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This magnitude of change is not uniform across all materials. Practical measurements of structural materials in Canada[4]

indicated that some materials,

such as (carbonate aggregate) concrete exhibited a significant change in conductivity with temperature, whereas lightweight bricks did not.

Heat flow to and from the structure The heat will flow to and from a building and between its individual components by conduction, convection and radiation. And for heat to pass through the solid structures it must first enter the structure’s surface by heat conducting from the adjacent convecting air to the surface and from the radiant input from all of the surfaces facing it. When considering heat flow from outdoors, the radiant heat flow from the sun and the sky will also be included. For convenient incorporation into the U value calculation, the various heat transfer coefficients are combined to produce the internal surface resistance,

Rsi, and external surface resistance Rse, (m2

K/W). So Rse = 1/ (hc + Ehr) and Rsi is = 1/

(1.2 Ehr + hc) where hc is the convective heat transfer coefficient, E is the emissivity factor (this takes account of the ability of the surface to radiate heat to its surroundings), and the radiative heat transfer coefficient, hr =4 s Ts

3 where s is the

Stefan Boltzman constant 5.67 x 10-8 W/m2

K, and

Ts is the surface absolute temperature (in Kelvin,

if the wind speed was 1.5m/s the value of hc would be 16.7 x 1.50.5

= 20.5W/m2 K. K. If

the wind speed subsequently increased to 3.5m/s the value of hc would increase to 31.24 W/m2

Radiation heat transfer will be dependant on the temperature of the object(s), the shape and emissivity. Typically dark objects will emit more radiation than lighter ones – they will have a higher emissivity and practically most building materials will have a high emissivity (with the maximum value

surface. The emissivity factor will also be significantly affected by the surrounding surfaces, as there will only be radiant heat flow from the surface if there is a suitable surface to absorb the radiation. (This receiving ‘surface’ may in practice be the massive heat sink of a very cold, clear night sky). Practically the radiant surroundings may change as vegetation alters around a building or adjacent buildings and landscaping are changed. To combine the two effects of the

variation of the values of hc and Ehr (simply to illustrate the point and not as a specific design example)

the value of Rse for a 1.5 m/s air speed passing over the surface with an emissivity of 0.3 would be 0.045 m2

K/W. Rse would be 0.028 m2

The thermal performance of a simple brick will depend on its temperature, moisture content and its age’

being 1). However the emissivity of a surface will change as a material becomes coated in particles of soot and dust in the air. The relationships that define the radiant heat transfer from a surface are very complex (a good discussion is provided in CIBSE Guide C 2007) and the equations used have been simplified and generalised for conditions that would be typical in building constructions. The value of the radiative heat

K). The tables (3.8 and 3.9) in CIBSE Guide A 2006 for Rse and Rsi have been developed using these relationships. Values of convective heat transfer

No matter how ‘accurate’ the thermal model may be, there must be realistic understanding of the U value

wwere determined by Jürges in 1928 for forced convection (that is, external wind or caused by air movement devices in the room) and by McAdams in 1954 for free convection, and these still form the basis of the many tabulated values. For the external convective heat transfer coefficient CIBSE Guide C 2007 suggests the use of the relationship[5] hc = 16.7cs

0.5 W/m2 being less than 3.5m/s. So, for example

transfer coefficient hr is dependent on the relative temperature of the surface to its surroundings; however, to accurately predict variations in this is extremely complex. The emissivity factor,

E, will vary directly with the emissivity of the

K for the air velocity, cs

surface and so is more straightforward to enumerate. This can be illustrated most markedly when considering, for example, a bitumen flat roof that has been coated with aluminium paint (as a means of reducing solar gain) that, when freshly applied, would have an emissivity of around 0.3. As the roof ages and accumulates particles from pollution, flora and fauna its emissivity will rise, depending on the condition, towards the emissivity of the original dark bitumen roof (0.9) so increasing the radiant heat loss from the

For a 3.5 m/s air speed passing over that same surface with an emissivity of 0.8, the value of K/W. If

the wind speed had stayed the same and the surface’s emissivity had

risen to 0.8, the value of Rse would still have reduced to 0.039 m2

to the original value of 0.045 m2

K/W compared K/W.

Practical implications This article has touched on some of the variables in the thermal performance of building constructions in use. Combined with the challenges of calculating a representative U value for building elements that are made of several layers of ‘non-homogenous’ (varying) materials means that a pragmatic approach to heat loss and energy calculations is required. No matter how ‘accurate’ the subsequent thermal model may be, there must be a realistic understanding that the underlying U value cannot be considered an absolute constant. © Tim Dwyer


1. BS EN ISO 6946:2007 Building components and building elements… Calculation method

2. Table A3.2, CIBSE Guide A, 2006

3. Abou A. Budawi,I. ‘Comparison of Thermal Conductivity Measurements of Building Insulation Materials under Various Operating Temperatures’, Journal of Building Physics, Vol. 29(2), October 2005

4. Hu, T. Lie, G et al, Thermal Properties of Building Materials at Elevated Temperatures. National Research Council, Canada, 1993

5. Loveday D L and Taki A H, ‘Outside surface resistance: proposed new value for building design’, Proc. CIBSE A: Building Serv. Eng. Res. Technol. 19(1) 23–29 (1998)

May 2011 CIBSE Journal 69

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