ASTEC

Engineers Guide

—————— ENGINEER'S GUIDE ——————

INTRODUCTION The purpose of this Engineer's Guide is to present the engineering physics

associated with the energy interactions of ASTEC coatings on buildings. The heat transfer equations, definitions, and property descriptions are intended as "review material" for technically trained people, but the information should be comprehensible to anyone with a college physics course background.

BACKGROUND SITUATION Heat transfer through building roofs and walls, through petrochemical tanks, and

through other industrial structures can be very expensive, not only from an energy point of view (i.e., cooling load cost, evaporation losses), but also from a maintenance and repair standpoint.

Traditionally, we have attempted to manage heat after it penetrated the structure by using construction materials with a good R-value (resistance to heat flow) and a low K-value (conductivity). However, R-value is directly proportional to the thickness of the construction material used, and increasing the R-value becomes unrealistic when cost exceeds the value of the energy saved. Moreover, mass insulation such as fiberglass wool is only effective if it is properly protected from humidity and water penetration. Should the roof leak (and they all do at one point or another!), the mass insulation becomes a compressed sponge with a greatly diminished R-value.

There are several factors which influence the heat transfer through a roof, a wall, a building, or a structure in general. These include, but are not limited to, the following:

Environmental Factors, which cannot be manipulated:

• Ambient air temperature • Solar radiation •Wind

Building Material Factors which can be manipulated:

• Material resistivity (R-value) • Surface solar reflectivity/absorptivity • Surface thermal radiation emissivity

Also, the geometric structure of the building itself is important as to how much and where heat will transfer. For instance, a 7-story building is exposed to more radiation on its walls than on its roof. Similarly, a single story building receives 70% to 90% of its radiation on the roof. Most industrial buildings, such as manufacturing plants, storage areas, etc., are single story buildings with galvanized metal roofs, asbestos tile roofs, built-up roofs (BUR), or concrete roofs. All of these construction materials absorb a high degree of solar radiation and offer very little resistance to heat transfer.

Heat Management Rationale In recent years, prevention has been the focus of heat management. It is more

effective and cheaper to prevent heat penetration than to deal with it once it has occurred. This prevention approach is evident in NASA's space vehicle re-entry program where the astronauts' capsule is protected from the atmosphere's intense heat with a ceramic tile shield. The shield's highly reflective surface prevents heat penetration to a great extent, and its high thermal emissivity quickly re-radiates any heat absorbed. NASA's heat management through radiation control led to the development of ASTEC, a ceramic liquid-applied elastomeric coating with high solar reflectivity and high thermal emissivity. The effective use of radiation control coatings (RCC) is predicated on two basic principles:

1. The best way to reduce heat transfer is to prevent it from entering the building. High solar reflectivity achieves this goal.

2. The best way to manage heat transfer is to re-emit as quickly as possible. High thermal emissivity addresses this issue.

The reflection and emission of radiation from a metal roof, a concrete surface, or any other opaque material originates within a few microns of the surface; hence both solar reflectivity1 (the fraction of solar irradiation reflected) and thermal emissivity2 (the rate of radiation emitted by a given surface compared to a blackbody at the same temperature) are functions of the surface state of a material rather than of its bulk properties. For this reason, the solar reflectivity and the thermal emissivity of a coated surface are characteristics of the coating (i.e., ASTEC) rather than that of the underlying surface.

The measured values for ASTEC white-colored coatings are a solar reflectivity of 0.83 in the UV range, a luminous reflectivity of .90 in the visible range of the solar spectrum, and a thermal emissivity of 0.92. ASTEC's average solar reflectivity of 0.86 means that only 14% of the incoming solar energy will be absorbed and converted to heat energy. The surface, to keep itself cooler, will be emitting radiation at 92% the rate of a "perfect emitter" (blackbody radiator) at the same temperature.

DEVELOPING THE MODEL The approach taken in this guide is to develop a heat transfer model and

equations for an outside roof (or wall) structure. The model will take into account the environmental factors of solar radiation, outside air temperature, and wind velocity, plus specific roof/wall construction, material properties, and indoor temperature, with and without ASTEC coating. Conservation of Energy

The first Law of Thermodynamics is known as the law of the conservation of energy. It stipulates that for a given system, energy is always conserved; it is never lost.

The energy balance is expressed as follows:

[Net Amount of Energy Added to System] = [Net Change in Stored Energy of System]

Or Energy In - Energy Out = Increase or Decrease in Energy of System

However, this conservation of energy equation is further simplified if the system (a roof or a wall, for instance) is already heated up. If the temperatures within the system are not changing, then the stored energy is not changing, and the right side of the above equation is equal to zero. This situation is called the "steady state" condition and allows us to write the steady state conservation of energy equation as:

Energy In = Energy Out

The second Law of Thermodynamics states that heat always travels from a "hot" region to a "colder" region. The terms "hot" and "cold" are relative terms in that an object with a lower temperature is "colder" whereas an object with a higher temperature is "hotter". Thermodynamics:

1. Energy is always conserved; it is never lost a. What goes in... must come out

2. Heat always travels from a "hot" region to a "colder" region. Therefore, the issues are:

• Flow of Heat in Buildings • Temperatures in Buildings

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1Solar reflectivity defines the ability to return or to bounce away incident radiation. In practice, it is the ability of a surface to reflect all or a percentage (86% in the case of ASTEC) of incident radiation such as solar radiation. The reflectivity of a surface is a measure of the amount of reflected radiation. However, solar reflectivity is wavelength dependent. ASTEC's solar reflectivity ranges from 0.83-0.92, the reflectivity being dependent primarily on the UV, visible, and IR wavelengths. Assuming a conservative average solar reflectivity of 0.86, this would indicate that 86% of the solar radiation is being reflected back into the atmosphere and that only 14% of the remaining solar radiation would be absorbed (cf. "absorptivity") and converted to heat energy.

