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Thursday, 27 October 2011 19:57

Formulae and Definitions

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In general there is a square root relationship between thickness d of a static air layer and air velocity v. The exact function depends on the size and shape of the surface, but for the human body a useful approximation is:

Still air acts as an insulating layer with a conductivity (a material constant, regardless of the shape of the material) of .026 W/mK, which has a heat transfer coefficient h (units of ) (the conductive property of a slab of material) of:

(Kerslake 1972).

Radiant heat flow () between two surfaces is approximately proportional to their temperature difference:

where T is the average absolute temperature (in Kelvin) of the two surfaces, is the absorption coefficient and is the Stefan-Boltzmann constant ( ). The amount of radiation exchange is inversely related to the number of intercepting layers (n):

Clothing insulation () is defined by the following equations:

where is intrinsic insulation, is (adjacent) air insulation, is total insulation, is average skin temperature, is the average temperature of the outer surface of the clothing, is air temperature, is the dry heat flow (convective and radiant heat) per unit of skin area and is the clothing area factor. This coefficient has been underestimated in older studies, but more recent studies converge to the expression

Often I is expressed in the unit clo; one clo equals .

McCullough et al. (1985) deduced a regression equation from data on a mix of clothing ensembles, using thickness of the textile (, in mm) and percentage covered body area () as determinants. Their formula for the insulation of single clothing items () is:

The evaporative resistance R (units of s/m) can be defined as:

(or sometimes , in )

For fabric layers, the air equivalent () is the thickness of air that provides the same resistance to diffusion as the fabric does. The associated vapour and latent heat () flows are:

where D is the diffusion coefficient (), C the vapour concentration () and the heat of evaporation (2430 J/g).

(from Lotens 1993). is related to R by:

where:

D is the diffusion coefficient for water vapour in air, .

 

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