loaded so heavily by the pressure of the atmosphere that they react elastically rather than dissipatively to vibrations imposed upon the walls of the panel. The acoustic effect is pronounced enough that it is easy to distinguish between identical evacuated and unevacuated panels merely by thumping them. XI. IMPROVED DEWAR TYPE VACUUM WALL FLASK Remarkably low heat transfer values can be obtained using a combination of a Dewar flask type radiation gap and an evacuated glass fiber layer. This structure for a five liter flask is illustrated in Fig. 12 and is called a TEST conditions: AT.= -97'C i = 1 CM 1 ANALOG RESUL NC STEEL ENVELOPE. s / / / />* c« k ■ 040 THT 0.20 CAL 8 ■ I0"*CA GM"'- C"' L CM"1 SEC -I.c-I V'/ / / / / /.-TH E0RETICAL / / / / / / ANALOG WITH ENVE RESULTS STEEL .OPE / X / / ✓ / / / / / / / / / / TES r" < T RESULTS 600 800 1000 1200 1400 r SEC Fig. 11. Temperature vs time on one side of a vacuum panel after applying a thermal shock to the other side. "super-Dewar" flask.16 The structure shown was designed for the storage of liquefied gases. The gain in insulation efficiency over a standard Dewar increased with reduction of the internal temperature. For example, in comparing a five liter "super-Dewar" flask with a standard Dewar of like capacity by measuring the times required to evaporate five liters of a liquefied gas, it was found that liquefied nitrogen lingered two or three times longer in the "super-Dewar" than in the standard Dewar, hydrogen, four times longer, and helium over ten times longer. It is important for the glass fiber layer to be on the high temperature side of the insulation because its function is to keep the temperature of the warmer side of the radiation gap as low as possible. Then the transfer of heat across the radiation gap is substantially reduced since total radiation across the gap is governed by the difference in the fourth powers of the two temperatures. The comparative data for liquefied gas storage on the two types of flasks is given in Table VII. The two flasks used were identical standard Dewars initially. Both of them were tested on liquid nitrogen storage first then standard Dewar number one was modified by surrounding it with a two cm thick layer of evacuated "B" fiber glass to convert it to a super-Dewar. The glass fiber mat had properly oriented fibers as previously described and DEWAR FLASK SUPER-DEWAR FLASK Fig. 12. Standard and super-Dewar structures. 5 H. M. Strong and F. P. Bundy, US Patent 2,776,776. 50 STRONG, BUNDY,AND BOVENKERK its density was about 7 lb per cu ft. The reflecting surfaces of the three Dewars were polished copper. The data in Table VII clearly show the marked improvement in insulating effect due to the glass fiber layer. In the absence of a temperature measurement on the middle wall, it is not possible to explain this remarkably low heat transfer rate in detail. But it is probable that the conductivity of the glass fiber layer near the inside surface was much reduced, possibly by as much as a factor of ten, at the liquefied gas temperatures over that measured at ~70°C. Various modifications of this structure would be likely to show similar effects. For example, multiple radiation gaps or a powder filled outer space might be used. But the glass fiber mat offers structural simplicity because small compact pads of it may be used in direct contact with the inner vessel to support it mechanically without loss of insulation. XII. CONCLUSIONS In evacuated, flat, thermal insulating panels, the conduction of the internal structure required to support the walls against the crushing load of atmospheric pressure proved to be the most critical factor. Grits, powders, grills and various kinds of cellular structures all develop unacceptably high conductivities when under compressive loading of the atmosphere. Pads made of fine glass (or glass-like) fibers oriented randomly in planes perpendicular to the temperature gradient and pressure axis proved to have remarkably low thermal conductivity which was quite insensitive to loading. Glass fiber pads of this type, enclosed in flat metal envelopes gave thermal conductivities in the range of 4 to 10 micro-calories/cm°C sec. Several other properties of a glass fiber supporting structure are of considerable significance. The radiation baffling of a 1-cm-thick layer is equivalent to that of several highly reflecting surfaces. The pore space between fibers is small enough that internal gas pressures up to about 100 n may be tolerated without significant impairment of insulating qualities. The thermal diffusivity of this type insulation is at least an order of magnitude lower than for common insulations due to the remarkably low thermal conductivity but relatively high capacity of the glass fiber mat. Remarkably low heat transfer rates were obtained in Dewar flasks while storing liquefied gases by surrounding the flasks with an evacuated glass fiber blanket. The stability, permanence of vacuum and high insulating efficiency of the glass fiber structure sealed in evacuated metal envelopes17 has been well established over a period of nine years of use. ACKNOWLEDGMENTS The authors are grateful to A. W. Hull, the late I. Langmuir, M. Hebb, and A. J. Nerad for valuable discussions, and to the Owens-Corning Fiberglas Corporation for supplying samples of especially prepared glass fiber mats. 17 H. M. Strong and F. P. Bundy, British Patent 715,174 and Canadian Patent 537,151. SCHENECTADY, N. Y.