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At least 109 records · Page 6

Heat Transfer in High-Temperature Fibrous Insulation

The combined radiation/conduction heat transfer in high-porosity, high-temperature fibrous insulations was investigated experimentally and numerically. The effective thermal conductivity of fibrous insulation samples was measured over the temperature range of 300-1300 K and environmental pressure range of 1.33 x 10(exp -5)-101.32 kPa. The fibrous insulation samples tested had nominal densities of 24, 48, and 72 kilograms per cubic meter and thicknesses of 13.3, 26.6 and 39.9 millimeters. Seven samples were tested such that the applied heat flux vector was aligned with local gravity vector to eliminate natural convection as a mode of heat transfer. Two samples were tested with reverse orientation to investigate natural convection effects. It was determined that for the fibrous insulation densities and thicknesses investigated no heat transfer takes place through natural convection. A finite volume numerical model was developed to solve the governing combined radiation and conduction heat transfer equations. Various methods of modeling the gas/solid conduction interaction in fibrous insulations were investigated. The radiation heat transfer was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. A genetic-algorithm based parameter estimation technique was utilized with this model to determine the relevant radiative properties of the fibrous insulation over the temperature range of 300-1300 K. The parameter estimation was performed by least square minimization of the difference between measured and predicted values of effective thermal conductivity at a density of 24 kilograms per cubic meters and at nominal pressures of 1.33 x 10(exp -4) and 99.98 kPa. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements at other densities and pressures. The numerical model was also validated by comparison with a transient thermal test simulating reentry aerodynamic heating conditions.

Daryabeigi, Kamran↗

Comparison of Classical and Charge Storage Methods for Determining Conductivity of Thin Film Insulators

Conductivity of insulating materials is a key parameter to determine how accumulated charge will distribute across the spacecraft and how rapidly charge imbalance will dissipate. Classical ASTM and IEC methods to measure thin film insulator conductivity apply a constant voltage to two electrodes around the sample and measure the resulting current for tens of minutes. However, conductivity is more appropriately measured for spacecraft charging applications as the "decay" of charge deposited on the surface of an insulator. Charge decay methods expose one side of the insulator in vacuum to sequences of charged particles, light, and plasma, with a metal electrode attached to the other side of the insulator. Data are obtained by capacitive coupling to measure both the resulting voltage on the open surface and emission of electrons from the exposed surface, as well monitoring currents to the electrode. Instrumentation for both classical and charge storage decay methods has been developed and tested at Jet Propulsion Laboratory (JPL) and at Utah State University (USU). Details of the apparatus, test methods and data analysis are given here. The JPL charge storage decay chamber is a first-generation instrument, designed to make detailed measurements on only three to five samples at a time. Because samples must typically be tested for over a month, a second-generation high sample throughput charge storage decay chamber was developed at USU with the capability of testing up to 32 samples simultaneously. Details are provided about the instrumentation to measure surface charge and current; for charge deposition apparatus and control; the sample holders to properly isolate the mounted samples; the sample carousel to rotate samples into place; the control of the sample environment including sample vacuum, ambient gas, and sample temperature; and the computer control and data acquisition systems. Measurements are compared here for a number of thin film insulators using both methods at both facilities. We have found that conductivity determined from charge storage decay methods is 102 to 104 larger than values obtained from classical methods. Another Spacecraft Charging Conference presentation describes more extensive measurements made with these apparatus. This work is supported through funding from the NASA Space Environments and Effects Program and the USU Space Dynamics Laboratory Enabling Technologies Program.

Swaminathan, Prasanna↗

Non-Destructive Evaluation of Wire Insulation and Coatings

The present invention uses the generation and detection of acoustic guided waves to evaluate the condition of the insulation on electrical wiring. Low order axisymmetric and flexural acoustic modes are generated in the insulated wire and travel partially in the center conductor and partially in the outer insulation. The stiffness of the insulation and the insulation's condition affect the overall wave speed and amplitude of the guided wave. Analysis of the received signal provides information about the age or useful life of the wire insulation. In accordance with the present invention, signal transmission occurs at one location on the electrical wire to be evaluated, and detection occurs at one or more locations along the electrical wire. Additional receivers can be used to improve measurement accuracy. Either the transmission transducer or one or more receiver transducers may be angled at other than 90 degrees to the wire. Generation of the guided waves can be accomplished by imparting a pressure pulse on the wire. Alternative embodiments include generation via a laser, such as a Q-switched laser or a laser diode.

