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112\ -- CHAPTER 5 1946 Guide of pipe. Note that the controlling resistances are R3 and Rt and that neglect of both Ri and Rt would not significantly influence the total re sistance, Rt. , On the basis of this resistance calculation the heat transfer from the surroundings to the cold water may be evaluated as: Jf = ----- = 21 Btu per (hour) (foot) or about 0.175 tons of refrigeration per 100 ft of pipe. Since the calculation is based on a 1 ft pipe length: gre = 21 Btu per hour. The temperature drops through the various resistances are now readily evaluated by Equation 12 as: <0--<sj tsa--tst aj--(a la:--If air to insulation surface = Ri grc = 0.22 X 21 = 4.6 F. through the insulation = R, grc = 3.9 X 21 = 82 F. through the pipe wall = R, grc = 8.5 X 10~4 X 21 = 0.02 F. pipe wall to cold water = Rt grc = 2.8 X 10"' X 21 = 0.06 F. The-solution was obtained on the assumption that the air temperature and the outside temperature differed by 20 F. In order to obtain a slightly better estimate of the rate of heat transfer the numerical solution should be repeated using the temperatures calculated from the previous listed temperature.differences. The foregoing problem serves to illustrate a general method of solving steady-state heat transfer problems. There are many problems which cannot be approximated by steady-state solutions. For instance, the problem of pipe line insulation in transient service; the behavior.of auto matically controlled thermoflow circuits; or the periodic absorption.of solar energy by roof and wall structures during the day and nocturnal radiation to the cold sky at night. The transient heat transfer problem differs from the steady-state in that energy storage rates need to be considered. Thus thermal capacity in addition to resistance effects is significant. The vector sum of the thermal capacitance and resistance is the thermal impedance. It is not within the scope of this chapter to deal with many of these problems. There are, however, solutions available in graphical form for certain special cases. Also a general approximate method may be employed which is analogous to the treatment of capacityresistance lumped parameter electrical circuits. REFERENCES I--The Metallic State, by H. Hume-Rothery (Oxford Press, 1931). *--Absorption and Extraction, by T. K. Sherwood (McGraw-Hill Co., 1937)., `' *--The Transmission of Heat by Radiation and Convection, by Griffith and Davis (Special Report No. 9, 1922, Department of Scientific and Industrial Research, His Majesty's Stationery Office, London, England). 4--Heat Insulation in Air Conditioning, by R. H. Heilman (Industrial and Engineering Chemistry, Vol. 28, July, 1936, p. 782). CHAPTER 6 .W- v; ^kleat <Z)randmi&sion C^oe^J-icientd oj? d^uiiclincj. ^y^Jalericiis Heat Transfer Symbols; Calculating Over-all Coefficients; Conductivity of Homogeneous Materials; Surface Conduct ance; Air Space Conductance; Practical Coefficients and Their Use; Computed Heat Transmission Coefficients; Roof Co efficients; Combined Ceiling and Roof Coefficients; Basement Floor, Basement Wall, and Concrete Slab Floor Coefficients, Condensation in Buildings THE design of conditioning or heating systems for buildings requires a knowledge of the thermal properties of the walls enclosing the space. The fate of heat flow through the walls under steady-state conditions at design temperatures is usually the basis for calculating the heat required. For a given wall under standard conditions the rate .is a specific value designated as U, the over-all coefficient of heat transmission. It may be determined by test in a guarded hot box apparatus or it may be computed from known values of the thermal conductance of the various components. Because testing of all combinations of building materials is impracticable, the procedure and necessary data for calcu lation of the value of U are given in this chapter, together with tables of computed values for the more common constructions. heat Transfer symbols U = over-all coefficient of heat transmission (air to air); the time rate of heat flow expressed' in Btu per (hour) (square foot) (Fahrenheit degree temperature difference between air on the inside and air on the outside of a wall, floor, roof or ceiling). The term is applied to the usual combinations of materials in construction and also to single materials, such as window glass, and includes the surface conductance on both sides. k -- thermal conductivity; the time rate of heat flow through a homogeneous material under steady conditions through unit area per unit temperature gradient in the direction perpendicular to the area. Its value is expressed in Btu per (hour) (square foot) (Fahren heit degree per inch). Materials are considered homogeneous when the valueNof k is not affected by variation in thickness or size of sample within the range normally used in'construction. C -- thermal conductance; the time rate of heat flow through a material from one of its surfaces to the other per unit temperature difference between the two surfaces. Its value is expressed in Btu per (hour) (square foot) (Fahrenheit degree). The term is applied to specific materials as used which may be either homogeneous or heterogeneous. / = film or surface conductance; the time rate of heat flow between a surface and the surrounding air. Its value is expressed in Btu per (hour) (square foot of surface) (Fahrenheit degree temperature difference). Subscripts i and o are used to differentiate between inside and outside surface conductances respectively. a =. thermal conductance of an air space; the time rate of heat flow.through an air space per unit temperature difference between the boundary surfaces. Its value is ex pressed in Btu per (hour)(square foot of area)(Fahrenheit degree). The conductance of an air space is dependent on the temperature difference, the height, the depth, the position and the character of the boundary surfaces. The relationships are not linear and accu rate values must be obtained by test and not by computation. R = thermal resistance. Its value is expressed in Fahrenheit degrees per (Btu) (hour) (square foot). It may represent any of the following and must therefore be properly described: 's ~ over-all or air-to-air resistance = resistance per unit thickness (resistivity) .113