Thermal emissivity is the ratio of the radiation intensity of a non-blackbody to the radiation intensity of a blackbody at the same temperature. This ratio, which is usually designated by the Greek letter e, is always less than or just equal to one. The emissivity characterizes the radiation or absorption quality of non-blackbodies. Emissivity is a physical property... just like weight, color, shape, etc. All materials have emissivity ranging from zero to one.

Roof/Wall Heat Transfer Model

The steady state conservation of energy equation (energy balance) is used to examine the outside surface of a roof or wall, where the "system" is considered the roof or wall surface. The surface is hot already (steady state condition) due to the solar energy absorbed by the surface. Also, because the surface is hot, it is losing energy to the air (by convection and by net thermal radiation) and through the roof or wall to the inside of the building (by conduction).

Wall/Roof Heat Transfer Model An "energy balance" (steady state conservation of energy) equation is written for the outside surface of the wall or roof: Energy entering surface = Energy leaving surface Solar energy absorbed by surface = Heat lost to outside air from surface (net thermal radiation + convection) + Heat conducted through wall from surface to inside

The flow of heat to, from, or through a roof, a wall, or a petrochemical tank will occur via one or more of the three modes of heat transfer: Mode Factors Radiation Conduction Convection

Solar Reflectivity Resistivity (R-value) Temperature

Thermal Emissivity Conductivity (K-value) Velocity

Conduction is defined as heat flow through matter resulting from the physical contact or the transmission of heat by molecular motion. Conduction is also explained as the "transfer of energy caused by physical interaction among molecular, atomic, and subatomic particles of a substance at different temperatures." Heat Transfer, Lindon C. Thomas - Professional Version, p.5. Hence, the effectiveness of insulation intended to reduce conduction heat transfer is inversely proportional to the conductivity (K-value) of the material and is directly proportional to the thickness of the material. Together, these two parameters determine the thermal resistance (R-value) of the material. For the rate of heat flow through a roof or wall, the conduction heat transfer (qconduct) is directly proportional to the surface area (Ax) of the roof, the material's conductivity (K), and the temperature difference (T1-T2) through the roof, and is inversely proportional to the roof's thickness (L). A heat flux is defined as the rate of heat transfer per unit area (q"=q/ A). One-dimensional molecular conduction heat transfer

qx = -kAx (∂T / ∂x)

qx = kAx ( [T1 – T2] / L)

q”conduct = k ( [T1 – T2] / L)

One-dimensional conduction heat transfer in a plate with T1 > T2,qy = 0 and qz = 0.

Convection occurs with the transfer of thermal energy by actual physical movement from one location to another of a substance in which thermal energy is stored. Convection heat transfer is the "special" case of conduction heat transfer at the surface between a solid and a fluid. The fluid flowing next to the solid surface develops a slow moving boundary layer (film layer), and heat is conducted through this film to or from the solid surface. The heat flux for convection heat transfer depends directly on the film coefficient (hfilm/ similar to conductivity) and directly on the bulk fluid solid surface temperature difference (Tsolid – Tfluid). Convection Heat Transfer Convection Heat Transfer is the "special" case of conduction heat transfer at the surface between a solid and a fluid. • The fluid develops a slow-moving boundary layer (the film) next to the solid surface. • Heat is "conducted" through this film - the process is called Convection Heat Transfer.

Convection Heat Flux • Heat flux for convection through a film (Newton's Law of Cooling): q convect = h film (T solid – T fluid) Where hfilm = Film coefficient = Value depends on fluid properties and how fast fluid is moving (faster velocity gives bigger h, more convection heat transfer) Tfluid = Bulk fluid temperature Tsolid = Wall temperature at fluid interface

Radiation heat transfer refers to the electromagnetic energy radiated by solids, liquids, and gases. Such radiant energy is in the form of electromagnetic waves covering the entire electromagnetic spectrum from the radio-wave portion of the spectrum through the infrared, visible, ultraviolet, x-ray, and gamma-ray portions.

For practical purposes, we can consider two types of radiation: solar radiation (energy emanating from the sun) and thermal radiation (energy emanating from objects on earth). However, all radiation heat transfer is proportional to the fourth power of a material's surface's absolute temperature and directly related to the surface's emissivity (fraction of a perfect "black" emitter). Radiation Heat Transfer Radiation heat transfer is the electromagnetic radiation emitted by a surface due to its temperature (excitation of electron levels). • Radiation heat flux equation: q”rad = ε SURFACE σ T4 SURFACE Where Tsurface = Absolute temperature (˚Kelvin = 273 + C˚) σ = Stefan-Boltzman Constant (5.670 x 10-8 W/m2 K4) εSURFACE = Emissivity, a property of the surface indicating what fraction of a perfect (black) emitter the surface is.

