Building Science

The Physics of Thermal Inertia in Low-Slope Roof Design

By Thomas J Taylor

January 13, 2021

Commercial building with a masonry facade

What are the key material properties?

In a previous article the use of thermal inertia to slow down heat flux through a roof assembly was discussed. In buildings where air conditioning costs dominate and heating use is relatively low, higher thermal inertia assemblies can potentially improve energy efficiency. This is particularly the case of buildings such as offices that are only occupied during daylight hours. Thermal inertia could delay the transmission of heat into a building towards the end of the day, increasing thermal comfort and allowing facility managers to reduce cooling during the day.

While the previous article provided an introduction to thermal inertia and its potential benefits, it didn't discuss the origin of the property. Also, the related but different terms, thermal inertia and thermal mass, were used somewhat interchangeably.

This article describes the material properties that contribute to thermal inertia and provides a basis for material selection when increased thermal inertia is a goal.


A building enclosure with high thermal inertia will slow down the transmission of heat. This effect has traditionally been used in the Mediterranean and other temperate climates to improve thermal comfort during the summer. As the building exterior surface heated up during the early afternoon period, high thermal inertia reduced the heat transmission into the interior. This was advantageous in the days before air conditioning. Today, designing with higher thermal inertia, as described in part one of this series, could improve energy efficiency in certain situations:

  • Buildings located in areas where energy costs are dominated by air conditioning.
  • Buildings only used during the day and not on a 24 hour basis. Thermal inertia can push heat loads into the evening, allowing for either temperature settings to be raised or HVAC fans speeds to be reduced.
  • For high thermal inertia within the roof assembly to have a significant effect, low to moderate rise buildings with larger footprints would be best.

Thermal Inertia Effects

There are two key characteristics of thermal inertia; the decrement factor and time delay, both of which can be readily modeled and experimentally verified. A schematic showing these is shown below:

The time delay is calculated as:

Φ = t[Tout(max)] - t[Tin(max)]

Where t[Tout(max)] and t[Tin(max)] are the time of day when the inside and outside surface temperatures reach maximum. The decrement factor, DF, is calculated from:

DF = (Tin(max) – Tin(min)) / (Tout(max) – Tout(min))

  • The time delay and decrement factor could be used by building designers and operators to better optimize thermostat specification, HVAC use, and temperature schedules. As noted earlier, a large time delay could significantly reduce daily AC cooling demands for office buildings.
  • Larger decrement factors can improve occupants' thermal comfort. Temperature swings are reduced, which in turn reduces HVAC cycling.
  • Importantly, high thermal inertia will not reduce the energy reaching the interior, it only delays the transmission. This can make increased thermal inertia part of a strategy to improve energy efficiency in buildings occupied during the day but not necessarily for those occupied on a 24-hour basis.

Roof Configurations and Thermal Properties

Building designers and construction professionals are familiar with the property of thermal resistance, which is a measure of the extent to which a material blocks or resists heat transfer. It is expressed as R-value or U-value, which are numerical descriptions of the extent to which a material can resist heat flow.

However, there is far less familiarity with the time delay of heat transfer, or the extent to which a material slows down or delays heat transfer. As will be seen, a material can have low thermal resistance but still delay heat transfer. This is the crux of the underlying properties "thermal diffusivity", "thermal mass" and "thermal inertia".

Fundamental Thermo-Physical Properties

There are three fundamental thermo-physical properties of materials that are the components of thermal diffusivity, thermal inertia, and thermal mass. These are thermal conductivity, density, and specific heat capacity.

Thermal Conductivity

Building design professionals are very familiar with thermal conductivity, k, measured as watts per meter per Kelvin (W/(m.K)). It is normally used to characterize individual materials, for example polyiso foam, and is a measure of the heat flow through a material when a temperature gradient of 1K (i.e 1°C) is applied.

A related term, the u-factor, is used to describe the thermal conductivity of a system. This could be a window, i.e. a combination of glass, air space, and frame etc.

