Technical Note

The Effectiveness of Reflective Foil as Thermal Insulation

The magnitude of the rate of heat loss from a warm, exposed surface via radiation relative to that by the combined convection-conduction process through the adjacent air is not generally appreciated. Consequently, reflective insulation, for example for hot water tanks, pipes and lofts, is often ignored. But is this justified ? The worthwhileness of such treatment for a particular application can be more easily understood if assessed in terms of an equivalent thickness of insulant.

Consider the steady-state, one-dimensional transfer equation for the heat passing through a uniformly thick layer of insulant attached to a plane wall, the other plane surface of the insulant being exposed to the air. If U is the overall heat transfer coefficient, then:

1 1 x - - + (1)

U h , + h c k

where h r and h e are, respectively, the radiative and combined convective--conductive heat transfer coefficients through the air and x and k are the thickness and effective thermal conductivity of the insulant, respectively. To a reasonable approximation, the radiative coefficient may be evaluated from:

h r = 4 f r e T 3 (2)

where tr is the Stefan-Boltzmann constant, e the emissivity of the exposed surface and T the mean of the absolute temperatures of this surface and the walls of the immediate environment, t

If U is to remain invariant, the effect of reducing the surface emissivity would be that less insulant would be required. The appropriate decrease in insulant thickness

x~ - x2 = k hr 2 + hc hr, + h (3)

85 Applied Energy (5) (1979)--O Applied Science Publishers Ltd, England, 1979 Printed in Great Britain

86 1. E. SMITH, S, D. PROBERT

To a first approximation, e.g. by ignoring the small change of outer surface temperature which would ensue because of the different thickness of insulant applied, h r may be evaluated from eqn. (2) for the bare insulant surface (i.e. hr~ ) and

with the reflective foil present (i.e. hr2 ). Thus hr~ = 6.2 W m - 2 K - ~ for e ~ = 0.95 and

h~2 = 0.3 W m - 2 K - ~ for e 2 = 0-05 when the exposed surfaces are typically in excess

of normal ambient temperatures. For a 1 m vertical surface at 10°C above ambient, h c = 2.7 W m -2 K-~ . Inserting these values into eqn. (3) and assuming that the effective thermal conductivity of a typical insulant is 4.5 × 10 _2 W m - ~ K-1 , the benefit of wrapping aluminium foil around the outside of the system can be seen to be approximately equivalent to applying an extra 10 mm of insulant.

Aluminium foil (e.g. cooking foil) may be purchased for about 0.13 £ m - 2 whereas glass-fibre blankets, 25ram thick (the thinnest of those readily available commercially) cost slightly in excess of 0.25 £m-2 , i.e. at a pro rata rate of about 0.10 £m- 2 for a 10 mm thick blanket. Thus it would appear that the insulant would be the 'better buy' for the considered situation.

Nevertheless, single-layer reflective foil can be economically attractive as a means of insulation for many appl icat ions--for example, where space is at a premium or where it is used as a sealed cladding, thereby preventing attrition of the covered insulant. Another recommended use is on the inner leaf facing a domestic 'radiator ' . Results from a study carried out at the Watson House Laboratories of the British Gas Corporat ion indicate that the presence of reflecting aluminium foil reduced the rate of heat loss through that part of the wall immediately behind the radiator by 55 per cent ! Thus radiators, designed and built with low emissivity rear sides, i.e. those which will face walls when installed, would appear to be worthy of further consideration.

Although dust in average domestic quantities does not lead to radical increases of the emissivity of vertical surfaces on which it becomes deposited, even a mono- molecular layer of condensation results in a dramatic loss of effectiveness of reflective surfaces. Thus aluminium foil should not be employed domestically for insulation purposes if condensation is likely to occur on i t - - fo r example, in pitched roofs of otherwise well insulated buildings which suffer considerable assaults from wind-driven rain in winter.

REFERENCE

1. H. C. HOTTEL and A. F. SAROFIM, Radiative transJbr, McGraw-Hill, New York, 1967.

I. E. SMITH and S. D. PROBERT,

School oJ" Mechanical Engineering, Cranfield Institute of Technology, Bedford MK43 OAL (Great Britain)