Solar radiation reaching the earth (i.e., the roof or walls of a building, or the surface of a tank) has a high energy content (Ultraviolet, Visible, and Near Infrared rays). It is transmitted on short wavelengths with high frequency. The higher the energy content, the higher the building surface temperature. The solar radiation flux normal to a surface is called "irradiation," G, and its value depends on time of year, time of day, location on earth, and local weather. An opaque roof or wall will either absorb or reflect the solar radiation hitting it. The solar absorptivity, αso|ar’ is the fraction of solar flux absorbed, while the solar reflectivity, pso]ar’ is the remaining fraction of the solar flux, which was reflected. Thus,

αsolar + psolar =1

Radiation: Solar and Thermal

• Solar o Emanating from the sun o High energy content (U/V, Visible, NIR) o Short wavelength, High frequency

• Thermal o Emanating from every object on earth o Low energy content (MIR, FIR, XIR) o Long wavelength, Low frequency

Thermal radiation has lower energy content (Middle Infrared, Far Infrared, and Extreme Infrared rays). This lower level energy travels on long wavelengths with low frequency. Everything on earth above absolute zero (-459%F or -273%C) radiates energy in the form of thermal radiation. Thus, not only is every surface emitting thermal radiation, but the surface is also being hit by thermal radiation emitted from those materials surrounding it. The surface's net thermal radiation flux, the emitted radiation minus the absorbed radiation from the surroundings, must be taken into account.

Net Thermal Radiation Heat Transfer, q"NET THERMAL Since all "earthly" objects emit thermal radiation at each other, the "net" thermal radiation for a given surface is what is needed: q"net thermal + q”emitted surface – q” absorbed surroundings { q” air + q” bldgs + q” ground + …} Therefore: q"net thermal = ε surface σT4 surface – α surface σT4 surroundings

and ε surface thermal ≈ α surface thermal

T surroundings ≈ Tair

Therefore: q"net thermal = ε surface σ (T4 surface – T4 air)

Since the thermal properties of absorptivity, reflectivity, and emissivity of a surface depend on wavelength (i.e., the temperature), the solar radiation and thermal radiation properties should not be expected to be the same (they aren't!). However, for thermal radiation surfaces, it can be shown that thermal emissivity and thermal absorptivity are related by:

ε surface thermal ≈ α surface thermal

SURFACE TEMPERATURES AND BUILDING LOAD EQUATIONS The development of the equations for calculating outside and inside surface temperatures and heat gains through roofs, walls, and tanks is presented below.

Outside Surface Thermal Calculations Looking at the equations below for calculating heat flux due to conduction3, convection4, and net thermal radiation5, each equation has the surface temperature as an unknown value. If the surface temperature can be determined, then the heat fluxes can also be calculated. By using the energy balance equation and substituting in the individual heat flux relations, it is shown below that the surface temperature of the wall or roof can be found. An energy balance equation is written for the outside surface of the wall or roof:

Energy In = Energy Out

Wall/Roof Heat Transfer Model

An "energy balance" equation is written for the inside surface of the wall or roof:

Energy entering surface = Energy leaving surface

q”CONDUCT = q”NET THERMAL RADIATION + q” CONVECT

Then the individual equations are substituted for each of the heat fluxes:

Absorption Net Thermal Radiation Convection Conduction

(l-p)G = εtherm σ (T4surf - T4air) + hfilm (Tsurf - Tair) + (K/L)(Tsurf - Tinside)

(l-p)G = εtherm σ T4surf - εtherm σ T4air + hfilm Tsurf - hfilm Tair + (K/L)Tsurf - (K/L)Tinside

(K/L)(Tsurf)+hfilm Tsurf +(εtherm σ) T4surf = (l-p)G +εtherm σ T4air +hfilmTair +(K/L)(Tinside)

Tsurf (hfilm + (K/L)) + (εtherm σ) T4surf = (l-p)G +εtherm σ T4air +hfilmTair +(K/L)(Tinside)

Tsurf + (εtherm σ /hfilm + (K/L) T4surf = ((l-p)G +εtherm σ T4air +hfilmTair +(K/L)(Tinside))/hfilm + (K/L)

For a given set of environmental conditions (G, Tajr , T insjde , hfilm) and given roof or wall properties (K, L, psolar, ethermal), rearranging the above equation allows us to solve for the surface temperature: Tsurf + [(εtherm σ) /(hfilm + (K/L))] T4

surf = [(l-p)G + hfilm Tair+ (K/L)Tinside air + εtherm σ T4outsideair] / (hfilm + (K/L))

(εtherm σ) /(hfilm + (K/L)) = C1 Tsurf + C1 T4

surf = C2 C1 and C2 are constants determined by the environmental condition values and material property values, but Tsurface can be solved iteratively (by estimating — which is quick with a computer!). Note that with the surface temperature determined, the heat flux through the wall or roof is easily calculated using the conduction heat flux equation.

Inside Surface Thermal Calculations The above equation calculates the outside surface temperature when the inside surface temperature is known. However, generally, the inside air temperature is known (or can be assumed) and the inside wall or roof temperature is an unknown. The inside surface temperature can be determined in conjunction (solved for simultaneously) with the outside surface temperature by writing another equation for the energy balance at the inside surface of the wall or roof:

Energy In = Energy Out

Wall/Roof Heat Transfer Model

An "energy balance" equation is written for the inside surface of the wall or roof:

Energy entering surface = Energy leaving surface

q”CONDUCT = q”NET THERMAL RADIATION + q” CONVECT

Then, substituting the individual heat flux equations with the inside conditions (h film inside, T air

inside) and inside wall or roof emissivity (ε thermal inside) gives the equation:

(K/L)(Tsurfout - Tsurf jn) = εinα(Tsurfin - Tairin) + hfilmin(Tsurfin - Tairin)

Thus, two independent equations have been developed with two independent unknowns (T

surface outside, T surface inside). The equations are able to be solved iteratively together (again estimating with the computer), and the inside wall or roof ceiling temperature is calculated. Note that more information is needed now: inside surface thermal emissivity, inside film coefficient, and inside room air temperature. Also, the heat flux radiated into the room and the heat flux convected to the inside air may be calculated separately, which may be important in thermal comfort determinations.

