Document ExabDoODGVnpzOq63ORK193nN

^14 CHAPTER 6 1946 Guide = resistance of a material (surface-to-surface) . f = film or surface resistance * i: -- = air space resistance CALCULATING OVER ALL COEFFICIENTS Prom Chapter 5, Equation 7, the total resistance to heat flow through a wall is equal numerically to the sum of the resistances in series. Then by definition, . ' where ' . V= = Rt Ri + Ri + Ri + * + Rn ' Ri, Ri, etc. are the individual resistances of the wall components.. Rt r - total resistance. (1) For a wall of a single homogeneous material of conductivity k and thick ness x, with surface coefficients /i and f0 V= 7i k + /o (2): For a compound wall of. three homogeneous materials in series, having conductivities k\, k2 and k3 and thicknesses xu x2 and x3 respectively, and laid together without air spaces, U1 Rt li _1__ , h x ,__ Xt_ + it (3)' For a wall with air space construction and consisting of two homo geneous, materials of conductivitiesA and k3,. thicknesses and *2, and separated by an air space of conductance a x, + kv -.+ (4) . In the case of types' of building materials, having non-uniform'or irregular sections such as hollow clay tile or concrete blocks, it is necessary to use the conductance C of the section unit as manufactured instead of a.conductivity k. The resistance of.the section ~ is therefore substi- X tuted for in Equations 2, 3 and 4. CONDUCTIVITIES AND CONDUCTANCES The method of calculating the over-all coefficient of heat transmission for a given construction is comparatively simple, but accurate values of conductivities and conductances must be used to obtain satisfactory results. In addition there are sometimes parallel' heat flow paths of different resistances in the same wall,, which require modification of the Heat Transmission Coefficients of Building Materials _________ '115 formula. In such cases calculated results should'be checked by test measurements. - ' The determination 'of the fundamental' conductivities and conduc tances requires considerable skill and experience. to obtain accurate results. It is recommended that thermal conductivities of homogeneous ' materials be determined by means of the Guarded Hot Plate l. For deter mination of conductances, a Guarded Hot Box method s is generally used. Tables 1 and 2 give conductivities and conductances which' are quite generally used in calculation and which have been selected.from various sources. Wherever possible the properties, of the material and test conditions are given. In selecting arid applying heat transmission values to any construction, caution is necessary, because coefficients for the same material may differ because of variations which occur, in test methods, in the materials themselves, or in. the temperature of the mater ial when tested. ' Conductivity of Homogeneous Materials. Thermal conductivity is a property of a homogeneous material and of types of building materials such as lumber, brick and stone which may be considered homogeneous. Most insulating riiaterials,. except air spaces and reflective types, are of a porous nature arid consist of combinations of solid matter with small air cells. The thermal conductivity of these . materials will vary with density, mean temperature, size of fibers or particles, degree and extent of bond between particles, moisture present, and the arrangement of fibers or particles within the material. The effect of density upon conductivity (at constant mean temperature) is illustrated for two fibrous materials in Fig. 1. It will be,noted that for each there is an optimum density for lowest conductivity: Typical variation of conductivity with mean temperature is shown in Fig. 2. Fig. 1. Typical ' Variation of Thermal Conductivity with Density--for Fibrous Material '0 1 2 '3 4 56 DENSITY POUNDS PER CUBIC FOOT Fig: 2. Typical Variation of _ Thermal Conductivity with'. Mean Temperature - '