9. Thermal Mass

Thermal Mass

The ability of a material to absorb heat as its temperature rises, and to release heat as it cools is an extremely useful tool in improving building energy performance and comfort.

Specific heat of materials

It enables energy storage within the actual materials of the building, attenuates temperature extremes, and provides valuable time delays in the flow of heat throughout a building.

There are many examples throughout history of buildings which made use of large amounts of thermal mass to moderate temperature extremes…

Specific heat of materialsIn some instances, it can even be considered a type of pseudo thermal resistance within building enclosure assemblies.

or delay the flow of heat through the assemblies of the enclosure.


There are many examples throughout history of buildings which made use of large amounts of thermal mass to moderate temperature extremes…

In some instances, it can even be considered a type of pseudo thermal resistance within building enclosure assemblies.

The specific heat capacity is defined as the amount of heat required to raise the temperature of a specified mass of material by a given temperature.


where: !Q = change in heat (J)

c = (mass) specific heat of material (J/kg°C) m = mass of the material (kg) !T = change in temperature (°C)

!Q = c m !T

The relationship between the temperature change and the heat required to make that change is given by:

Specific heat of materialsThis property of a material, which permits storage and subsequently release heat, creates what is known as the thermal flywheel e!ect due to its ability to moderate or even out temperature swings.

This property is also referred to as the thermal capacitance or thermal mass of a material.

Its e#ect can be experienced in many older buildings constructed of massive materials, as they can remain relatively cool even through extended periods of extreme heat.

Values of specific heat for some common construction materials:

material (J/kg°C) material (J/kg°C) gold 126 concrete (structural) 880lead 128 marble 879platinum 134 aluminum 900silver 238 limestone 908brass 380 plaster (sand) 920copper 385 brick (common) 920iron 452 concrete (light) 962wood (oak) 500 brick (hard) 1,000wood (white pine) 600 plaster (light) 1,000wood (balsa) 700 polycarbonate sheet (Lexan) 1,470stone 753 ice (-10°C) 2,050granite 790 ethyl alcohol 2,400glass (window glass) 830 water 4,186

Specific heat of materialsSometimes, the specific heat capacity is defined on the basis of unit volume rather than unit mass, and is then referred to as the volumetric heat capacity, or the amount of heat required to raise the temperature of a specified volume of material by a given temperature.


where: !Q = change in heat (J) "c = volumetric heat capacity (J/m3°C) " = density (kg/m3) c = (mass) specific heat of material (J/kg°C)

v = volume of the material (m3) !T = change in temperature (°C)

!Q = ("c) v !T

For any given material, the value of specific heat identifies the amount of heat energy the material absorbs as its temperature is raised.


It does not however indicate how rapidly the material absorbs or releases this energy, and for this we must look at a combination of other material properties…

Thermal di!usivity is a property which characterizes the speed at which a temperature change – or front – propagates through a material, and is defined as follows:

Thermal di#usivity

α = λ

ρc where:$ = thermal di#usivity (m2/s)

% = thermal conductivity (W/m°K)

" = density of the material (kg/m3)

c = (mass) specific heat capacity (J/kg°K)

For materials with a high thermal di!usivity, temperature fronts move rapidly and the material adjusts its temperature quickly to that of its surroundings.

Thermal properties of some common construction materials:

materialmass specific heat capacity density

volumetric heat capacity

thermal conductivity

thermal di!usivity

c " "c # $ = #/"cJ/kg°K kg/m3 MJ/m3°K W/m°K m2/s (x10-6)

wood (oak) 500 760 0.38 0.17 0.45wood (pine) 600 450 0.27 0.12 0.44granite 790 2,700 2.13 3.00 1.41window glass 830 2,600 2.16 1.05 0.49adobe brick 836 1800 1.50 0.60 0.40marble 879 2,563 2.25 2.50 1.11concrete 880 2,250 1.98 1.32 0.67limestone 908 2,360 2.14 1.30 0.61sand plaster 920 1,860 1.71 0.72 0.42common brick 920 1,920 1.77 0.72 0.41gypsum wallboard 1,090 800 0.87 0.16 0.18soil (14% moisture) 1,170 1,200 1.40 0.37 0.3polycarbonate 1,470 1,200 1.76 0.19 0.11water 4,168 1,000 4.17 0.58 0.14