Thermal conductivity is measured when heat flow has equilibrated and it doesn't include any time delay.


Density is a measure of the mass per unit volume, ρ=m/v. While this is straightforward for most materials, products such as polyiso can be harder to define. There are the facers and a small density gradient within the foam. Later, as values are listed, the facers will be ignored and the foam's density considered as an average.

Specific Heat Capacity

Specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 kelvin, or Cp = J/(kg.K). It is worth considering the simple diagram above, showing the measurement of thermal conductivity. At the onset, heat flow through the material is delayed by its specific heat capacity. It takes energy to raise its temperature, an action required before heat can then transmit.

Derived Thermo-Physical Properties

As noted, the fundamental properties described earlier are all measured at equilibrium and do not include any time lag or delay. For that, the following derived properties need to be considered.

Thermal Diffusivity

Thermal diffusivity is a measure of the rate at which a temperature propagates from one point to another point in a material. It's the rate of transfer of heat from a hot side to a cold side and is calculated as:

In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'. In a sense, thermal diffusivity is what is meant when the topic of thermal inertia is discussed casually.

Thermal Inertia

Thermal inertia is the slowness with which the temperature of a material approaches that of its surroundings. It is a product of thermal conductivity, density, and specific heat capacity. From a building enclosure perspective, it could be considered as the rate at which the interior surface can supply heat into the interior, assuming a temperate climate.

It is arguable that thermal inertia is not the best property to use to characterize a building enclosure component in terms of thermal lag.

Thermal Mass

It is often broadly thought that thermal mass is essentially equivalent to gravimetric mass. Conceptually, this gives rise to the view that the more massive a construction the better. However, consider two blocks - one of steel and one of concrete - each having the same gravimetric mass. The two materials have different specific heat capacities and are not equivalent in terms of thermal properties. In addition, steel has a significantly higher thermal conductivity versus concrete.

Thermal mass is a property of a material that enables it to store heat and is the product of density and specific heat capacity:

Importantly, thermal mass doesn't fully describe thermal lag. High thermal mass would change the decrement factor, dampening out heat transmission but is only indirectly linked to thermal delay.

Roof Component Thermal Properties

Two deck types are predominant in North American construction of big-box type architecture; steel and concrete. Two possible idealized roof assemblies are shown below, based on the two roof deck types:

  • Both systems have most roof assembly layers adhered. The steel deck system has a first layer of mechanically attached gypsum board to act as a substrate for the adhered first layer of polyiso.
  • Thermal bridging is either minimal in the steel deck based system or absent in the concrete deck system (ignoring any real world penetrations).
  • The first layer of gypsum board in the steel deck case could be used as a substrate for a vapor retarder.

The membrane, adhesive layers, and steel deck are relatively thin and have no significant insulating properties. The following table shows the fundamental and derived thermo-physical properties of the other components:

thermal inertia chart

  • Polyiso and HD Polyiso specific heat values are estimates.
  • Concrete properties are very dependent on aggregate type and moisture level. Data shown represents average values for dry concrete.

Unsurprisingly, the data shows that concrete has significantly higher thermal mass and inertia versus the other materials compared in the table. As discussed in the first part of this series, insulation is best placed closest to the building exterior, and thermally massive materials placed closest to the interior. The southeast region tends to use concrete decks more than many other regions of the US, largely for improving the strength of the roof deck. This could also mean that, especially for those buildings occupied only during the day, such as offices, schools, and the like, have better opportunity for energy-efficiency benefits with well-designed roof insulation systems.


  • Thermal property data could be used in modeling exercises to better understand how to design and optimize energy-efficient buildings.
  • Clearly, concrete has a far higher thermal mass and inertia than other materials commonly used in roof assemblies.
  • Very lightweight concrete and gypsum board have very similar thermal mass, thermal inertia, and density, but have notably different properties for thermal diffusivity and conductivity.

Thermal property data is fundamental to the materials used in low slope roof assemblies. However, it needs to be converted into values specific for the thickness and weight of actual roof products. That will be a topic for the next part of this series.