Roof or Wall Thermal Resistance In the heat flux conduction equation above, the "K/L" term represents the thermal conductance for a solid wall or roof. For a composite multi-layer wall or roof, this "K/L" is replaced by the "overall conductance" U, which is the inverse of the sum of the thermal resistances of each sublayer. So the "K/L" term in all the equations above can be replaced by (for the generalized case) becomes:

K/L → U = 1/ΣR Using this R-approach, any type of wall or roof can be analyzed by determining its ΣRthermal value. It is only necessary to know the individual R's for the solids and air spaces, and/or the attic conditions. Approximate Building Loads As mentioned earlier, poorly protected single story industrial buildings may receive 70-90% of their total heat load through their roof. By using the above equations to determine the roof heat flux for such a building, q"roof non-ASTEC , we can assume the roof is 80% of the total load and thus estimate the total building load as:

q"building non-ASTEC = q"roof non-ASTEC / 0.80 To compare the effect on building load when ASTEC coating is used, the roof heat flux with ASTEC, q"roof ASTEC , would be determined from the equations. To this ASTEC roof heat flux would be added 25% of the non-ASTEC roof heat flux, which represents the estimated load from the walls (untreated) of the building. This is calculated as:

q"building ASTEC = q"roof ASTEC + 0.25 q"roof non-ASTEC Thus, the building's cooling load reduction due to using the ASTEC coating is the difference in the two building heat fluxes multiplied by the roof area:

Cooling Load Reduction = (q”building non-ASTEC – q” building ASTEC ) x Roof Area Roof Thermal Expansion For metal roofs, the expansion and contraction of the metal is often a maintenance and repair concern due to possible fastener and seam damage. The fractional change in length of a material due to a one-degree change in temperature is given by the coefficient of expansion, β. To calculate the extension (or contraction) of a material due to a temperature change, the change in length is given by:

Length Change = β x Length x Temperature Change It should be noted that if the temperature change is sudden, as can happen with a sun-and-clouds situation, the material can be quickly expanding and contracting - and the

higher the roof temperature, the greater this change in length. This effect is known as "thermal shock." Using the above mathematical formulations for all three modes of heat transfer we can calculate the heat transfer through a surface with and without ASTEC.

q" SOLAR ABSORBED = q" NET THERMAL RADIATION + q" CONVECTION + q" CONDUCTION

We can solve heat flux problems for a given environmental condition (G, Tair , and Tinside) and given surface properties (psolar , εthermal) and determine the roof surface temperature, the inside temperature, the heat flux reduction, the cooling load reduction, and the energy savings in Kilowatt-hours. Input Values Needed

For the calculation of outside and inside surface temperatures and the heat flux through the roof or wall, site specific values are needed for the elements in the three following groups:

Roof/Wall Thermal Properties Reference 1) Outside surface solar reflectivity Table 1 2) Outside surface thermal emissivity Table 1 3) Inside surface thermal emissivity Table 1 4) Total surface-to-surface thermal resistance Table 1

Environmental Conditions Reference 1) Outside air temperature Specified by User 2) Inside air temperature Specified by User 3) Solar radiation flux Tables 4 / 5

Other Values Reference 1) Outside air film coefficient Given 2) Inside air film coefficient Given

Values for these input variables are presented in tables found at the end of this guide. Examples:

The following two examples illustrate ASTECs energy analysis of:

1. A metal roof without insulation or air conditioning but with ASTEC protection. J

2. A metal roof with insulation, air conditioning, and ASTEC protection.

Calculations can be produced for similar energy savings for any kind of surface (concrete, galvanized metal, asbestos tiles, etc.) with and without ASTEC.

Calculating Roof Top and Bottom Temperatures With Roof Heat Flux

(metric units input)

Case 1: Metal Roof without insulation but with ASTEC protection and A/C Input Roof Thermal Properties top reflectivity = 0.8 top emissivity = 0.9 bottom emissivity = 0.25 total resistance = 0.002 (m °K)/W 0.011357 (hr ft °F)/Btu Input Environmental Conditions outside air temp = 35 °C 95 °F inside air temp = 20 °C Aircon1 68 °F solar radiation = 750 W/m2 237.96 Btu/(hr - ft2) Other Values Used stefan-boltzmann =5.67E-08 W/(m2 °K4) 1. 71E-09 Btu/(hr ft2 ° K4) outside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) inside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) Solution Procedure Step 1: Guess a roof surface temp => 37.6 °C 99.68 °F

If calculated surface temp is lower, guess bigger surface temp in Step 1 Step 2: Compare calculated surface temp => 37.61306 °C Roof surface temp = 37.61306 °C 99.70351 °F Roof bottom temp = 37.36105 °C 99.24989 °F Roof heat flux = 126.0075 W/m2 39.97967 Btu/(hr - ft2)

1. Building is air conditioned

Calculating Roof Top and Bottom Temperatures With Roof Heat Flux

(metric units input)

Case 2: Metal Roof without insulation and without ASTEC but with A/C Input Roof Thermal Properties top reflectivity = 0.25 top emissivity = 0.25 bottom emissivity = 0.25 total resistance = 0.002 (m °K)/W 0.011357 (hr ft °F)/Btu Input Environmental Conditions outside air temp = 35 °C 95 °F inside air temp = 20 °C Aircon1 68 °F solar radiation = 750 W/m2 237.96 Btu/(hr - ft2) Other Values Used stefan-boltzmann =5.67E-08 W/(m2 °K4) 1. 71E-09 Btu/(hr ft2 ° K4) outside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) inside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) Solution Procedure Step 1: Guess a roof surface temp => 66.4 °C 151.52 °F