Thermal properties of some common construction materials:

materialmass specific heat capacity density

volumetric heat capacity


thermal di!usivity


polycarbonate 1,470 1,200 1.76 0.19 0.11water 4,168 1,000 4.17 0.58 0.14gypsum wallboard 1,090 800 0.87 0.16 0.18soil (14% moisture) 1,170 1,200 1.40 0.37 0.26adobe brick 836 1800 1.50 0.60 0.40common brick 920 1,920 1.77 0.72 0.41sand plaster 920 1,860 1.71 0.72 0.42wood (pine) 600 450 0.27 0.12 0.44wood (oak) 500 760 0.38 0.17 0.45window glass 830 2,600 2.16 1.05 0.49limestone 908 2,360 2.14 1.30 0.61concrete 880 2,250 1.98 1.32 0.67marble 879 2,563 2.25 2.50 1.11granite 790 2,700 2.13 3.00 1.41

material mass specific heat capacity

density volumetric heat capacity


thermal di!usivity


lead 128 11,350 1.45 35 24

gold 129 19,300 2.49 314 126

platinum 134 21,450 2.87 72 25

tin 210 7,290 1.53 67 44

silver 238 10,500 2.50 415 166

brass 380 8,553 3.25 105 32

copper 386 8,940 3.45 390 113

zinc 387 7,140 2.76 132 48

iron (pure) 452 7,897 3.57 72 20

stainless steel 460 7,680 3.53 16 5

mild steel 500 7,850 3.93 45 11

aluminum 897 2,740 2.46 220 90

Thermal properties of some common metals:

material mass specific heat capacity

density volumetric heat capacity


thermal di!usivity


stainless steel 460 7,680 3.53 16 5

mild steel 500 7,850 3.93 45 11

iron (pure) 452 7,897 3.57 72 20

platinum 134 21,450 2.87 72 25

lead 128 11,350 1.45 35 24

brass 380 8,553 3.25 105 32

tin 210 7,290 1.53 67 44

zinc 387 7,140 2.76 132 48

aluminum 897 2,740 2.46 220 90

copper 386 8,940 3.45 390 113

gold 129 19,300 2.49 314 126

silver 238 10,500 2.50 415 166

Thermal properties of some common metals:

The impact of thermal di!usivity is most readily apparent in situations with non-steady state conditions.

One simple application is where there is a step change in temperature at one location, and the system responds accordingly over time.

Thermal di#usivity

Looking at the example of a semi-infinite body at a constant initial temperature T0:

initial temperature T0

Step changeThe temperature on the face undergoes a step change to a new temperature T1. The temperature at a location x from the surface and at time t is given by:

T ( x ,t )= T0 + (T1−T0 ) erfc

x4αt

⎛⎝⎜

⎞⎠⎟

initial temperature T0

xT1

The right-most expression is known as the complementary error function.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

erfc

(s)

s

Complementary error function

erfc s( )

erfc(0) = 1

erfc(0.5) ≅ 0.5

erfc(+&) = 0

Step change

T ( x ,t )= T0 + (T1−T0 ) erfc

x4αt

⎛⎝⎜

⎞⎠⎟

erfc(0) = 1

erfc(0.5) ≅ 0.5

erfc(+&) = 0

xinitial temperature T0T1

Depending on the value of the expression within the parentheses, the complementary error function has the following values:

Step change

T ( x ,t )= T0 + (T1−T0 ) erfc 0.5( ) = T0 + (T1−T0 ) (0.5)

=T0 +0.5T1−0.5T0 = 0.5(T0 +T1)

Since: erfc(0.5) ≅ 0.5


This is the temperature half way between the original temperature T0, and the new temperature T1.

This gives us an indication of how the “0.5 temperature front” moves into the material over time.

x4αt

⎛⎝⎜

⎞⎠⎟= 0.5

Solving the expression in the parentheses for either x or t will identify the location of this “0.5 temperature front” as it moves through the material.

Step change


x0.5 = 0.5 4αt = αt

t0.5 =

x 2

α

Notice that the equation is a function of the thermal di!usivity $ of the material.

gives x-location of the 0.5 front at a given time

gives time for the 0.5 front to reach a certain location

Another application is where there is a periodic variation in temperature at one location, and the system responds accordingly.