Sources Used

  1. Verbeke, S., Thermal inertia in dwellings. Quantifying the relative effects of building thermal mass on energy use and overheating risk in a temperate climate. PhD Thesis, University of Antwerp, 2017.
  2. Balaji, N. C., Mani, M., and Venkatarama, R. B. V., Thermal performance of building walls. 1st IBPSA Italy Conference, Building Simulation, 2013, pp. 151 – 159.

About the Author

Thomas J Taylor, PhD is the Building & Roofing Science Advisor for GAF. Tom has over 20 year’s experience in the building products industry, all working for manufacturing organizations. He received his PhD in chemistry from the University of Salford, England, and holds approximately 35 patents. Tom’s main focus at GAF is roofing system design and building energy use reduction. Under Tom’s guidance GAF has developed TPO with unmatched weathering resistance.

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By Authors Thomas J Taylor

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Polyiso installation
Building Science

Designing with Polyiso

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Within the insulation layer the temperature has a gradient between the hot and cold side, i.e. between inside and outside.As an example, consider a building in the winter to illustrate the point. The interior is 70 °F with 40% RH, like the example on the chart above. The temperature gradually drops from the innermost part of the insulation until at the outermost part it will be at the exterior, cold temperature. The plotting of temperature through the insulation thickness is referred to as the temperature gradient of that system. Using the example, if the temperature gets to the dew point of 45°F at any point in that system then water would be expected to condense on the nearest surface. This is shown in the following diagram:Summarizing, in this example the interior air has 40% of the total water vapor that it can support. But as the air migrates up through the roof system, it gets cooler until the point where it can no longer hold onto the water vapor and condensation occurs. In the example shown above, that's at 45°F and just inside the insulation layer.As will be discussed later, dew point calculations can be used to inform the placement of a vapor retarder layer when used.When a dedicated vapor retarder layer is not used, it is good practice to ensure that the dew point is in the upper layer of polyiso insulation. This will lower the risk of interior air migrating up through the roof assembly and condensing on a surface below its dew point.Using Vapor Retarders with PolyisoVapor retarders can be used to limit humidity ingress to the roof assembly. Under certain circumstances, depending on the building use and location, condensation can occur as discussed in the previous dew point discussion. In general there are four basic building conditions that can be considered:1. Buildings with Standard Amounts of Occupancy-Generated MoistureThese are the most common situations covering for example, office, retail, and warehouse spaces. The risk of having a condensation issue is low and good roofing practices such as sealing around penetrations may likely suffice.2. Buildings with Larger Amounts of Occupancy-Generated MoistureThis category includes apartments and other multiple residency buildings, paper mills, laundries, buildings with indoor swimming pools, and the like. In fact, anything that doesn't fit into category 1 above should be evaluated to determine humidity levels. The building's air handling and ventilation systems should be carefully specified to take into account the moisture loading.3. Construction–Related MoistureMost construction practices release some amount of moisture into the building space. These can be relatively short term such as drywall installation and painting. However, some practices can release large amounts of water over a considerable time frame into the building. These include poured in place concrete floors and roof decks.4. Concrete Roof DecksThese can present a challenge for roof system designers especially in new construction. Regardless of the type of concrete, significant amounts of water remain after curing is completed. Allowing concrete to thoroughly dry is most appropriate; however, it is often reasonably impractical. Dealing with potential moisture in concrete decks is beyond the scope of this article, but guidance can be found elsewhere.It is recommended that a building science professional experienced in designs for Categories 2, 3, and 4 be involved to determine whether a vapor retarder should be used and what type.Specification of