If calculated surface temp is lower, guess bigger surface temp in Step 1 Step 2: Compare calculated surface temp => 66.4 °C Roof surface temp = 66.4 °C 151.52 °F Roof bottom temp = 66.4 °C 150.3572 °F Roof heat flux = 342.9916 W/m2 108.8244 Btu/(hr - ft2) Astec, The Total Solution Case 1 Roof Heat Flux with Astec = 126.0075 W/m2 39.97967 Btu/(hr - ft2) Case 2 Roof Heat Flux without Astec = 342.9916 W/m2 108.8244 Btu/(hr - ft2)

Heat Flux reduction with Astec = 63.26221 %

1. Building is air conditioned

Cooling Load Reduction with ASTEC Q building non-astec = Q roof non-astec / 0.8 428.7395 Q building astec = Q roof astec + 0.25 Q roof non-astec 211.7554 AC Reduction = Q building non-astec + Q building astec 216.984

Case 1: Metal without insulation but with ASTEC protection and A/C AC Reduction = 428.7395 W/m2 - 211.7554W/m2

Cooling Load Reduction = 216.984 W/m2 68.84469 Btu/(hr - ft2) Sample Area: 1000 m2 Sample Savings: 216984 Watts or 740414.6 Btu/hr or 61.71332 tons of refrigeration

1. Building is air conditioned

Calculating Roof Top and Bottom Temperatures

With Roof Heat Flux (metric units input)

Case 3: Metal Roof without insulation or A/C but with ASTEC protection Input Roof Thermal Properties top reflectivity = 0.8 top emissivity = 0.9 bottom emissivity = 0.25 total resistance = 0.002 (m °K)/W 0.011357 (hr ft °F)/Btu Input Environmental Conditions outside air temp = 35 °C 95 °F inside air temp = 40 °C No A/C1 104 °F solar radiation = 750 W/m2 237.96 Btu/(hr - ft2) Other Values Used stefan-boltzmann =5.67E-08 W/(m2 °K4) 1. 71E-09 Btu/(hr ft2 ° K4) outside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) inside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) Solution Procedure Step 1: Guess a roof surface temp => 66.4 °C 151.52 °F

If calculated surface temp is lower, guess bigger surface temp in Step 1 Step 2: Compare calculated surface temp => 44.69073 °C Roof surface temp = 44.69073 °C 112.4433 °F Roof bottom temp = 44.62162 °C 112.3189 °F Roof heat flux = 34.5584 W/m2 10.96469 Btu/(hr - ft2)

1. Building is not air conditioned

Calculating Roof Top and Bottom Temperatures

With Roof Heat Flux (metric units input)

Case 4: Metal Roof without insulation or A/C and without ASTEC protection Input Roof Thermal Properties top reflectivity = 0.25 top emissivity = 0.25 bottom emissivity = 0.25 total resistance = 0.002 (m °K)/W 0.011357 (hr ft °F)/Btu Input Environmental Conditions outside air temp = 35 °C 95 °F inside air temp = 40 °C No A/C1 104 °F solar radiation = 750 W/m2 237.96 Btu/(hr - ft2) Other Values Used stefan-boltzmann =5.67E-08 W/(m2 °K4) 1. 71E-09 Btu/(hr ft2 ° K4) outside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) inside air film coeff =5.7 W/(m2 °C) 1.003786 Btu/(hr ft2 °F) Solution Procedure Step 1: Guess a roof surface temp => 75.2 °C 167.36 °F

If calculated surface temp is lower, guess bigger surface temp in Step 1 Step 2: Compare calculated surface temp => 75.23265 °C Roof surface temp = 75.23265 °C 167.4188 °F Roof bottom temp = 74.6949 °C 166.4508 °F Roof heat flux = 268.8753 W/m2 85.30875 Btu/(hr - ft2) Astec, The Total Solution Case 1 Roof Heat Flux with Astec = 34.5584 W/m2 10.96469 Btu/(hr - ft2) Case 2 Roof Heat Flux without Astec = 268.8753 W/m2 85.30875 Btu/(hr - ft2)

Heat Flux reduction with Astec = 87.14705 %

1. Building is not air conditioned

Inside Temperature Reduction with ASTEC (Assume 80% heat flux through roof, 20% through walls in non-ASTEC building)

Tinside astec = Toutside + (Tinside non-astec – Toutside) X (Q roof astec + 0.25Q roof non-astec) / (Q roof non-astec/0.8) Tinside astec = 35 + 1.314118 Tinside astec = 36.31412 °C 97.36541 °F

MARKET DEMAND Some of the brightest ideas and some of the smartest inventions never made it to the

market simply because they did not meet customers' requirements.

Unfortunately, some great concepts have also been exaggerated by quasi-manufacturers who sell on the basis of marketing rather than real benefits.

Informed consumers have become more demanding. In order to meet customers' expectations, this new approach using radiation control technology had to provide a total solution to roof management as well as heat management. Above all, to meet customers' expectations, radiation control technology has to do more than claim heat management efficiency, it has to be proven case by case with a clear measurement of heat flux reduction and a specific statement of cooling load reduction based on scientific evidence.

Educated consumers have been able to distinguish between unsubstantiated marketing claims and scientifically proven systems. Furthermore, it is now well accepted that an experienced manufacturer has to demonstrate the effectiveness of his system not only in laboratory conditions but in actual field applications with world-class end users.

