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52-463: PDRC may refer to: Passive daytime radiative cooling , a solar radiation management strategy to reverse global warming . People's Democratic Reform Committee , a political pressure group in the 2013–14 Thai political crisis . Puntland Development Research Center , a local non-governmental organization in Puntland, Somalia. Topics referred to by
104-439: A cell imposes upper limits on size, as the volume increases much faster than does the surface area, thus limiting the rate at which substances diffuse from the interior across the cell membrane to interstitial spaces or to other cells. Indeed, representing a cell as an idealized sphere of radius r , the volume and surface area are, respectively, V = (4/3) πr and SA = 4 πr . The resulting surface area to volume ratio
156-439: A solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces ), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as
208-535: A sphere , are assigned surface area using their representation as parametric surfaces . This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration . A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory , which studies various notions of surface area for irregular objects of any dimension. An important example
260-748: A 2022 study reorted that widespread application "is severely restricted because of the complex and expensive processes of preparation". Similarly, a 2020 study reported that "scalable production of artificial photonic radiators with complex structures, outstanding properties, high throughput, and low cost is still challenging". This has advanced research of simpler structures for PDRC materials possibly better suited for mass production. PDRC coatings such as paints may be advantageous given their direct application to surfaces, simplifying preparation and reducing costs, although not all coatings are inexpensive. A 2022 study stated that coatings generally offer "strong operability, convenient processing, and low cost, which have
312-623: A PDRC surface in tropical climates should have a solar reflectance of at least 97% and an infrared emittance of at least 80% to reduce temperatures. The study applied a BaSO 4 - K 2 SO 4 coating with a "solar reflectance and infrared emittance (8–13 μm) of 98.4% and 95% respectively" in the tropical climate of Singapore and achieved a "sustained daytime sub-ambient temperature of 2°C" under direct solar intensity of 1000 W m . Humidity and cloud coverage significantly weaken PDRC effectiveness. A 2022 study noted that "vertical variations of both vapor concentration and temperature in
364-447: A clear day, solar irradiance can reach 1000 W/m with a diffuse component between 50 and 100 W/m . As of 2022 the average PDRC had a cooling power of ~100–150 W/m . Cooling power is proportional to the installation's surface area . The most useful measurements come in a real-world setting. Standardized devices have been proposed. Evaluating atmospheric downward longwave radiation based on "the use of ambient weather conditions such as
416-517: A given smooth surface. It was demonstrated by Hermann Schwarz that already for the cylinder, different choices of approximating flat surfaces can lead to different limiting values of the area; this example is known as the Schwarz lantern . Various approaches to a general definition of surface area were developed in the late nineteenth and the early twentieth century by Henri Lebesgue and Hermann Minkowski . While for piecewise smooth surfaces there
468-440: A goal of thermal emittance of 90%. For example, increasing reflectivity from 0.2 (typical rooftop) to 0.9 is far more impactful than improving an already reflective surface, such as from 0.9 to 0.97. Studies have reported many PDRC benefits: PDRC has been claimed to be more stable, adaptable, and reversible than stratospheric aerosol injection (SAI). Wang et al. claimed that SAI "might cause potentially dangerous threats to
520-519: A high concentration of tiny pores, which scatter light effectively at the boundary between the polymer and the air. This scattering enhances both solar reflectance (more than 96%) and thermal emittance (97% of heat), lowering surface temperatures six degrees below the surroundings at noon in Phoenix. This process is solution-based, aiding scalability. Dye of the desired color is coated on the polymer. Compared to traditional dye in porous polymer, in which
572-652: A high cooling potential. The cooling potential of desert regions is likely to remain relatively unfulfilled due to low population densities, reducing demand for local cooling, despite tremendous cooling potential. Temperate climates have a high radiative cooling potential and greater population density, which may increase interest in PDRCs. These zones tend to be "transitional" zones between dry and humid climates. High population areas in temperate zones may be susceptible to an "overcooling" effect from PDRCs due to temperature shifts from summer to winter, which can be overcome with
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#1732790618538624-436: A low-cost industrial material, to achieve high solar reflectance and high mid-infrared emittance. A significant feature of this material is its ability to absorb atmospheric moisture, aiding evaporative cooling . This tripartite mechanism allows for efficient cooling under varying atmospheric conditions, including high humidity or given limited access to clear skies. Surface area The surface area (symbol A ) of