R-ValuePolyiso is manufactured to meet the ASTM C1289 Standard Specification for Faced Rigid Cellular Polyisocyanurate Thermal Insulation Board. ASTM C1289 specifies the thermal resistance at a mean temperature of 75°F for various product thicknesses and requires that the values at 40 and 110°F be made available upon request.Important features of manufacturer's published R-values are:The values are an average across a temperature range. The test methods need the insulation specimen to have a hot and a cold side at least 40°F apart. Most reputable test labs use a difference of 50°F for accuracy. A published value at 75°F is actually an average R-value across the range of 50 to 100°F.To take into account the diffusion of gas out of, and air into the polyiso foam, the values are based on projected "Long Term Thermal Resistance" or LTTR, obtained by rapidly aging thin slices of the foam.The Polyisocyanurate Insulation Manufacturers Association, PIMA, conducts a third-party certification program to independently validate LTTR values. This is referred to as the PIMA QualityMark™ program. The LTTR values are considered as "labelled R-values" to be used by building design professionals.Label R-values represent a 15-year time-weighted average value. They can help a design professional estimate a building's energy efficiency without having to be concerned about long-term loss of performance, which is already factored into the value.Building design professionals designing roofs for ASHRAE climate zones 6 and 7 may need to use the R-value reported for a mean temperature of 40°F.Attachment PatternsThe various fastener patterns for polyiso have been mentioned in the previous sections. However, due to the impact of fasteners on thermal bridging and wind uplift resistance, the key points are summarized here:For systems that have both mechanically attached membrane and insulation, the membrane attachment provides the wind uplift resistance. The polyiso insulation fasteners are simply there to hold the insulation flat during the roof installation and to resist long term lateral movement.Typical fastener patterns are shown here:For systems with adhered single-ply membrane and mechanically attached polyiso boards, the insulation fasteners provide the wind uplift load resistance. This is the case whether both layers of polyiso are mechanically attached or only the bottom layer (in which case the upper layer would be adhered).Manufacturers have tested the fasteners per board required to meet wind uplift resistance requirements for these combined mechanically attached and adhered systems. The number of fasteners needed depends on the board size and thickness. For common systems, the numbers are shown in the table below:For each of these combinations above, manufacturers' handbooks provide fastener patterns.The number of fasteners for these combined mechanically attached and adhered systems is very large, for example a 125,000 s.f. big box type roof could require around 50,000 fasteners, resulting in significant thermal bridging.When installing over a steel deck, to reduce thermal bridging and to make for a more robust system with reduced condensation risk, it is advisable to only attach the first layer of polyiso and to adhere all subsequent layers and the membrane.If the first layer of polyiso is attached and the rest of the system adhered, then using a 1.5" thickness for that first layer would help to bury the thermal bridging fasteners. It could also put the dividing line between first and second polyiso layers below the dew point, which is advisable.ConclusionsPolyiso is a cost-effective roof insulation and has the advantage that its permeability is low. Good design and installation practices can result in low risks of condensation even for buildings with higher than normal humidity levels.When designed correctly, mechanically attached components with two layers of polyiso having staggered and offset joints can be part of a successful roof system.Adhered insulation and membrane roof systems have advantages including reduced or eliminated thermal bridging, lowered condensation risks, and better wind uplift resistance.In cases where building use anticipates higher interior humidity levels and/or the local climate suggests higher condensation risk, then a building science professional should be consulted as to vapor retarder use and specification.Building designers and specifiers are advised to use the labelled R-values shown for a mean temperature of 75°F. For projects in ASHRAE climate zones 5 and 6, values at 40°F could be used depending on the building's geometry and local energy costs.