The marketplace has since dictated the criteria for a successful solar radiation control system:

1. Energy saving radiant heat barrier The radiation control coating should be based on proven technology and it should

maintain a high solar reflectivity with a high thermal emissivity. Energy savings should be calculated using recognized energy balance equations.

2. Reduced heat transfer Heat reduction based on scientific energy balance equations must be measured in specific

terms (W/m2orBTU/ft2-hr).

3. Better heat management A high thermal emissivity is the only cost effective way to re-radiate absorbed solar heat.

4. Reduced cooling load The ability to calculate the cooling load reduction on a structure will provide the means to

determine the payback period and the real lifecycle cost of a system. Cooling load reduction can be expressed in financial savings per Kilowatt-hour based on the reduction in power requirements (W/m2 or BTU/ft2 - hr or in terms of tons of refrigeration).

5. Protection against ultraviolet degradation Specific ASTM or other internationally recognized testing methods can quantify the

U/V resistance of radiation control coatings (RCC).

6. Long lasting waterproofing Protection against solar heat penetration is insufficient when considering a total solution.

Proper surface waterproofing is necessary to "make the system complete."

7. Surface structural integrity Roof surfaces require a monolithic application in order to maintain a uniform

quality of insulation and waterproofing. Finish coats should not chip, crack, or flake. 8. Corrosion control

In the case of galvanized metal a proven rust inhibitor is essential to protect the metal from corrosion due to high levels of relative humidity water penetration, leaks, etc. The metal priming coat should neither penetrate nor discolor the finish coat.

9. Environmentally friendly products The preservation of the environment is no longer a debatable issue. Radiation control coatings

should be water-based.

10. Low lifecycle cost factors

a) Longevity. It is not sufficient to have a short payback period. Lower lifecycle cost requires a. system to guarantee a longer surface life for several years.

b) Low installation cost Initial installation cost should also be supported by a labor warranty offered by a factory-trained applicator. c) Low surface maintenance and repairs. This is particularly true of roof surfaces. Adequate surface preparation (corrosion control and waterproofing) plus an effective finish coat with exceptional thermal properties will create the condition for a more stable roof surface temperature. Lower and more stable roof surface temperature will prevent thermal shock and minimize maintenance and repair costs.

d) Reduced capital expenditures. Cooler surface temperatures mean less heat transfer and more energy savings. Less heat transfer also minimizes the need for additional capital investments (i.e., air conditioning equipment).

How Does ASTEC Meet Customers' Needs?

Criteria

ASTEC

Energy Savings

Provides high solar reflectivity: more than 0.86 Limits radiant heat absorption to below 14% Reduces surface temperatures by as much as 20" C Reduces energy consumption by 40% to 65% ASTEC's Harmonized Classification Code: 6R06.90.000

Reduced Heat Transfers

Measured and calculated heat transfer reductions: 50% to 70% Better Heat Management

Thermal Emissivity: 0.92

U/V Protection

Uses high density ceramic component to resist ultraviolet penetration and to maintain its color. ASTM C-25 Accelerated Weathering

Long-lasting Waterproofing WPM #8: Tensile Strength: 167 PSI

Elongation: 245% break WPM #9: Tensile Strength: 792 PSI Elongation: 683% break

Structural Integrity Every component of the ASTEC system is highly flexible and provides a strong adhesion for a monolithic application.

Corrosion Control ASTEC's metal primer seal (B-16-71) inhibits corrosion and prevents oxidation from air and humidity. Salt-spray/ Salt-fog resistance ASTM B-117-90.

Protection of the Environment

ASTEC products are waterbased and offer a clean and aesthetic architectural appearance.

Lifecycle Cost

Minimal labor cost due to ease of application; 7- to 10-year product amortization cost due to warranty; reduced maintenance and repair costs due to stable surface temperatures; and energy savings due to cooling load reductions.

Sound Attenuation

ASTEC is proven to dampen vibration and to deaden sound.

Cost-effective Installation

Application by brush, roller, or power spray equipment.

Warranty

Manufacturer's Product warranty. Labor warranty by factory-trained ASTEC applicators.

Low-cost Maintenance

Easy do-it-yourself repair. Annual inspection during warranty period.

Lower Roof Repair Cost

Virtual elimination of thermal shock on metal surfaces.

Brand Name Recognition

ASTEC is #1: It was the first ceramic-based liquid-applied RCC , and it remains the world leader with a strong technical support team dedicated to its exclusive factory-trained dealers in every continent of the world. A 20-year proven record. Prestigious client reference list: Industrial sector Commercial sector Petrochemical sector Residential sector Military sector

Fire-safe Products

Self-extinguishing, Class A fire rating. ASTM D-1360.