676-1150: A vapor-permeable, IR-transparent, and solar-reflecting insulation layer," 300% higher ambient cooling power was demonstrated. This could extend the shelf life of food by 40% in humid climates and 200% in dry climates without refrigeration . The system however requires water "re-charges" to maintain cooling power. A dual-mode asymmetric photonic mirror (APM) consisting of silicon-based diffractive gratings could achieve all-season cooling, even under cloudy and humid conditions, as well as heating. The cooling power of APM could perform 80% more when compared to standalone radiative coolers. Under cloudy sky, it could achieve 8 °C more cooling and, for heating, 5.7 °C. The cooling potential of various areas varies primarily based on climate zones , weather patterns, and events. Dry and hot regions generally have higher radiative cooling power (up to 120 W m ), while colder regions or those with high humidity or cloud cover generally have less. Cooling potential changes seasonally due to shifts in humidity and cloud cover. Studies mapping daytime radiative cooling potential have been done for China, India,
728-414: Is a common broadband emitter. Most PDRC materials are broadband, primarily due to their lower cost and higher performance at above-ambient temperatures. Combining PDRCs with other systems may increase their cooling power. When included in a combined thermal insulation , evaporative cooling , and radiative cooling system consisting of "a solar reflector, a water-rich and IR-emitting evaporative layer, and
780-507: Is a unique natural notion of surface area, if a surface is very irregular, or rough, then it may not be possible to assign an area to it at all. A typical example is given by a surface with spikes spread throughout in a dense fashion. Many surfaces of this type occur in the study of fractals . Extensions of the notion of area which partially fulfill its function and may be defined even for very badly irregular surfaces are studied in geometric measure theory . A specific example of such an extension
832-410: Is credited to Archimedes . Surface area is important in chemical kinetics . Increasing the surface area of a substance generally increases the rate of a chemical reaction . For example, iron in a fine powder will combust , while in solid blocks it is stable enough to use in structures. For different applications a minimal or maximal surface area may be desired. The surface area of an organism
884-431: Is defined by the formula Thus the area of S D is obtained by integrating the length of the normal vector r → u × r → v {\displaystyle {\vec {r}}_{u}\times {\vec {r}}_{v}} to the surface over the appropriate region D in the parametric uv plane. The area of the whole surface is then obtained by adding together
936-432: Is different from Wikidata All article disambiguation pages All disambiguation pages Passive daytime radiative cooling Passive daytime radiative cooling ( PDRC ) (also passive radiative cooling , daytime passive radiative cooling , radiative sky cooling , photonic radiative cooling , and terrestrial radiative cooling ) is the use of unpowered, reflective/ thermally-emissive surfaces to lower
988-430: Is growing with an estimated "market size of ~$ 27 billion in 2025." PDRC surfaces are designed to be high in solar reflectance to minimize heat gain and strong in longwave infrared (LWIR) thermal radiation heat transfer matching the atmosphere's infrared window (8–13 μm). This allows the heat to pass through the atmosphere into space . PDRCs leverage the natural process of radiative cooling, in which
1040-635: Is important in several considerations, such as regulation of body temperature and digestion . Animals use their teeth to grind food down into smaller particles, increasing the surface area available for digestion. The epithelial tissue lining the digestive tract contains microvilli , greatly increasing the area available for absorption. Elephants have large ears , allowing them to regulate their own body temperature. In other instances, animals will need to minimize surface area; for example, people will fold their arms over their chest when cold to minimize heat loss. The surface area to volume ratio (SA:V) of
1092-468: Is the Minkowski content of a surface. While the areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a great deal of care. This should provide a function which assigns a positive real number to a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the surface area is its additivity :
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#17327906185381144-823: Is the Minkowski content of the surface. r = Internal radius, h = height s = slant height of the cone, r = radius of the circular base, h = height of the cone r → u {\displaystyle {\vec {r}}_{u}} = partial derivative of r → {\displaystyle {\vec {r}}} with respect to u {\displaystyle u} , r → v {\displaystyle {\vec {r}}_{v}} = partial derivative of r → {\displaystyle {\vec {r}}} with respect to v {\displaystyle v} , D {\displaystyle D} = shadow region The below given formulas can be used to show that