Periodic variation

T (t )= T2 sin

2πttp

⎛

⎝⎜⎞

⎠⎟

where:

tp = period of cycle

T2 = amplitude

xT

Temperature variation at surface:

T ( x ,t )= T2 (e− x /dp ) sin2πttp

− xdp

⎛

⎝⎜⎞

⎠⎟

Periodic variation

reduction in amplitude

time delay

dp =

αtp

π= periodic penetration depth (m)

= depth at which the amplitude is reduced to 37% of the original

Temperature variation at location x from the surface:

Periodic variation

37%

dp

Ground heat flowThe temperature of the ground typically exhibits less variation than does the temperature of the air, reducing in amplitude at increasing depth.

There is also a noticeable lag behind the mean air temperatures.

Ground heat flowThis means that building foundations are exposed to less severe temperature extremes than above-grade portions of the building.

Note that the energy stored in a material as a result of its specific heat does not involve any change in phase of the material – only the temperature.


This is referred to as sensible heat storage.

If a phase change occurs, it is necessary to add or remove a certain amount of heat – referred to as latent heat – during which time there is no change in temperature.

Latent heat of materials

This phase change process has the potential of storing large quantities of heat, and is referred to as latent heat storage.


The latent heat of vaporization is the heat required to transform a material from a liquid to a vapour.

The latent heat of fusion is the heat required to transform a material from a solid to a liquid.

A class of materials known as eutectic salts (para'n-like materials) is one type of phase change material (PCM) that has occasionally been used in such construction applications.

One of the limitations of using latent heat as a means of storing energy is that the temperature swing in question must straddle the temperature over which the phase change of the material occurs, which is why reference is made to them being temperature-specific.

This limitation is clearly not present when using sensible heat as a storage mechanism.


Because of these limitations, the use of latent heat has never seen extensive use as a heat storage mechanism except in quite limited applications.

This may change however with research into new materials…

Another limitation that was discovered with certain PCM’s is that after a number of freeze-thaw cycles they lose their ability to completely thaw out, limiting their long-term thermal storage potential.


A fairly recent innovation has been to embed phase change materials (PCM) at a microscopic scale within typical construction materials.

One example is gypsum wallboard, a widely used interior-surfacing material, where tiny spheres of para'n 5-10 microns in diameter are encapsulated within acrylic shells and mixed with the gypsum.


The para'n changes phase at about 23°C, which is quite close to comfortable interior air temperature.

This product has the capacity to store about 250 KJ/m2 over its phase change temperature.

Another building product with the trade name EcoCore, exploits similar properties of a PCM, enclosed within steel panels. It is installed as floor panels in locations which receive direct sunlight, and thus can benefit most from temperature variations in the space.

Latent heat of materialsEcoCore: How it works

12:0

0 AM

2:00

AM

4:00

AM

6:00

AM

8:00

AM

10:0

0 AM

12:0

0PM

2:00

PM

4:00

PM

6:00

PM

8:00

PM

10:0

0 PM

12:0

0 AM

Inte

rior T

empe

ratu

re

Typical O!ceEcoCore O!ce

ENERGY SAVINGS

PEAK LOAD

OFFSET

PEAK LOAD REDUCTION

EcoCore Perimeter Solution

Using EcoCore in the perimeter zone of the office will help to reduce the overall peak load in the space and delay the occurrence of the peak

load to later in the day. By reducing the overall peak load the amount of cooling required to keep the space comfortable is reduced. In

addition, by delaying the peak to later in the day the load can often be handled with free economizer cooling or with reduced rate electricity.

55

EcoCore Reduces and Offsets Peak Load to Save Energy

Solar load warms the panels during the day.As the panels warm the phase changematerial melts absorbing energy.

As the panels cool overnight the phasechange material solidifies.

The energy is stored in the panels to bereleased during non-peak hours.

2:00PM 8:00PM 2:00AM

EcoCore Brochure:Perimeter Solutions 3/8/12 2:16 PM Page 5

The text and images used in this presentation have been obtained from a number of di!erent sources. This information has been assembled speci"cally for the delivery of the course CIVL 478 Building Science & the Building Enclosure, and forms an integral part of the course material which is required for examination.

The presentation is intended for educational purposes only, to be used solely by students enrolled in the course. It is not to be distributed electronically or in hard copy format to any other party.

Greg Johnson

Documents

9. Thermal Mass