Eric I Madaras↗

Application of Ultrasonic Guided Waves for Evaluating Aging Wire Insulation

Aging wiring has become a critical issue to the aerospace and aircraft industries due to Shuttle and aircraft incidents. The problem is that over time the insulation on wire becomes brittle and cracks. This exposes the underlying conductive wire to the potential for short circuits and fire. Popular methods of monitoring aging wire problems focuses on applying electrical sensing techniques that are sensitive to the conductor's condition, but not very sensitive to the wire insulation's condition. Measurement of wire insulation stiffness and ultrasonic properties by ultrasonic guided waves is being examined. Experimental measurements showed that the lowest order extensional mode could be sensitive to stiffness changes in the wire insulation. To test this theory conventional wire samples were heat damaged in an oven, in a range of heating conditions. The samples were 12, 16, and 20 gauge and the heat damage introduced material changes in the wire insulation that made the originally flexible insulation brittle and darker in color. Results showed that extensional mode phase velocity increased for the samples that were exposed to heat for longer duration.

Anastasi, Robert F.↗

Heat Transfer In High-Temperature Multilayer Insulation

The combined radiation/conduction heat transfer in high-temperature multilayer insulations for typical reentry of reusable launch vehicles from low Earth orbit was investigated experimentally and numerically. The high-temperature multilayer insulation investigated consisted of gold-coated reflective foils separated by alumina fibrous insulation spacers. The steady-state heat transfer through four multilayer insulation configurations was investigated experimentally over the temperature range of 300-1300 K and environmental pressure range of 1.33 10(exp -5)-101.32 kPa. It was shown that including the reflective foils reduced the effective thermal conductivity compared to fibrous insulation sample at 1.5 times the density of the multilayer sample. A finite volume numerical model was developed to solve the governing combined radiation/conduction heat transfer equations. The radiation heat transfer in the fibrous insulation spacers was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. The numerical model was validated by comparison with steady-state experimental data. The root mean square deviation between the predicted and measured effective thermal conductivity of the samples was 9.5%.

Daryabeigi, Kamran↗

Microsphere insulation systems

A new insulation system is provided that contains microspheres. This insulation system can be used to provide insulated panels and clamshells, and to insulate annular spaces around objects used to transfer, store, or transport cryogens and other temperature-sensitive materials. This insulation system provides better performance with reduced maintenance than current insulation systems.

Allen, Mark S.↗

Thermal insulating conformal blanket

The conformal thermal insulating blanket may have generally rigid batting material covered by an outer insulating layer formed of a high temperature resistant woven ceramic material and an inner insulating layer formed of a woven ceramic fiber material. The batting and insulating layers may be fastened together by sewing or stitching using an outer mold layer thread fabricated of a high temperature resistant material and an inner mold layer thread of a ceramic fiber material. The batting may be formed to a composite structure that may have a firmness factor sufficient to inhibit a pillowing effect after the stitching to not more than 0.03 inch. The outer insulating layer and an upper portion of the batting adjacent the outer insulating layer may be impregnated with a ceramic coating material.

