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HEATINC VENTILATING AIR CONDITIONING GUIDE 1944 in temperature of 1 F between the air on the inside and that on the outside of the wall, floor, roof or ceiling. k -- thermal conductivity; the amount of heat expressed in Btu transmitted in one hour through 1 sq ft of a homogeneous material 1 in. thick for a difference in temperature of 1 F between the two surfaces of the material. The conductivity of any material depends on the structure of the material and its density. Heavy or dense materials, the weight of which per cubic foot is high, usually transmit more heat than light or less dense materials, the weight of which per cubic foot is low. C = thermal conductance; the amount of heat expressed in Btu transmitted in one hour through X sq ft of a non-homogeneous material for the thickness or type under consideration for a difference in temperature of 1 F between the two surfaces of the ** material. Conductance is usually used to designate the heat transmitted through such heterogeneous materials as plasterboard and hollow clay tile. / = film or surface conductance; the amount of heat expressed in Btu transmitted by radiation, conduction and convection fron> a surface to the air surrounding it, or vice versa, in one hour per square foot of the surface for a difference in temperature of 1 F between the surface and the surrounding air. To differentiate between inside and outside wall (or floor, roof or ceiling) surfaces, j\ is used to designate the inside film or surface conductance and /0 the outside film or surface conductance. * a * thermal conductance of an air space; the amount of heat expressed in Btu trans mitted by radiation, conduction and convection in one hour through an area of 1 sq ft of an air space for a temperature difference of 1 F. The conductance of an. air space depends on the mean absolute temperature, the width, the position and the character of the materials enclosing it. R " resistance or resistivity which is the reciprocal of transmission, conductance, or conductivity, -j- -- over-all or air-to-air resistance. -j- -- internal resistivity. ~~ = internal resistance. -j- = film or surface resistance. a -- air space resistance. Examples of the application of the over-all coefficient U for determining the heat transfer by transmission, are given in Chapter 6. FORMULAS FOR CALCULATING OVER-ALL COEFFICIENTS The simplest method of combining the coefficients for the individual parts of the wall is to use the reciprocals of the coefficients and treat them as resistance units. The total over-all.resistance of a wall is equal numerically to the sum of the resistances of the various parts, and the reciprocal of the over-all resistance is likewise the over-all heat trans mission coefficient of the wall. For a wall built up of a single homogeneous material of conductivity k and x inches thick the over-all resistance, RU ft + x T 0) If the coefficients/i,/0 and k, together with the thickness of the material x are known, the over-all coefficient U may be readily calculated as the reciprocal of the total heat resistance. : For a compound wall built up of three homogeneous materials having 88 CHAPTER 4. HEAT TRANSMISSION COEFFICIENTS conductivities ki, k2 and k3 and thicknesses x\, x2 and x3 respectively, and laid together without air spaces, the total resistance, U fi + ki k2 k. (2) For a wall with air space construction consisting of two homogeneous materials of thicknesses Xi and x2, and conductivities k2 and k2, respectively, separated to form an air space of conductance a, the over-all resistance, 1 * + *L+J_+^ +J- U fi ki a ki Jo (3) Likewise any combination of homogeneous materials and air spaces can be put into the wall and the over-all resistance of the combination may be calculated by adding the resistances of the individual sections of the wall. In certain special forms of construction such as tile with irregular air spaces it is necessary to consider the conductance C of the unit as built instead of the unit conductivity k, and the resistance of the section is equal to -X-. The method of calculating the over-all heat transmission coefficient for a given wall is comparatively simple, but the selection of the proper coefficients is often complicated. In some cases the construc tion of the wall is such that the substituting of coefficients in the accepted formula will give erroneous results. This is the case with irregular cored out air spaces in concrete and tile blocks, and walls in which there are parallel paths for heat flow through materials having different heat resistances. In such cases it is necessary to resort to test methods to check the calculations, and in practically all cases it has been necessary to determine fundamental coefficients by test methods. Conductivity coefficients for loose fibrous materials which are based on tests in the hot plate apparatus are generally applicable only to horizontal heat flow through walls where the material is confined by the wall surfaces. Such coefficients do not necessarily apply where the material is placed loosely between ceiling joists if there is a considerable amount of con vection through the material, especially during cold weather when , the heat flow is upward. According to one investigator1, the actual rate of heat flow through the loose insulating material may be somewhat greater than that indicated by the hot plate test, but in another case2, there was found to be a negligible difference between horizontal and vertical heat flow through loose materials. Conductivity of Homogeneous Materials The thermal conductivity of homogeneous materials is affected by several factors. Among these are the density of the material, the amount of moisture present, the mean temperature at which the coefficient is determined, and for fibrous materials the arrangement of fiber in the material. There are many fibrous materials used in building construe- ^he Effect of Convection in Ceiling Insulation, by G. B. Wilkes and L. R. Vianey (A.S.H.V.E. Journal Section of Heating, Piping Air Conditioning, February. 1943, p. 102). *Heat Transmission Through Insulation as Affected by Orientation of Walls, by F. B. Rowley and C, E. Lund (A.S.H.V.E. Journal Section of Heating, Piping 6* Atr Conditioning, July, 1943, p. 361). 89