# Calculating U-Values with Reflective Foil Insulation

Heat travels by conduction, convection and radiation. Radiant heat travels in waves, and heat transfer by radiation, unlike conduction and convection, can travel between two surfaces separated by a vacuum. The majority of heat transfer through a body of still air is by radiation. However, radiation across a gap can be significantly reduced by using a reflective surface adjacent to the gap.

The thermal radiation between two surfaces is dependent on the emissivity of the two surfaces, where emissivity (ε) is the ratio of the emissive power of the surface and the emissive power of an ideal black body. Conventions in BS EN ISO 6946 for calculating thermal resistance and thermal transmittance stipulate that the surface of material, where emissivity is unknown, should be assumed to have an emissivity of 0.9.

Reflective foil insulation, such as Thermal Economics Alreflex 2L2, insulates a construction element which includes one or more un-ventilated air cavities by reflecting radiated heat energy back into the adjacent air cavity; thus having a low emissivity (or a high heat reflectance). Reflective foil products can be easily modelled within bespoke U-Value calculation software such as the BRE U-Value Calculator via editing the thermal properties of the un-ventilated air layer, by changing the emissivity of one of the bounding surfaces to match the specified emissivity of the foil surface from manufacturer’s data.

If using the BRE U-Value Calculator, an emissivity of 0.9 will always be assumed for the opposite surface, and this cannot be edited.

## Example U-Value Calculation: Alreflex 2L2FR

A solid masonry wall built with 225mm brickwork is to be insulated with 6mm Thermal Economics Alreflex 2L2 FR, and plasterboard finish. Alreflex 2L2 FR is reflective bubble and foil insulation, with a tested thermal resistance of 0.19m2KW-1, and an emissivity of 0.03 on both faces. To obtain the lowest U-Value, the Alreflex 2L2 FR will be suspended in the middle of a cavity, created by installing battens against the brickwork; mechanically fixing the Alreflex 2L2 FR to the battens and sealing all joints with Thermal Economics Alu Tape to create a vapour barrier; installing battens against the Alreflex 2L2 FR and covering the construction with 12.5mm plasterboard.

The homogenous brickwork and plasterboard layers will be entered into the BRE U-Value Calculator software as normal, using thermal conductivity of 0.77Wm-1K-1 and 0.21Wm-1K-1 respectively. The Alreflex 2L2 FR should be inputted as a solid material, but “R 0.190” should be typed into the thermal conductivity field. The prefix “R” denotes within the BRE U-Value Calculator that a specified thermal resistance is being used; otherwise the BRE U-Value Calculator will erroneously calculate an R-value of 0.032m2KW-1 for the layer.

The un-ventilated air cavities are included within the calculation by inserting an air layer 22mm thick, either side of the Alreflex 2L2 FR layer. The BRE U-Value Calculator will automatically assume a default emissivity of 0.9 and determine the thermal resistance of the air layer to be 0.18m2KW-1 at an assumed temperature of 10ºC. This can be changed by either ‘double-clicking’ on the air layer, or ‘right-clicking’ and selecting ‘Edit air layer’ from the drop-down menu. This will open a dialogue box as shown in Figure 1. The thermal properties of the still air layer can be changed by selecting ‘Use specified emissivity’ and inputting “0.03”. This will correctly calculate the thermal resistance of the air layer as 0.71m2KW-1 at an assumed temperature of 10ºC. However, it must be remembered that the air layers are inhomogeneous, because they are bridged by timber battens with thermal conductivity of 0.13Wm-1K-1 at the default dry-lining timber fraction of 0.118 (11.8%).

The assumed thermal conductivities and bridging fractions used in this example are the generic values in BR 443. An example of a U-Value calculation with reflective foil insulation using the BRE U-Value Calculator is shown in Figure 2.

Fig 1. Click to view larger image Fig 2. Click to view larger image

## Effect of Overprinting on Foils

Surface emissivity is not necessarily uniform, as many foil-faced products are overprinted. This can have an enormous effect on the radiated heat flow because the surface becomes more like an ideal black body (which is a perfect emitter) rather than an ideal white body (which is a perfect reflector). In which case the thermal resistance of the air layer should be a calculated, area-weighted average value, using the formula in BR 443 (section 4.8.2, note 2):

Where R1 is the thermal resistance with a surface emissivity of a reflective surface, at an assumed temperature of 10ºC; R2 is the thermal resistance with a default emissivity of 0.9, at an assumed temperature of 10ºC; A1 is the proportional area of the surface with emissivity of a reflective surface, and A2 is the proportional area of the surface with the default emissivity. The emissivity of the reflective surface would normally be provided by the manufacturer, but where this is not known a value of 0.2 can be assumed for a low-emissive surface. At present, there is not a default proportion of overprinting area where manufacturer’s data is not available. However, in such circumstances the British Board of Agrément have a policy of assuming 40% of the surface is over-printed.

Example: A new, masonry cavity wall is to be insulated with a polyisocyanurate partial-fill insulation board, which has a foil surface overprinted with company logos on both sides. The thermal resistance of the 50mm un-ventilated air cavity is calculated as:

Which is evaluated so that R= 0.28m2KW-1.

## About the Author:

John Hefford is the Senior Technical Consultant at Thermal Economics, and is a qualified OCDEA accredited by National Energy Services. In addition to carrying out thermal calculations, Hefford also leads the Fair Regulation working group at TIMSA. Thermal Economics will also provide free-of-charge U-Value calculations using our products; or help with modelling Thermal Economics products in U-Value calculations can be obtained by calling the Thermal Economics Technical Office on 01582 544255 or by e-mailing info@thermal-economics.co.uk.

## Comments

Dear John,

This has been very useful and topical - I was at a network meeting of several OCDEAs last Monday - and this was a subject for discussion and debate. Would it please be possible to have a similar example for an insulated slpoing ceiling to sloping roof, please?

Andy Ball OCDEA

Hi Andy,

Thank you for your comment - I have been in touch with John who was glad to provide us with a new blog post to answer your question. Please simply visit our blog page to view this.

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