Mildew/Fungus Resistance

ASTM D-3273-73T

ASTEC is the Total Solution

TABLES

Table 1 Building Material Properties

Table 2 Roof's Airspace Resistances

Table 3 Attic's Airspace Resistances

Table 4 Clear Day Solar Radiation Values

Table 5 Cities and Solar Radiation

Table 1 Building Material Properties

Ref: Chapter 22,1989 ASHRAE Fundamentals Handbook

Material Type and Description Material Density Thermal Resistance

R-Value Solar Reflectance

Thermal Emittance

(Kg/m3) (Ibm/ft3) K m2/W (h ft2°F)/BTU Roofing Aluminum sheet 0.55 0.1 Galvanized iron, oxidized 0.2 0.25 Asbestos cement shingles 1900 118.61 0.037 0.210112 0.27 0.89 Asphalt roll roofing 1100 68.67 0.026 0.147646 0.07 0.9 Asphalt shingles 1100 68.67 0.077 0.437259 0.07 0.9 Wood shingles 0.166 0.942663 0.41 0.9 Masonry Brick, fired clay 2000 124.86 1.00* 5.679* 0.93 Clay tile, one cell (102 mm / 4.02 in.) 0.2 1.136 0.35 0.85 Concrete, stone aggregate 2200 137.34 0.60* 3.407* 0.35 0.87 Concrete, low density aggregate 1200 74.91 2.00* 11.357* 0.35 0.87 Concrete, foam/cellular 1000 62.43 3.00* 17.036* 0.35 0.87 Cement plaster, sand 1860 116.12 1.39* 7.893* 0.35 0.88 Gypsum plaster low-density (127 mm / 5.0 in.) 720 44.95 0.32 1.817 0.8 0.9 Gypsum plaster, sand (127 mm/5.0 in.) 1680 104.88 0.09 0.511 0.8 0.9 Note: Asterisk (*) indicates R-value per meter (ft) of thickness and needs to be reduced for actual thickness used

Building Material Properties

Ref: Chapter 22,1989 ASHRAE Fundamentals Handbook Material Type and Description Material Density Thermal Resistance

R-Value Solar Reflectance

Thermal Emittance

(Kg/m3) (Ibm/ft3) K m2/W (h ft2°F)/BTU Building Board Asbestos-cement 1900 118.61 1.73* 9.823* Gypsum/plaster (12.7 mm / 0.5 in.) 800 49.94 0.079 0.449 0.91 Plywood (12.7 mm/0.5 in.) 540 33.71 0.11 0.625 0.33 0.9 Vapor/permeable felt 0.011 0.062 Hardwoods 700 43.7 6.0* 34.071* 0.41 0.9 Softwoods 500 31.21 7.5* 42.59* 0.41 0.9 Insulating Materials Mineral fiber batt (90 mm / 3.54 in.) 25 1.56 2.63 14.935 0.93 Glass fiber 100 6.24 27.7* 157.3* Expanded polystyrene 2 0.125 4.35* 24.702* Mineral fiberboard - Core/roof insulation 260 16.23 20.4* 115.84* - Acoustical tile 290 18.1 19.8* 112.44* Loose-fill pertite, expanded 90 5.62 21.0* 119.25* Spray polyurethane foam 32 1.998 41.0* 232.82* Note: Asterisk (*) indicates R-value per meter (ft) of thickness and needs to be reduced for actual thickness used

Table 2 ROOF'S AIRSPACE RESISTANCES

Ref: Chapter 22,1989 ASHRAE Fundamentals Handbook

Parameters: t = airspace thickness; EI, E2 = emissivity values of surfaces facing airspace There are two cases for which the airspace resistance will be found: Case 1: Normal materials give an effective emissivity of 0.82 (Ei = E2 = 0.9) Case 2: One surface has low emissivity (Ei = 0.25, i.e. galvanized iron) and the other surface has regular emissivity (E2 = 0.9). This situation provides an effective emissivity of 0.20

ROOF AIRSPACE R-VALUE Thickness of Airspace cm in. cm in. cm in. cm in. 1.27 0.5" 1.91 0.75" 3.81 1.5" 8.89 or

> 3.5" or>

(m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu Horizontal Airspace

Case 1:E = 0.82 0.136 0.77 0.15 0.85 0.166 0.94 0.176 1 Case 2: E = 0.20 0.294 1.67 0.37 2.1 0.491 2.79 0.601 3.41 45° Sloped Airspace

Case 1:E = 0.82 0.136 0.77 0.148 0.84 0.16 0.91 0.159 0.9 Case 2: E = 0.20 0.294 1.67 0.37 2.1 0.451 2.56 0.439 2.49

Table 3

ATTIC'S AIRSPACE RESISTANCES

Ref: Chapter 22,1989 ASHRAE Fundamentals Handbook

Rtotal = Rroof + Rattic air + Rceiling Parameters: Attic ventiliation, outside air temperature (OAT), ceiling R-value, roof surface temperature.

AIR ATTIC R-VALUE OAT Roof

Temp No Ventilation Case Natural Ventilation Case Forced Ventilation Case Ceiling R Values Ceiling R Values (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu (m2K)/W °Fft2hr/Btu 1.76 10 3.52 20 1.76 10 3.52 20 32 °C/90 °F

49°C/120°F 0.1057 0.6 0.211 1.2 0.264 1.5 0.845 4.8 1.532 8.7

60°C/140°F 0.1057 0.6 0.229 1.3 0.317 1.8 1.109 6.3 1.884 10.7

71°C/160°F 0.1057 0.6 0.247 1.4 0.37 2.1 1.268 7.2 2.236 12.7

38°C/100°F

49°C/120°F 0.1057 0.6 0.158 0.9 0.176 1 0.475 2.7 0.828 4.7

60°C/140°F 0.1057 0.6 0.194 1.1 0.247 1.4 0.792 4.5 1.303 7.4

71°C/160°F 0.1057 0.6 0.229 1.3 0.335 1.9 1.039 5.9 1.708 9.7

NOTE: If two reflective surfaces are used on the inside attic surfaces, ADD the next values; if only one reflective surface is used, then ADD only half of the following values: 0.81 4.6 0.898 5.1 0.989 5.1 1.057 6 1.057 6

Table 4

Clear Day Solar Radiation Values For a Horizontal Surface

The ASHRAE "Clear Sky/Day" method of calculating solar radiation (insolation) values is based on a standard (low moisture) atmosphere model. The parameters used to determine the radiation values on an hourly basis are:

1 Time of year (earth's declination angle) 2 Time of day (hour angle) 3 Location on earth (latitude angle)

The radiation values calculated below have set two of the above parameters at the following values:

(a) Mid-summer is chosen: June/July for the Northern Hemisphere January/Feb. for the Southern Hemisphere This means the declination angle is set at 22°

(b) Solar noon-time is chosen: the highest point in the sky each day at the location.

