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A brief guide and free tool for the calculation
of the thermal mass of building components
Daniel Rüdisser, © 2018
In the following text, I will try to provide essential information on thermal mass calculation for building
applications. The second part is a brief guide to understanding and using my free Excel-calculator.
Summary for users not willing to read the whole text…
Putting it in a nutshell, the most relevant application of the tool will be the optimisation (=maximisation) of
thermal mass on the interior surfaces of buildings. This will help to reduce the daily temperature swings inside
the building. By increasing the internal mass, your wall, floor, or ceiling should be able to absorb most of the
solar inputs during the day and release the accumulated heat through natural ventilation during the night.
For this purpose, you will have to maximise the resulting figure "internal areal heat capacity" in the tool. As you
will see, this property depends mainly on the internal surface layer - up to a few centimetres or even millimetres
below the surface. Therefore in order to achieve high thermal capacity, you will have to choose a material with
high thermal conductivity and density of this topmost internal layer.
I regard the other calculation results (time shifts, periodic transmittance…) as being of minor importance.
However, to fully understand the topic or for special applications, I still recommend reading the whole text
below…
Introduction
The following calculations are based on the methods described in standard ISO 13786. Without explicitly
mentioning it, the standard applies well-known calculation methods used in electrical engineering to describe
the behaviour of components in alternating current circuits. The calculations are carried out by utilising matrices
of complex numbers.
In order to analytically solve these equations, the boundary conditions (temperatures or heat-fluxes), as well as
the resulting variables (temperatures and heat-fluxes), are assumed to be of a sinusoidal shape having a period
of 24 hours. Even if this sounds like a severe limitation, it is actually an appropriate and useful assumption. The
consideration of a sinusoidal shape is suitable since the actual, average daily temperature swings essentially
correspond to sine waves - or have at least a dominant sinusoidal component (see Fourier theorem). The
restriction to periodic lengths of 24 hours is also reasonable, as a cyclic temperature variation can only be
expected within this 24h time-frame.
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Internal thermal admittance
The calculation result value thermal admittance describes the ability of a surface to absorb and release heat
(energy) upon a periodic sinusoidal temperature swing with a period of 24h. The value represents the amplitude
of the heat-flux (=maximum value) caused by a 1 K (°C) temperature swing. The temperature on the opposite
side of the wall is assumed to be held constant. Due to the linearity of the underlying equations, you can simply
multiply the value with any other temperature amplitudes to get the corresponding heat fluxes. E.g. if you want
to estimate the maximum heat flux into/out of your wall caused by an internal temperature swing of 6 °C, and
the internal thermal admittance of your wall is 5 W/(m²K), then the maximum heat-flux will be 6 K * 5 W/(m²K) =
30 W/m². Therefore the "response" of this wall to a sinusoidal 6 °C periodic temperature swing will be a
sinusoidal heat flux absorbing up to a maximum of 30 Watt per square meter during the day and releasing the
same 30 W/m² at night.
The ability of a wall to absorb energy during the day is crucial to avoid summertime overheating - or to reduce
cooling costs. The internal thermal admittance can be used to evaluate this ability. However, the internal areal
heat capacity, which is almost proportional to this value, is actually more suitable for this job (see below).
Time-shift - internal thermal admittance
The heat flux caused by the temperature swing is time-shifted, meaning that it does not have its maxima and
minima simultaneously. The heat flux usually leads the swings in ambient temperature - whereas the actual
surface temperature of the wall will lag. So if the displayed output value for the time shift is "2:00" (like in the
example above), the maximum heat-flux in/out of the wall will occur 2 hours earlier than the temperature
maximum/minimum.
This time shift is just a "side-effect" of the heat buffering and cannot really be influenced/designed without
changing the heat capacity of the wall. It is actually a consequence of the wall's lagging/trailing surface
temperature, as the difference between the surface temperature and the ambient temperature is relevant for the
resulting heat flux.
External thermal admittance
Corresponding to the internal thermal admittance (see above) the external thermal admittance describes the
ability to buffer heat upon external temperature swings. Again, it is assumed that the temperature on the
opposite side is held constant.
Regarding the significance of this value, please refer to external heat capacity below.
Time-shift - external thermal admittance
Again, corresponding to the internal time shift, this result value indicates for how long the heat-flux
maxima/minima will lead the temperature maxima/minima.