1196-561: Is warmer than the ambient air, or when its sub-ambient surface temperature is within the range of several degrees". Each type can be advantageous for certain applications. Broadband emitters may be better for horizontal applications, such as roofs, whereas selective emitters may be more useful on vertical surfaces such as building facades , where dropwise condensation is inconsequential and their stronger cooling power can be achieved. Broadband emitters can be made angle-dependent to potentially enhance performance. Polydimethylsiloxane (PDMS)
1248-528: The solar spectrum and atmospheric LWIR window (8 to 14 μm), whereas selective emitters only emit longwave infrared radiation. In theory, selective thermal emitters can achieve higher cooling power. However, selective emitters face challenges in real-world applications that can weaken their performance, such as from dropwise condensation (common even in semi-arid climates) that can accumulate on even hydrophobic surfaces and reduce emission. Broadband emitters outperform selective materials when "the material
1300-668: The space mirror proposals of "deploying giant reflective surfaces in space", Munday claimed that "the increased reflectivity likely falls short of what is needed and comes at a high financial cost." PDRC differs from the reflective surfaces approach by "increasing the radiative heat emission from the Earth rather than merely decreasing its solar absorption". The basic measure of PDRCs is their solar reflectivity (in 0.4–2.5 μm) and heat emissivity (in 8–13 μm), to maximize "net emission of longwave thermal radiation " and minimize "absorption of downward shortwave radiation ". PDRCs use
1352-488: The 2010s, attributable to a breakthrough in the use of photonic metamaterials to increase daytime cooling in 2014, along with growing concerns over energy use and global warming. PDRC can be contrasted with traditional compression-based cooling systems (e.g., air conditioners) that consume substantial amounts of energy, have a net heating effect (heating the outdoors more than cooling the indoors), require ready access to electric power and often employ coolants that deplete
1404-1026: The Earth (...) If only 1%–2% of the Earth’s surface were instead made to radiate at this rate rather than its current average value, the total heat fluxes into and away from the entire Earth would be balanced and warming would cease. The estimated total surface area coverage is 5×10 m or about half the size of the Sahara Desert . Desert climates have the highest radiative cooling potential due to low year-round humidity and cloud cover, while tropical climates have less potential due to higher humidity and cloud cover. Costs for global implementation have been estimated at $ 1.25 to $ 2.5 trillion or about 3% of global GDP, with expected economies of scale . Low-cost scalable materials have been developed for widescale implementation, although some challenges toward commercialization remain. Some studies recommended efforts to maximize solar reflectance or albedo of surfaces, with
1456-689: The Earth cools by releasing heat to space . PDRC operates during daytime. On a clear day, solar irradiance can reach 1000 W/m with a diffuse component between 50-100 W/m . The average PDRC has an estimated cooling power of ~100-150 W/m , proportional to the exposed surface area . PDRC applications are deployed as sky-facing surfaces. Low-cost scalable PDRC materials with potential for mass production include coatings , thin films , metafabrics, aerogels , and biodegradable surfaces. While typically white, other colors can also work, although generally offering less cooling potential. Research, development, and interest in PDRCs has grown rapidly since
1508-444: The Earth's surface area to PDRC would stabilize surface temperatures. Regional variations provide different cooling potentials with desert and temperate climates benefiting more than tropical climates , attributed to the effects of humidity and cloud cover . PDRCs can be included in adaptive systems, switching from cooling to heating to mitigate any potential "overcooling" effects. PDRC applications for indoor space cooling
1560-492: The Earth’s basic climate operations" that may not be reversible, and thus preferred PDRC. Munday noted that although "unexpected effects will likely occur" with the global implementation of PDRC, that "these structures can be removed immediately if needed, unlike methods that involve dispersing particulate matter into the atmosphere, which can last for decades." When compared to the reflective surfaces approach of increasing surface albedo, such as through painting roofs white, or
1612-484: The United States, and across Europe. Dry regions such as western Asia, north Africa, Australia and the southwestern United States are ideal for PDRC due to the relative lack of humidity and cloud cover across the seasons. The cooling potential for desert regions has been estimated at "in the higher range of 80–110 W m ", and 120 W m . The Sahara Desert and western Asia is the largest area on earth with such