This means the hour angle is (0°) zero degrees

Thus, the calculation of "Clear Day" summer noon-time radiation is reduced to only one parameter: The latitude angle for that location

Summer Noon-Time Radiation on a Horizontal Surface

Latitude (degrees)

Zenith Angle (1)

Clear Sky Hourly Radiation

Conservative Hourly Radiation(2)

W/m2 Btu/(h ft2) W/m2 Btu/(h ft2)

0° 22° 950 301 855 271 10° 12° 1000 317 900 285 20° 2° 1018 323 915 290 30° 8° 1012 321 910 288 40° 18° 980 311 880 279 50° 28° 900 285 810 257 60° 38° 775 246 700 222 Notes:

(1) Zenith angle is the angle between the incoming solar radiation and a vertical line.(2) The “conservative Value is 90% of the clear sky value to account for moisture, pollution, etc.

Using Table 4 with a city’s latitude gives the solar radiation value for that city.

Table 5

CITIES and SOLAR RADIATION

Clear day, summer, noon-time City Country Latitude Solar Radiation W/m2 Btu/(hr ft2) AFRICA Cairo Egypt 30° 910 288 Johannesburg S. Africa 26° 912 289 Lagos Nigeria 6° 880 279 ASIA Bangkok Thailand 13° 905 287 Bombay India 18° 912 289 Colombo Sri Lanka 7° 887 281 Hong Kong China 22° 914 290 Jakarta Indonesia 6° 882 280 Kuala Lumpur Malaysia 3° 865 274 Manila Philippines 14° 907 288 New Delhi India 13° 905 287 Singapore Singapore 1° 860 273 MIDDLE EAST Dhahran Saudi Arabia 26° 906 287 Muscat Oman 23° 913 289 Kuwait City Kuwait 29° 909 288 EUROPE Budapest Hungary 48° 825 261 Izmir Turkey 38° 885 281 Lisbon Portugal 38° 885 281 Prague Czech Republic 50° 810 257 CARIBBEAN Nassau Bahamas 25° 918 291 Montego Bay Jamaica 18° 912 289 Sto Domingo Dominican Republic 18° 912 289 San Juan Puerto Rico 18° 912 289 Port of Spain Trinidad & Tobago 10° 900 285 NORTH AMERICA Acapulco Mexico 17° 911 289 Merida Mexico 21° 916 290 Mexico, D.F. Mexico 20° 915 290 Ottawa Canada 45° 850 269

SOUTH AMERICA Bogota Colombia 5° 877 278 Buenos Aires Argentina 35° 895 284 Caracas Venezuela 10° 900 285 Guyaquil Ecuador 3° 870 276 Lima Peru 12° 903 286 Manaus Brazil 3° 870 276 Montevideo Uruguay 35° 895 284 Recife Brazil 9° 891 282 Salvador Brazil 13° 905 287 Santa Cruz Bolivia 17° 911 289 Santiago Chile 35° 895 284 Sao Paulo Brazil 23° 913 289 CENTRAL AMERICA Belmopan Belize 17° 911 289 Guatemala, DF Guatemala 15° 908 288 San Pedro Sula Honduras 16° 909 288 Tegucigalpa Honduras 14° 907 288 San Salvador El Salvador 13° 905 287 Managua Nicaragua 12° 903 286 San Jose Costa Rica 10° 900 285 Panama City Panama 9° 891 282 USA (Detailed Listing) Albuquerque NM 35° 895 284 Atlanta GE 34° 898 285 Baltimore MD 39° 883 280 Bismarck ND 47° 831 831 Boise ID 44° 852 270 Boston MA 42° 866 275 Burlington VT 44° 852 270 Charleston SC 33° 901 286 Charleston WV 38° 886 281 Cheyeen WY 41° 873 277 Chicago IL 42° 866 275 Cincinnati OH 39° 883 280 Concord NH 43° 859 272 Dallas TX 33° 901 286 Denver CO 40° 880 279 Des Moines IA 42° 866 275 Detroit Ml 42° 866 275 Fairbanks AK 33° 901 286 Hartford CT 42° 866 281 Honolulu HI 21° 914 290 Indianapolis IN 40° 880 279 Jakson MS 39° 883 280 LasVegas NV 36° 892 283 Little Rock AR 35° 895 284 Los Angeles CA 34° 898 285

Louisville KY 38° 886 281 Memphis TN 35° 895 284 Milwaukee Wl 43° 859 272 Minneapolis MN 45° 845 268 Montgomery AL 32° 904 287 Newark NJ 41° 873 277 New Orleans LA 30° 910 288 New York NY 41° 873 277 Oklahoma City OK 35° 895 284 Omaha NE 41° 873 277 Ortando FL 29° 911 289 Philadelphia PA 40° 880 279 Phoenix AZ 33° 901 286 Pierre SD 44° 852 270 Portland ME 44° 852 270 Portland OR 46° 838 266 Providence Rl 42° 866 275 Raleigh NC 36° 892 283 Richmond VA 38° 886 281 Salt Lake UT 41° 873 277 Seattle WA 48° 824 261 St. Louis MO 39° 883 280 Washington DC 39° 883 280 Wichita KS 38° 886 281 Wilmington DE 40° 880 279