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Periodic thermal transmittance
The output value of periodic thermal transmittance describes the heat flux induced by a temperature swing on
the OPPOSITE side of the component, assuming that the ambient temperature on the same side of the wall is
held constant. Although it seems that the periodic thermal transmittance, along with its phase shift, is the
favourite topic of quite some building scientists and insulation marketing specialists, the effect of the periodic
thermal transmittance can nowadays be neglected for most building applications. Based on modern insulation
standards (low U-values), the heat flux variations that will actually be induced by temperature swings on the
opposite side of the building component will be minor. To illustrate this, we can use the tool to calculate the
effect on the periodic thermal transmittance of light-weight insulation vs. heavy-weight insulation. We can
demonstrate this with a simple wall (or roof) consisting solely of 20 cm of reinforced concrete and 15 cm of
external insulation. A high external temperature variation of +/-15 °C is assumed (=a range of 30°C). Based on
these assumptions, we get the following results:
Light-weight insulation (25 kg/m³): temperature swings internal surface: +/- 0.10°C, heat-flux: +/- 0.77 W/m²,
phase-shift: 7.6 hours
Heavy-weight insulation (250 kg/m³): temperature swings internal surface: +/- 0.04°C, heat-flux: +/- 0.34
W/m², phase-shift: 14.6 hours
This means that effect can be seen very well from a relative point of view. However, the difference is hardly
relevant regarding its absolute impact, as the resulting total heat fluxes are minor compared to other heat
sources (e.g. unshaded or open windows).
Time-shift of periodic thermal transmittance
The value describes the lag that the heat wave induced by a temperature swing on the opposite side of the wall
will have. In order to stay in line with the other time shift values, the negative sign expresses that the heat flux
lags the temperature swings on the other side of the wall. Often it is stated that a time shift of 12 hours should
be targeted, as this means that the maximum of the heat waves will arrive on the other side of the wall when the
temperatures are lowest (or vice versa). Regarding building components matching modern building standards,
this rule can be considered obsolete, as the actual surface temperature swings that are caused by temperature
swings on the opposite side of the building component are usually within the range of tenths or even a few
hundredths degrees Celsius. The resulting fluxes are, therefore, typically negligible.
Internal areal heat capacity
The value of the internal heat capacity describes the ability of a building component to buffer heat during a
diurnal cycle. The value specifies the amount of heat that can be buffered by one square meter during one day
on a temperature swing of 1 degree; therefore, its unit is kJ/m²K. Since the underlying equations are linear, it is
possible to multiply this value with any other temperature amplitude to calculate the corresponding amount of
heat that can be buffered.
The areal heat capacity is calculated by integrating the heat fluxes described by the thermal admittances for a
whole day. Unlike the definitions of the “single” thermal admittances are defined, the internal areal heat capacity
considers temperature swings on both sides of the building component. Applying complex-number algebra, it
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can be calculated based on internal admittance and periodic transmittance. Depending on the actual temporal
phase shift of the periodic transmittance, it can either increase – or decrease the capacity compared to a
situation with constant external temperatures. However, as mentioned above, the influence of the periodic
transmittance will be minor for high insulation standards. For this reason, the internal areal heat capacity is
usually largely proportional to the internal thermal admittance.
It is essential to have a sufficiently large internal heat capacity to avoid overheating risks in summer and/or to
reduce related cooling costs. On a summer day, the total heat capacity of the interior of the building should be
able to absorb the excess heat during the daytime to subsequently discharge it during the nighttime by using
natural ventilation at lower outdoor temperatures. The larger the amount of available internal heat capacity is,
the lower the internal temperature swings will be. Obviously, on the first hand, daytime heat fluxes into the
building should be restricted through optimal shading and by keeping windows and doors closed.
In order to determine the total heat capacity of a room, the specific areal heat capacities of all constructions are
multiplied by their actual surfaces (ceiling, floor, wall-1, wall-2,…) and subsequently added. Using the provided
tool, you will find out that the areal heat capacity depends primarily on the material of the innermost layer. This
material should be sufficiently thermally conductive and exhibit a high heat capacity (mainly determined by its
bulk density and conductivity).
This means: a concrete ceiling will be significantly better than a suspended ceiling, a stone floor will perform
better than a parquet floor (or even carpet), a thick gypsum-fibre board will outperform thin gypsum-plaster
board, etc.
External areal heat capacity
Corresponding to the internal areal heat capacity, it describes the ability of a building component to buffer heat
on a diurnal temperature cycle on the external surface. Again the heat flux originating from temperature swings
on the opposite (now internal) side of the building are also being considered (but usually of minor significance).