Barney, Andrea↗

Thermal Insulation Strips Conserve Energy

Launching the space shuttle involves an interesting paradox: While the temperatures inside the shuttle s main engines climb higher than 6,000 F hot enough to boil iron for fuel, the engines use liquid hydrogen, the second coldest liquid on Earth after liquid helium. Maintained below 20 K (-423 F), the liquid hydrogen is contained in the shuttle s rust-colored external tank. The external tank also contains liquid oxygen (kept below a somewhat less chilly 90 K or -297 F) that combines with the hydrogen to create an explosive mixture that along with the shuttle s two, powdered aluminum-fueled solid rocket boosters allows the shuttle to escape Earth s gravity. The cryogenic temperatures of the main engines liquid fuel can cause ice, frost, or liquefied air to build up on the external tank and other parts of the numerous launch fueling systems, posing a possible debris risk when the ice breaks off during launch and causing difficulties in the transfer and control of these cryogenic liquid propellants. Keeping the fuel at the necessary ultra-cold temperatures while minimizing ice buildup and other safety hazards, as well as reducing the operational maintenance costs, has required NASA to explore innovative ways for providing superior thermal insulation systems. To address the challenge, the Agency turned to an insulating technology so effective that, even though it is mostly air, a thin sheet can prevent a blowtorch from igniting a match. Aerogels were invented in 1931 and demonstrate properties that make them the most extraordinary insulating materials known; a 1-inch-thick piece of aerogel provides the same insulation as layering 15 panes of glass with air pockets in between. Derived from silica, aluminum oxide, or carbon gels using a supercritical drying process - resulting in a composition of almost 99-percent air - aerogels are the world s lightest solid (among 15 other titles they hold in the Guinness World Records), can float indefinitely on water if treated to be hydrophobic, and can withstand extremely hot temperatures (from 1,100 F to 3,000 F depending on the type of aerogel) down to cryogenic levels, making this "frozen smoke" ideal for use in space. Because of its low weight and ability to withstand temperature extremes, an aerogel was even used as the space-based catcher s mitt to trap comet particles and space dust for NASA s Stardust mission, launched in 1999. All of this remarkable technology s characteristics were ideal for NASA s purposes except one: The aerogels were extremely brittle. Through a long-term partnership between Kennedy Space Center and Aspen Aerogels Inc., of Northborough, Massachusetts, researchers developed a flexible, durable form of aerogel that NASA has since used as cryogenic insulation for space shuttle launch systems. Through Aspen Aerogels, the technology has made oil pipeline insulation, extreme weather clothing, and infrared shielding for combat helicopters.

Source record↗

Insulation-Testing Cryostat With Lifting Mechanism

The figure depicts selected aspects of an apparatus for testing thermal-insulation materials for cryogenic systems at temperatures and under vacuum or atmospheric conditions representative of those encountered in use. This apparatus, called "Cryostat-100," is based on the established cryogen-boil-off calorimeter method, according to which the amount of heat that passes through an insulation specimen to a cryogenic fluid in a container, and thus the effective thermal conductance of the specimen, is taken to be proportional to the amount of the cryogenic fluid that boils off from the container. The design of Cryostat-100 is based partly on, and incorporates improvements over, the design of a similar prior apparatus called "Cryostat-1" described in "Improved Methods of Testing Cryogenic Insulation Materials" (KSC-12107 & KSC- 12108), NASA Tech Briefs, Vol. 24, No. 12 (December 2000), page 46. The design of Cryostat-100 also incorporates the best features of two other similar prior apparatuses called "Cryostat-2" (also described in the cited prior article) and "Cryostat- 4." Notable among the improvements in Cryostat-100 is the addition of a lifting mechanism that enables safe, rapid, reliable insertion and removal of insulation specimens and facilitates maintenance operations that involve lifting. As in Cryostat-1, the cold mass is a vertical stainless-steel cylindrical vessel subdivided into a larger measurement vessel with smaller thermal-guard vessels at both ends. During operation, all three vessels are kept filled with liquid nitrogen near saturation at ambient pressure (temperature .77.4 K). The cold mass of Cryostat-100 has a length of 1 m and diameter of 168 mm. Each specimen has a corresponding nominal length and inner diameter and a nominal thickness of 25.4 mm. Specimens that are shorter and have thicknesses between 0 and 50 mm are also acceptable. Bulk-fill, foam, clam-shell, multilayer insulation, and layered materials can be tested over a very wide range of thermal transmission: apparent thermal conductivity from 0.01 to 60 mW/m-K and heat flux from 0.1 to 500 W/sq m. A test in Cryostat-100 can be conducted at any desired gas pressure between ambient atmospheric pressure at one extreme and a vacuum with residual pressure <10(exp -5) torr (<1.33 10(exp -3) Pa) at the other extreme. The residual gas (and purge gas) is typically nitrogen, but can be any suitable purge gas (e.g., helium, argon, or carbon dioxide). Usually, the temperature on the warm boundary of the insulation specimen is maintained near the ambient value (approximately 293 K), while the boiling of liquid nitrogen at atmospheric pressure in the cold mass maintains the temperature on the cold boundary of the specimen at approximately 77 K.