By Authors Thomas J Taylor

March 17, 2021

Commercial roofers installing polyiso insulation
Building Science

Polyiso Insulation Explained

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This makes the impact of air conditioning greater than winter heating. Introduction Preventing water intrusion into the built environment during precipitation has always been regarded as the basic function of the roof. However, reducing heat flow through the building enclosure is a very important secondary function. Maintaining interior thermal comfort has always been an important part of residential construction, but it wasn't until the early 1970s that the use of thermally insulated steel roof decks became commonplace in commercial construction due to the need to lower building energy costs. Polyisocyanurate thermal insulation, commonly referred to as polyiso, has proven to be popular due to a combination of its cost effectiveness (i.e. cost per insulation unit), efficiency (i.e. insulation value per unit thickness), and fire resistance, as compared to some competitive materials. Polyiso has recently come to represent over 75% of the commercial roof insulation market. However, as polyiso has grown in popularity, so has the interest in understanding a more exacting insulation value of this material. With rising energy costs it is more important to accurately specify heating, ventilation, and air conditioning equipment (HVAC). In addition, once a building is completed, it is important that the owner/occupier be able to better anticipate future energy costs from a budgetary perspective. How Polyiso Is Made With any foam insulation material, the process begins with the plastic or polymer precursor materials being in the liquid phase. Gaseous blowing agent(s) is introduced either by some form of injection into the process or through chemical reactions that create the polymer matrix. Initially, the blowing agent(s) is present as an extremely fine dispersion. In the case of polyiso, pentane is used as the blowing agent and during the subsequent development of the matrix, heat is released. The heat causes the dispersed pentane to expand, forming gaseous cells. Growth of these cells ultimately results in cell impingement, the entire process being indicated schematically below: When the cells impinge, surface tension tends to cause the material between two cells to thin, and material between multiple cells to thicken. This results in so called cell windows and struts, as indicated here: The characteristics of the windows and struts, such as thickness, size, and number, influence the overall thermal resistance of the foam along with the blowing gas composition as discussed later. Key characteristics of polyiso are; The cells are 99% closed. This means that moisture doesn't condense within polyiso and that it limits the diffusion of moisture carrying air up through the roof assembly. The cell material, i.e. the polymer, represents less than 5% of the total foam volume. When it's said that shipping polyiso is like shipping air, it's because 95% of the weight is the gas within the cells. The material is a thermoset – in a fire situation it won't melt and then drip down through openings in the roof deck. Also, it is not affected by solvents unlike some other foams such as polystyrene. How Polyiso Insulates There are three ways in which heat can travel through a foam material, these being conduction, convection, and radiation, as shown schematically below; Conduction – closed cell foams, such as polyiso, consist of the polymer cells and the gas in those cells. The cell material, i.e. the polymer, represents less than 5% of the total foam volume and therefore, the thermal conduction of that material accounts for a very minor fraction of the total heat transfer. Furthermore, the path along the polymer from the hot side to the cold side is convoluted. Manufacturers strive for low foam density and polymer conduction can be generally considered to be negligible. The gaseous mixture within the cells represents more than 95% of the total foam volume. That gas phase accounts for essentially all of the thermal conduction through polyiso. The blowing agent used to create the foam will have a certain conductivity, however over time that blowing agent may diffuse out of the foam and air could diffuse in. The diffusion of gas into and out of polyiso is slower than for other polymer foams, such as those based on polystyrene. Convection is the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids, from a hot surface towards a colder surface. In foams such as polyiso, the cells are too small for any convection to occur. Also, the temperature difference across each individual cell is too small to cause convection. Radiation – thermal energy radiates from hot surfaces and is absorbed by materials depending on their opacity and thickness. Polyiso doesn't totally block thermal radiation; cell walls are considered to be too thin to absorb thermal radiation, however cell struts are thought to absorb and then re-radiate thermal energy. Manufacturers aim to make small cells, i.e. more cells per unit volume, to be more effective at blocking thermal radiation. Insulation's Benefit for a Roof Insulation has two main effects on heat flux into and out of a building. During the summer, flux of the heat from the sun down into a building is reduced. Similarly, reflective membranes also reduce the amount of heat but do so by reflection. During the winter, insulation reduces the heat flux out from the building, thereby lowering heating costs. Insulation delays the flux of