From a practical point of view, the external areal heat capacity can be interesting if you are interested in reducing
the temperature swings of your façade. This can be a matter of comfort, but there is also another important
aspect: it is a significant disadvantage of modern polystyrene facades that they exhibit extremely low external
heat capacities. This is a consequence of the combination of lightweight insulation materials with only a very thin
layer of render. The lack of heat capacity leads to high surface temperatures during the daytime and – maybe
even more problematic – to low surface temperatures during the night. Due to the extremely low heat capacity,
the comparably low radiative cooling effect, linked to clear night skies, can lower the façade temperatures even
below ambient air temperatures. Consequently, relative humidity levels on the surfaces are elevated, and the dew
point is often reached. The façade temperatures, slightly lower than ambient temperature, can enable or
significantly boost the growth of algae or fungi on the façade. This problem is currently addressed by adding
problematic chemical growth inhibitors to the renders or colours, which pose a threat to the environment.
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Application notes for the tool
General
The Excel tool is split into four sheets with different functionalities:
• Calculation-Tool
This is the main sheet where the calculation is performed. Enter your material layers and surface
resistance values here to get the results (also on this sheet).
• Interactive Chart
On this page, an interactive diagram illustrates the temperature and heat-flux variations over time. You
can set ambient temperature swings for one or both sides of the building component and view the
resulting hea -fluxes and temperatures on both surfaces of the component.
• Materials
On this sheet, I have provided typical material data for 200 commonly used materials. You can copy &
paste values to the calculation sheet.
• Validation example
On the last sheet, the validation example provided by the standard ISO 13786 is calculated to prove the
validity of the algorithm.
Surface resistances Rsi and Rse
Apart from the material layers, you will have to enter the correct surface resistances for your calculation. These
describe the heat transfer from an environment into or out of the surfaces of a building component. They
represent a simplified model, as the actual heat exchange results from a combination of the three physical
processes (radiation, convection, and conduction). More on the theory and recommended values can be found
on the HTflux website (https://www.htflux.com/en/documentation/boundary-conditions/surface-resistance-heat-
transfer-coefficient/).
Please note that for the purpose of standard capacity calculations, it is recommended to use a value of
0,13 m²K/W for all cases when the heat fluxes are predominately caused by the internal temperature swings and
there is no, or only little net average heat flux during one day. This means that when you would normally use
0.10 or 0.17 m²K/W for upward or downward heat-flux on U-value calculations for ceilings or floors, it might be
more appropriate to use 0,13 m²K/W for either case to calculate heat-capacities. Whenever the major heat-flux
caused by the 24h temperature swings is greater than the average net outflow or inflow and, therefore, the total
heat-flux changes its direction (sign) two times a day, it will be more suitable to use this value.
Internal walls, ceilings, floors
Of course, you can also use the tool to calculate the heat capacities of internal building components. In this case,
just use the same surface resistance value (usually 0.13 m²K/W) for each side of the component. The labels
"internal" and "external" will then only serve as a reference to identify the specific side of the wall.
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Floors with ground contact
You can also use the tool to calculate floors' (or walls’) internal areal heat capacity with ground contact. For this
purpose, I recommend adding a 2m thick layer of soil (e.g. use clay/silt of the material list) to the external side of
the building component. Of course, only the internal result values will be of interest in this case. (For the chart,
you would then use the monthly or yearly average soil temperature in this depth).
Chart
The chart will help you to understand the buffering effect of your building component, as well as the occurring
phase shifts on both sides. In order to better understand the effects, you can apply a temperature swing on only
one side – or you can apply temperature swings on both surfaces to reflect a more realistic situation. The 24h
temperature variations can be defined by specifying an average temperature, a temperature amplitude, as well as
a specific time for the maximum temperature.
Of course, the occurring temperature variations would also depend on the resulting heat fluxes going through
your component, but they primarily depend on solar inputs and ventilation. Therefore, a full-blown dynamic
building performance simulation would be required to precisely determine the actual temperature swings.
However, in order to understand the process and estimate the potential range of the surface temperatures and
heat fluxes, it is sufficient to apply realistic assumptions for the internal and external temperatures.
Material list
The tool also includes a list of material parameters for approx. 200 common materials. You can use copy&paste
to transfer the appropriate materials as layers to the calculation sheet. For accurate calculations, you should use
the precise values that you should usually find on the data sheet of the specific product. If you use our HTflux
Software you can use additional materials from the online material database.
Download-link to free calculation tool (bottom of page):
https://www.htflux.com/en/free-calculation-tool-for-thermal-mass-of-building-components-iso-13786/
For more detailed analysis, simulations, material properties database, etc. please make use of our HTflux
Software.
www.htflux.com, Daniel Rüdisser, © 2018
This excel tool is developed for free use and distribution. The tool has been validated, however, we accept
no liability for the calculation results or any losses or damages connected to them.