Fesmire, James↗

Thermal Performance of Cryogenic Multilayer Insulation at Various Layer Spacings

Multilayer insulation (MLI) has been shown to be the best performing cryogenic insulation system at high vacuum (less that 10 (exp 3) torr), and is widely used on spaceflight vehicles. Over the past 50 years, many investigations into MLI have yielded a general understanding of the many variables that are associated with MLI. MLI has been shown to be a function of variables such as warm boundary temperature, the number of reflector layers, and the spacer material in between reflectors, the interstitial gas pressure and the interstitial gas. Since the conduction between reflectors increases with the thickness of the spacer material, yet the radiation heat transfer is inversely proportional to the number of layers, it stands to reason that the thermal performance of MLI is a function of the number of layers per thickness, or layer density. Empirical equations that were derived based on some of the early tests showed that the conduction term was proportional to the layer density to a power. This power depended on the material combination and was determined by empirical test data. Many authors have graphically shown such optimal layer density, but none have provided any data at such low densities, or any method of determining this density. Keller, Cunnington, and Glassford showed MLI thermal performance as a function of layer density of high layer densities, but they didn't show a minimal layer density or any data below the supposed optimal layer density. However, it was recently discovered that by manipulating the derived empirical equations and taking a derivative with respect to layer density yields a solution for on optimal layer density. Various manufacturers have begun manufacturing MLI at densities below the optimal density. They began this based on the theory that increasing the distance between layers lowered the conductive heat transfer and they had no limitations on volume. By modifying the circumference of these blankets, the layer density can easily be varied. The simplest method of determining the thermal performance of MLI at cryogenic temperature is by boil-off calorimetry. Several blankets were procured and tested at various layer densities at the Cryogenics Test Laboratory at Kennedy Space Center. The densities that the blankets were tested over covered a wide range of layer densities including the analytical minimum. Several of the blankets were tested at the same insulation thickness while changing the layer density (thus a different number of reflector layers). Optimizing the layer density of multilayer insulation systems for heat transfer would remove a layer density from the complex method of designing such insulation systems. Additional testing was performed at various warm boundary temperatures and pressures. The testing and analysis was performed to simplify the analysis of cryogenic thermal insulation systems. This research was funded by the National Aeronautics and Space Administration's Exploration Technology Development Program's Cryogenic Fluid Management Project

Johnson, Wesley Louis↗

Aerogel Insulation Applications for Liquid Hydrogen Launch Vehicle Tanks

Aerogel based insulation systems for ambient pressure environments were developed for liquid hydrogen (LH2) tank applications. Solutions to thermal insulation problems were demonstrated for the Space Shuttle External Tank (ET) through extensive testing at the Cryogenics Test Laboratory. Demonstration testing was performed using a 1/10th scale ET LH2 intertank unit and liquid helium as the coolant to provide the 20 K cold boundary temperature. Cryopumping tests in the range of 20K were performed using both constant mass and constant pressure methods. Long-duration tests (up to 10 hours) showed that the nitrogen mass taken up inside the intertank is reduced by a factor of nearly three for the aerogel insulated case as compared to the un-insulated (bare metal flight configuration) case. Test results including thermal stabilization, heat transfer effectiveness, and cryopumping confirm that the aerogel system eliminates free liquid nitrogen within the intertank. Physisorption (or adsorption) of liquid nitrogen within the fine pore structure of aerogel materials was also investigated. Results of a mass uptake method show that the sorption ratio (liquid nitrogen to aerogel beads) is about 62 percent by volume. A novel liquid nitrogen production method of testing the liquid nitrogen physical adsorption capacity of aerogel beads was also performed to more closely approximate the actual launch vehicle cooldown and thermal stabilization effects within the aerogel material. The extraordinary insulating effectiveness of the aerogel material shows that cryopumping is not an open-cell mass transport issue but is strictly driven by thermal communication between warm and cold surfaces. The new aerogel insulation technology is useful to solve heat transfer problem areas and to augment existing thermal protection systems on launch vehicles. Examples are given and potential benefits for producing launch systems that are more reliable, robust, reusable, and efficient are outlined.