heat into or out of a building. Polyiso has "thermal inertia" unlike, for example, reflective membranes which do not have this effect. For buildings such as offices, this delaying effect is a very important benefit of insulation. It means that the maximum air conditioning effort due to heat flux through the roof is required for less hours of the day. Specification of Thermal Resistance Polyiso is manufactured to meet the ASTM C1289 Standard Specification for Faced Rigid Cellular Polyisocyanurate Thermal Insulation Board. C1289 specifies the thermal resistance at a mean temperature of 75°F for various product thicknesses and requires that the values at 40 and 110°F be made available upon request. Important features of manufacturer's published R-values are; The values are an average across a temperature range. The test methods need the insulation specimen to have a hot and a cold side which are required to be at least 40°F apart. Most reputable test labs use a difference of 50°F for accuracy. So, a published value at 75°F is actually an average R-value across the range of 50 to 100°F. To take into account the diffusion of gas out of, and air into, foam, the values are based on projected "Long Term Thermal Resistance" or LTTR, obtained by rapidly aging thin slices of the foam. Beginning in 2003, the Polyisocyanurate Insulation Manufacturers Association, PIMA, established a third party certification program to independently validate LTTR values. This is referred to as the PIMA QualityMark™ program. The LTTR values are considered as "labelled R-values" to be used by building design professionals. Label R-values represent a 15-year time-weighted average value. They can help a design professional estimate a building's energy efficiency without having to be concerned about long term loss of performance, this being factored into the value. Validation of Label R-values The PIMA QualityMark™ program requires participating manufacturers to meet the following R-values for the various product thicknesses. The PIMA QualityMark™ program requires each manufacturing facility to submit to an annual verification of LTTR values. During verification, independent third-party representatives visit each facility and select a minimum of five boards for testing. The overall process is administered by FM Global. The results of a 2015 PIMA QualityMark verification testing are summarized below: A total of 33 samples were tested for each thickness at a mean temperature of 75°F. These values, obtained from a third party independent process, are reassuring especially given the large number of samples involved (33 samples x 5 specimens = 165 tests). The PIMA Quality Mark program exists to ensure that member manufacturers are held accountable to produce product meeting published label values. R-Value and Temperature As noted earlier, the ASTM polyiso specification requires that the value at 75°F must be published and that values at 40 and 110°F be available on request. The mean reference temperatures for the ASHRAE Climate Zones for winter and summer conditions, assuming an indoor design temperature of 68°F are shown here: From the data, it's clear that the R-value reported for a mean temperature of 75°F is appropriate for summer, and in many cases, for winter. Building design professionals designing roofs for ASHRAE climate zones 6 and 7 may need to use the R-value reported for a mean temperature of 40°F when evaluating winter heating requirements. Also, electricity costs are about four times the cost of natural gas on a British Thermal Unit of energy equivalent basis. When specifying insulation, if gas heat is being used then summer air conditioning costs could dominate and the R-value at the 75°F mean temperature could be the most important. The "R-Value Rule" While knowledge of a material's R-value is important to the commercial building market for the HVAC specifier and building owners/occupiers, home owners and individual consumers are generally unable to verify claims as to the thermal resistance. In the aftermath of the 1970's energy crisis, fraudulent R-value claims became so widespread the US Congress passed a consumer-protection law in response, the "R-Value Rule". The R-Value Rule "requires home insulation manufacturers, professional installers, new home sellers, and retailers to provide R-value information, based on the results of standard tests." Polyiso is used as continuous insulation in residential wall systems and roof assemblies in many apartment and high rise condominium buildings. It is unfeasible for polyiso manufacturers to differentiate between products going into residential versus commercial applications. Therefore, in practice the R-Value Rule covers all polyiso meaning that labeled R-values are legally enforceable. Conclusions Thermal conductivity of polyiso, in common with most other foams, is dominated by the thermal conduction of the cell gases. Contrary to popular understanding, R-values are reported as an average across a temperature range and do not represent a value at an exact temperature. For example, the reported R-value at 75°F is normally measured across a range from 50 to 100°F and should be noted as a mean R-value. Building designers and specifiers are advised to use the labelled R-values shown for a mean temperature of 75°F. For projects in ASHRAE climate zones 6 and 7, values at 40F °could be used depending on the building's geometry and local energy costs. Want to learn more? See my recent article in Interface.

By Authors Thomas J Taylor

October 07, 2020

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