CPD PROGRAMME Material
Brick (outer) Brick (inner)
Concrete block (heavy)
Concrete block (light)
Mineral wool (quilt)
Plaster (dense) Plaster (light) Plasterboard Steel
Wood Thermal conductivity
Density Specific heat
λ (W·m-1·K-1) ρ (kg·m-³) Cp, (J·kg-1 0.77 0.56 1.75
1,750 1,750 2,300
0.20 0.042
0.57 0.18 0.21 50
0.13 600 12
1,300 600 700
7,800 500
Figure 1: Example thermal properties of materials
diffusivity. So, considering the data in Figure 1, the thermal diffusivity of common materials ranges from about 1.4 x 10-5 steel down to towards 8 x 10-7
for for concrete
materials. Materials with higher thermal diffusivity values can be more effective for cyclic heat storage at greater depth than materials with lower values. The thermal effusivity, ·K-1
€ β = (λ·ρ·Cp)0.5 J·m-2 s-0.5 , is used to
represent the capacity of a material to absorb and release heat. This relationship is also known as the ‘thermal inertia’. It can be particularly useful when examining multi- layered structures with thin layers. Materials with high thermal effusivity will more readily dissipate heat from their surface, and so will be suitable for storage as well as having a high storage capacity. However, at a surface of a wall or roof there are additionally the convective and radiative coefficients that will more directly dominate the amount of heat transfer. The amount of heat flow will be determined by the surface roughness, shape and emissivity (for radiation) and the speed and turbulence of the air passing across the surface (for convection). The thermal admittance procedure2
€ is
based around a regular (and theoretical) 24-hour cycle of heating and cooling loads. The fundamental variables in the method may be calculated using an application of the standard non-steady state heat flow equation3
that considers how much heat
is stored in, and how much heat passes from, a small element of thickness x (m) of the structure in a time period t (s), in order to determine the change in its temperature, θ (K). So this can be shown,
www.cibsejournal.com in classical differential format as:
δθ δt = α δ2θ
δx2 and this is
rearranged in CIBSE Guide A3 to be
To solve this, matrices are applied (see €
Guide A3 for full details and a worked example). The resulting solution takes the internal and external surface resistances, and applies matrix coefficients to represent each of the layers (m, n…. etc.)
1 Rsi 0 1
⋅ m1 m2 m3
m1
⋅ n1 n3
n2 n1
... 1 −Rse
that using matrix multiplication can be reduced to
directly used to provide the key, non-steady state factors used in the admittance method. This calculation may be readily undertaken for single layer structures; however, to tackle more than one layer requires lengthy matrix manipulation and is better suited to computer methods (it employs imaginary number notation and can be quite straightforwardly laid out in a spreadsheet, as in the example at http://goo. gl/rxOoF). The principal values used in admittance method, as derived from the four matrix coefficients, are: Thermal admittance, Y (W·m-2
and the four coefficients, M1 €
·K-1 ),
provides the name for the method itself and is also a key parameter in determining the response of the internal surface of the building fabric to heat. It is a measure of
to M4
M3 M1 0 1
M2 M4
, are then
δ2 θ δx2
= ρc λ
δθ δt
·K-1 Diffusivity Effusivity ) α, (m²·s-1 ) β, (J·m-
1,000 4.40E-07 1,000 1,000
1,000 1,030
1,000 1,000 1,000 450
3.33E-07 3.40E-06
4.38E-07 3.00E-07 3.00E-07 1.42E-05
1,000 2.60E-07 ²·K-1 1,161
3.20E-07 990 7.61E-07 2,006
346 23
861 329 383
13,248 255
s-0.5 )
the ease by which energy will pass through the internal surface of the element to, or from, the room per degree of temperature difference between the surface at a particular time and the ‘room’ average temperature (environmental temperature is used to represent the room’s temperature). This is simplified, based on a 24-hour sinusoidal cycling of heat flow into the surface and, in electrical terms, the U value is analogous to the reciprocal of the total resistance (conductance), and Y additionally includes the susceptance that accounts for the storage effects of the structure. It is closely associated with the admittance time lead, ω (hours), that provides the time delay between the peak heat flow passing through the surface into the room and the time of the peak room temperature. As can be seen in Figure 2, the value
of thermal admittance is predominantly affected by the part of the wall closest to the room – as the wall increases in thickness, the value of admittance practically approaches a constant value. For very thin walls and those with low thermal conductivity, the U value and Y value are the same. This would be the assumption made for elements such as windows and doors. (Note that the thermal admittance, Y,
is completely unrelated to the ‘y-value’ as used as a performance metric for thermal
Admittance U value
6.0 5.0 4.0 3.0 2.0 1.0 0
A
B C
100 200 300 Thickness (mm)
Material
A B
C – insulation All specific heat capacities are 1,000 J kg-1 ·K-1
Figure 2: Comparison of U value and admittance for example single skin walls4
Density ρ (kg·m-3
2,400 1,000 25
)
Thermal conductivity λ (W·m-1
·K-1 1.52
0.24 0.35
)
January 2013 CIBSE Journal
71
U value and Y value (Wm-2
K-1
)
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