Fesmire, J. E.↗

New Techniques to Evaluate the Incendiary Behavior of Insulators

New techniques for evaluating the incendiary behavior of insulators is presented. The onset of incendive brush discharges in air is evaluated using standard spark probe techniques for the case simulating approaches of an electrically grounded sphere to a charged insulator in the presence of a flammable atmosphere. However, this standard technique is unsuitable for the case of brush discharges that may occur during the charging-separation process for two insulator materials. We present experimental techniques to evaluate this hazard in the presence of a flammable atmosphere which is ideally suited to measure the incendiary nature of micro-discharges upon separation, a measurement never before performed. Other measurement techniques unique to this study include; surface potential measurements of insulators before, during and after contact and separation, as well as methods to verify fieldmeter calibrations using a charge insulator surface opposed to standard high voltage plates. Key words: Kapton polyimide film, incendiary discharges, brush discharges, contact and frictional electrification, ignition hazards, insulators, contact angle, surface potential measurements.

Buhler, Charles↗

The Structural Heat Intercept-Insulation-Vibration Evaluation Rig (SHIVER)

NASA is currently investigating methods to reduce the boil-off rate on large cryogenic upper stages. Two such methods to reduce the total heat load on existing upper stages are vapor cooling of the cryogenic tank support structure and integration of thick multilayer insulation systems to the upper stage of a launch vehicle. Previous efforts have flown a 2-layer MLI blanket and shown an improved thermal performance, and other efforts have ground-tested blankets up to 70 layers thick on tanks with diameters between 2 3 meters. However, thick multilayer insulation installation and testing in both thermal and structural modes has not been completed on a large scale tank. Similarly, multiple vapor cooled shields are common place on science payload helium dewars; however, minimal effort has gone into intercepting heat on large structural surfaces associated with rocket stages. A majority of the vapor cooling effort focuses on metallic cylinders called skirts, which are the most common structural components for launch vehicles. In order to provide test data for comparison with analytical models, a representative test tank is currently being designed to include skirt structural systems with integral vapor cooling. The tank is 4 m in diameter and 6.8 m tall to contain 5000 kg of liquid hydrogen. A multilayer insulation system will be designed to insulate the tank and structure while being installed in a representative manner that can be extended to tanks up to 10 meters in diameter. In order to prove that the insulation system and vapor cooling attachment methods are structurally sound, acoustic testing will also be performed on the system. The test tank with insulation and vapor cooled shield installed will be tested thermally in the B2 test facility at NASAs Plumbrook Station both before and after being vibration tested at Plumbrooks Space Power Facility.

Cryogenic Fluid Management↗

Wrapped Multilayer Insulation

New NASA vehicles, such as Earth Departure Stage (EDS), Orion, landers, and orbiting fuel depots, need improved cryogenic propellant transfer and storage for long-duration missions. Current cryogen feed line multilayer insulation (MLI) performance is 10 times worse per area than tank MLI insulation. During each launch, cryogenic piping loses approximately 150,000 gallons (equivalent to $300,000) in boil-off during transfer, chill down, and ground hold. Quest Product Development Corp., teaming with Ball Aerospace, developed an innovative advanced insulation system, Wrapped MLI (wMLI), to provide improved thermal insulation for cryogenic feed lines. wMLI is high-performance multilayer insulation designed for cryogenic piping. It uses Quest's innovative discrete-spacer technology to control layer spacing/ density and reduce heat leak. The Phase I project successfully designed, built, and tested a wMLI prototype with a measured heat leak 3.6X lower than spiral-wrapped conventional MLI widely used for piping insulation. A wMLI prototype had a heat leak of 7.3 W/sq m, or 27 percent of the heat leak of conventional MLI (26.7 W/sq m). The Phase II project is further developing wMLI technology with custom, molded polymer spacers and advancing the product toward commercialization via a rigorous testing program, including developing advanced vacuuminsulated pipe for ground support equipment.