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1664-423: The area of the whole is the sum of the areas of the parts . More rigorously, if a surface S is a union of finitely many pieces S 1 , …, S r which do not overlap except at their boundaries, then Surface areas of flat polygonal shapes must agree with their geometrically defined area . Since surface area is a geometric notion, areas of congruent surfaces must be the same and the area must depend only on
1716-412: The areas of the pieces, using additivity of surface area. The main formula can be specialized to different classes of surfaces, giving, in particular, formulas for areas of graphs z = f ( x , y ) and surfaces of revolution . One of the subtleties of surface area, as compared to arc length of curves, is that surface area cannot be defined simply as the limit of areas of polyhedral shapes approximating
1768-550: The atmosphere" can have a considerable impact on radiative coolers. The authors reported that aerosol and cloud coverage can weaken the effectiveness of radiators and thus concluded that adaptable "design strategies of radiative coolers" are needed to maximize effectiveness under these climatic conditions. The formation of dropwise condensation on PDRC surfaces can alter the infrared emittance of selective PDRC emitters, which can weaken their performance. Even in semi-arid environments, dew formation. Another 2022 study reported that
1820-422: The atmosphere, which would allow for local but not global cooling." Currently the Earth is absorbing ~1 W m more than it is emitting, which leads to an overall warming of the climate. By covering a small fraction of the Earth with thermally emitting materials, the heat flow away from the Earth can be increased, and the net radiative flux can be reduced to zero (or even made negative), thus stabilizing (or cooling)
1872-633: The cooling potential of most of southeast Asia and the Indian subcontinent is significantly diminished in the summer due to a dramatic increase in humidity, dropping as low as 10–30 W/m . Other similar zones, such as tropical savannah areas in Africa, see a more modest decline during summer, dropping to 20–40 W/m . However, tropical regions generally have a higher albedo or radiative forcing due to sustained cloud cover and thus their land surface contributes less to planetary albedo. A 2022 study reported that
1924-725: The cooling power of selective emitters "may broaden the narrowband emittances of the selective emitter and reduce their sub-ambient cooling power and their supposed cooling benefits over broadband emitters" and that: Our work shows that the assumed benefits of selective emitters are even smaller when it comes to the largest application of radiative cooling – cooling roofs of buildings. However, recently, it has been shown that for vertical building facades experiencing broadband summertime terrestrial heat gains and wintertime losses, selective emitters can achieve seasonal thermoregulation and energy savings. Since dew formation appears less likely on vertical surfaces even in exceptionally humid environments,
1976-450: The cost and technical difficulties inherent in large-scale precise lithography " (2022), or "due to complex nanoscale lithography/synthesis and rigidity" (2021). The polyacrylate hydrogel film from the 2022 study has broader applications, including potential uses in building construction and large-scale thermal management systems. This research focused on a film developed for hybrid passive cooling. The film uses sodium polyacrylate ,
2028-632: The dye is mixed in the polymer, the new design can cool more effectively. A 2018 study reported significantly lowered coating costs, stating that "photonic media, when properly randomized to minimize the photon transport mean free path, can be used to coat a black substrate and reduce its temperature by radiative cooling." This coating could "outperform commercially available solar-reflective white paint for daytime cooling" without expensive manufacturing steps or materials. Many thin films offer high solar reflectance and heat emittance. However, films with precise patterns or structures are not scalable "due to
2080-480: The efficiency of passive radiative cooling surfaces and technologies. A 2020 study proposed using a "tilt strategy and wind cover strategy" to mitigate wind effects. The researchers reported regional differences in China, noting that "85% of China's areas can achieve radiative cooling performance with wind cover" whereas in northwestern China wind cover effects would be more substantial. Bijarniya et al. similarly proposes
2132-473: The global carbon neutrality goal. Environmentally friendly bio-based renewable materials should be an ideal material to devise PDRC systems." Advanced photonic materials and structures, such as multilayer thin films, micro/nanoparticles, photonic crystals , metamaterials , and metasurfaces , have been reported as potential approaches. However, while multilayer and complex nano-photonic structures have proven successful in experimental scenarios and simulations,
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2184-424: The infrared window (8–13 μm) for heat transfer with the coldness of outer space (~2.7 K ) to radiate heat and subsequently lower ambient temperatures with zero energy input. PDRCs mimic the natural process of radiative cooling , in which the Earth cools itself by releasing heat to outer space ( Earth's energy budget ), although during the daytime, lowering ambient temperatures under direct solar intensity. On
