Thermal conductivity and thermal resistance When considering solid materials, brick, plaster, insulation etc., the ease by which heat flows through is measured by its thermal conductivity, λ. If the temperatures on the two faces of a very large sheet of material are kept constant (but different from each other) then the heat flowing directly between the two faces as shown in Figure 1 will be Q12
=λ/d x A x (θ1 - θ2
Q = heat flow (W), d = thickness (depth) of block (m), A = area of block (m2
), θ
= temperature of surface (°C) and λ = thermal conductivity (W/mK). The term λ/d is called the conductance K), and the inverse, d/λ, is the
(W/m2 resistance, R (m2 K/W), with calculations
of R to running to three decimal places when establishing the individual resistances of layers[1]
. The R value
is frequently used to publicise the insulating capacity of a material of a particular thickness such a insulation boards and mats. The value of the conductivity for materials may be obtained from tables (that have themselves been developed from laboratory tests) such as those in CIBSE Guide A 2006 – Section 3. Materials with low values of thermal conductivity (below about 0.05 W/mK) being commonly referred to as ‘thermal insulation’ However, the value for the actual installed material will not necessarily be the same as the tabulated λ as it will be affected by its moisture content and, to an extent, its actual temperature.
Moisture content In broad terms the thermal conductivity will relate to the density of a material. So intuitively a lightweight thermal block will be a better insulator than
Figure 1: A section of a very large plane of material
Face 2 Thickness, d
the common (dense) housebrick. This situation can change completely if the materials are allowed to absorb water, as might happen while stored on-site prior to construction. The air spaces will be filled by water, which is a relatively good conductor of heat, and the overall thermal conductivity of the material will be increased. In properly constructed buildings this excess water will dry out. However, where there is poor weathering, or insufficient protection from water rising from the ground, elements may hold large amounts of water, so increasing the conductivity and potentially having significant effects on heat flow through the associated structure. For example, the standard moisture content for a brick protected from the weather (for example, on the inside skin of a construction or covered
by tiling) is taken as 1% (by volume) [2]
Area, A Face 1
. If subsequently that same brick is used in the outer face of a wall (or a protective covering fails in an existing wall) the moisture content may rise towards the standard ‘exposed’ value of 5%. Each additional % (by volume) of water content in a brick will increase the thermal conductivity by about 10%, and as in this case it would rise by 20%, so its thermal resistance would consequently fall. So for a 105mm lightweight clay brick with a protected λ of 0.40 W/mK, the R value would fall from (0.105/0.40) = 0.263m2 0.219m2
K/W to (0.105/0.48) = K/W. Where poor design, or extreme 68 CIBSE Journal May 2011
conditions, lead to condensation occurring in the structure, the water content of the materials will increase, so reducing the thermal resistance. This in turn is likely to exacerbate the condensation problem as it is likely to reduce the temperature of the fabric.
Temperature The actual temperature of the material will also affect its thermal conductivity. In the range of temperatures typically used in buildings, the thermal conductivity will increase in most materials as temperature rises. Tabulated values of conductivity would normally be based on the material being at a temperature of 10°C. In most cases any variation from this reference temperature is ignored. However, where there are temperatures that significantly vary from 10°C, or for specific materials, there may be a case for examining the effect. The variation in the value of λ with temperature, θ, is difficult to generalise. However, there have been several studies that have measured the impact of temperature on thermal conductivity. For example a study[3] undertaken in Saudi Arabia measured the temperature effect on the thermal conductivity of a number of insulation materials. The results for rock wool are shown in Figure 2, and indicate an increase in thermal conductivity of more than 10% between the standard tabulated values at 10°C and those temperatures that may prevail when undertaking cooling load calculations.
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Density, kg/m3 ) watts, and where
0.0460 0.0440 0.0420 0.0400 0.0380 0.0360 0.0340 0.0320 0.0300
50
54.4
71.2
75.5
82.5
125.7
135.6
0
5
10
15
20
25 Mean temperature (°C) Figure 2: The measured effect of temperature on thermal conductivity of rock wall at various densities
30
35
40
45
Thermal conductivity (W/mK)
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