Dye, Scott A.↗

Wrapped Multilayer Insulation

New NASA vehicles, such as Earth Departure Stage (EDS), Orion, landers, and orbiting fuel depots, need improved cryogenic propellant transfer and storage for long-duration missions. Current cryogen feed line multilayer insulation (MLI) performance is 10 times worse per area than tank MLI insulation. During each launch, cryogenic piping loses approximately 150,000 gallons (equivalent to $300,000) in boil-off during transfer, chill down, and ground hold. Quest Product Development Corp., teaming with Ball Aerospace, developed an innovative advanced insulation system, Wrapped MLI (wMLI), to provide improved thermal insulation for cryogenic feed lines. wMLI is high-performance multilayer insulation designed for cryogenic piping. It uses Quest's innovative discrete-spacer technology to control layer spacing/ density and reduce heat leak. The Phase I project successfully designed, built, and tested a wMLI prototype with a measured heat leak 3.6X lower than spiral-wrapped conventional MLI widely used for piping insulation. A wMLI prototype had a heat leak of 7.3 W/m2, or 27 percent of the heat leak of conventional MLI (26.7 W/m2). The Phase II project is further developing wMLI technology with custom, molded polymer spacers and advancing the product toward commercialization via a rigorous testing program, including developing advanced vacuuminsulated pipe for ground support equipment.

Dye, Scott A.↗

Aerogel-Based Insulation Materials for Cryogenic Applications

Many different aerogel-based materials are now being used in thermal insulation systems for cryogenic applications. These materials include flexible composite blankets, bulk-fill particles, and polymer composites in both evacuated and non-evacuated environments. In ambient environments, aerogels provide superior thermal performance compared to conventional polymeric foam and cellular glass insulations while offering unique advantages in solving problems with weathering, moisture, and mechanical damage. Aerogels are also used as spacer materials in multilayer insulation systems. These layered systems provide combined structural-thermal capability for cryogenic systems in either vacuum-jacketed or externally-applied insulation designs. Test data (effective thermal conductivity) include a wide range of both commercial and experimental aerogel materials. Testing was performed using laboratory cryostats and standard methods including full range vacuum (from ambient pressure to high vacuum) and boundary temperatures 293 K and 78 K. Examples of aerogel-based insulation systems are given for both evacuated and non-evacuated applications.

aerogel layered composites↗

Layered Thermal Insulation Systems for Industrial and Commercial Applications

From the high performance arena of cryogenic equipment, several different layered thermal insulation systems have been developed for industrial and commercial applications. In addition to the proven areas in cold-work applications for piping and tanks, the new Layered Composite Insulation for Extreme Environments (LCX) has potential for broader industrial use as well as for commercial applications. The LCX technology provides a unique combination of thermal, mechanical, and weathering performance capability that is both cost-effective and enabling. Industry applications may include, for example, liquid nitrogen (LN2) systems for food processing, liquefied natural gas (LNG) systems for transportation or power, and chilled water cooling facilities. Example commercial applications may include commercial residential building construction, hot water piping, HVAC systems, refrigerated trucks, cold chain shipping containers, and a various consumer products. The LCX system is highly tailorable to the end-use application and can be pre-fabricated or field assembled as needed. Product forms of LCX include rigid sheets, semi-flexible sheets, cylindrical clam-shells, removable covers, or flexible strips for wrapping. With increasing system control and reliability requirements as well as demands for higher energy efficiencies, thermal insulation in harsh environments is a growing challenge. The LCX technology grew out of solving problems in the insulation of mechanically complex cryogenic systems that must operate in outdoor, humid conditions. Insulation for cold work includes equipment for everything from liquid helium to chilled water. And in the middle are systems for LNG, LN2, liquid oxygen (LO2), liquid hydrogen (LH2) that must operate in the ambient environment. Different LCX systems have been demonstrated for sub-ambient conditions but are capable of moderately high temperature applications as well.

thermal conductivity↗

Aerogel-Based Insulation Materials for Cryogenic Applications

Many different aerogel-based materials are now being used in thermal insulation systems for cryogenic applications. These materials include flexible composite blankets, bulk-fill particles, and polymer composites in both evacuated and non-evacuated environments. In ambient environments, aerogels provide superior thermal performance compared to conventional polymeric foam and cellular glass insulations while offering unique advantages in avoiding problems with weathering, moisture, and mechanical damage. Aerogels are also used as spacer materials in multilayer insulation systems. These layered systems provide combined structural-thermal capability for cryogenic systems in either vacuum-jacketed or externally-applied insulation designs. Test data (effective thermal conductivity) include a wide range of both commercial and experimental aerogel materials. Testing was performed using laboratory cryostats and standard methods including full range vacuum (from ambient pressure to high vacuum) and boundary temperatures 293 K and 78 K. Examples of aerogel-based insulation systems are given for both evacuated and non-evacuated applications.

heat transfer↗