2236-476: The modification of PDRCs to adjust for temperature shifts. While PDRCs have proven successful in temperate regions, reaching the same level of performance is more difficult in tropical climes. This has primarily been attributed to the higher solar irradiance and atmospheric radiation, particularly humidity and cloud cover. The average cooling potential of tropical climates varies between 10 and 40 W m , significantly lower than hot and dry climates. For example,
2288-460: The ozone or have a strong greenhouse effect , Unlike solar radiation management , PDRC increases heat emission beyond simple reflection. A 2019 study reported that "widescale adoption of radiative cooling could reduce air temperature near the surface, if not the whole atmosphere." To address global warming, PDRCs must be designed "to ensure that the emission is through the atmospheric transparency window and out to space, rather than just to
2340-698: The prospect of large-scale utilization". PDRC coatings have been developed in colors other than white while still demonstrating high solar reflectance and heat emissivity. Coatings must be durable and resistant to soiling, which can be achieved with porous PDRCs or hydrophobic topcoats that can withstand cleaning, although hydrophobic coatings use polytetrafluoroethylene or similar compounds to be water-resistant. Negative environmental impacts can be mitigated by limiting use of other toxic solvents common in paints, such as acetone . Non-toxic or water-based paints have been developed. Porous Polymers Coating (PPC) exhibit excellent PDRC performance. These polymers have
2392-405: The same term [REDACTED] This disambiguation page lists articles associated with the title PDRC . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=PDRC&oldid=1113537888 " Category : Disambiguation pages Hidden categories: Short description
2444-536: The shape of the surface, but not on its position and orientation in space. This means that surface area is invariant under the group of Euclidean motions . These properties uniquely characterize surface area for a wide class of geometric surfaces called piecewise smooth . Such surfaces consist of finitely many pieces that can be represented in the parametric form with a continuously differentiable function r → . {\displaystyle {\vec {r}}.} The area of an individual piece
2496-407: The surface air temperature and humidity instead of the altitude-dependent atmospheric profiles ," may be problematic since "downward longwave radiation comes from various altitudes of the atmosphere with different temperatures, pressures, and water vapor contents" and "does not have uniform density, composition, and temperature across its thickness." Broadband emitters possess high emittance in both
2548-865: The surface area of a sphere and cylinder of the same radius and height are in the ratio 2 : 3 , as follows. Let the radius be r and the height be h (which is 2 r for the sphere). Sphere surface area = 4 π r 2 = ( 2 π r 2 ) × 2 Cylinder surface area = 2 π r ( h + r ) = 2 π r ( 2 r + r ) = ( 2 π r 2 ) × 3 {\displaystyle {\begin{array}{rlll}{\text{Sphere surface area}}&=4\pi r^{2}&&=(2\pi r^{2})\times 2\\{\text{Cylinder surface area}}&=2\pi r(h+r)&=2\pi r(2r+r)&=(2\pi r^{2})\times 3\end{array}}} The discovery of this ratio
2600-507: The temperature of a building or other object. It has been proposed as a method of reducing temperature increases caused by greenhouse gases by reducing the energy needed for air conditioning , lowering the urban heat island effect , and lowering human body temperatures . PDRCs can aid systems that are more efficient at lower temperatures, such as photovoltaic systems , dew collection devices, and thermoelectric generators . Some estimates propose that dedicating 1–2% of
2652-534: The thermoregulatory benefits of selective emitters will likely persist in both humid and dry operating conditions. Rain can generally help clean PDRC surfaces covered with dust, dirt, or other debris. However, in humid areas, consistent rain can result in water accumulation that can hinder performance. Porous PDRCs can mitigate these conditions. Another response is to make hydrophobic self-cleaning PDRCs. Scalable and sustainable hydrophobic PDRCs that avoid VOCs can repel rainwater and other liquids. Wind may alter
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#17327906185382704-817: The use of a wind shield in areas susceptible to high winds. PDRC surfaces can be made of various materials. However, for widespread application, PDRC materials must be low cost, available for mass production, and applicable in many contexts. Most research has focused on coatings and thin films, which tend to be more available for mass production, lower cost, and more applicable in a wider range of contexts, although other materials may provide potential for specific applications. PDRC research has identified more sustainable material alternatives, even if not fully biodegradable . A 2023 study reported that "most PDRC materials now are non-renewable polymers, artificial photonic or synthetic chemicals, which will cause excessive CO 2 emissions by consuming fossil fuels and go against
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