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96 CHAPTER 4 .1948 Guide T, = temperature, Fahrenheit degrees, absolute. 7b -- standard temperature to which correction is to be made, Fahrenheit degrees absolute. Tf = temperature of gas flowing, Fahrenheit degrees, absolute. u = internal energy, Btu per pound of fluid. V = velocity in feet per second. Ve -- critical velocity, feet per second. Fbo = velocity of sound, feet per second. Vm = velocity in feet per minute. v = specific volume, cubic feet per pound; W weight of gas flowing, pounds per hour. . ' Y = expansion factor--correcting for expansion of gas under reduced downstream pressure. z -- elevation above some arbitrary datum, in feet. REFERENCES V-Friction Factors for Pipe Flow, by Lewis F. Moody {AS.M.E. Transactions. 66, 1944. 671-678: Dis cussion. idem. 66, 1944, 678-684). History of Orifice Meters and the Calibration. Construction, and Operation of Orifices for Metering. Report of the Joint A.Gji.--AJSM.E. Committee on Orifice Coefficients (American Society of Mechanical Engineers, 1935). , `"Ga Measurement Committee Report No. 2. Natural Gas Department (American Gas Association. 1935). 4--Thermodynamic Properties of Steam, by Joseph H. Keenan and Frederick G. Keyes (John Wiley & Sons, Inc.. 1936). . ^Discharge Coefficients of Long Radius Flow Nozzles When Used with Pipe Wall Pressure Taps. P,y H- S. Bean, S. R. Beitler, and R. E. Sprenkle {AS.M.E. Transactions, 63, 1941. 439-442; Discussion, idem. 63, 1941, 442-445). BIBLIOGRAPHY [A] Principles of Thermodynamics, by G. A. Goodenough (Henry Holt & Co.). [B] Principles of Engineering Thermodynamics, by Paul J. Kiefer and Milton C. Stuart (John Wiley & Sons, Inc., 1944). [Cl Fluid Mechanics, by Russell A. Dodge and Milton J. Thompson (McGraw-Hill Book Co., 1937). [D] Fluid Mechanics, by R. C. Binder (Prentice-Hall, Inc., 1943). . [E[ The Physics of Solids and Fluids, by P. P. Ewald, H. Poschl and L. Prandtl (Biackie, 1936). [F] A Study of the Data on the Flow of Fluids in Pipes, by Emory Kemler, Hydraulic Paper HYD-55-2 (A.S.M.E. Transactions 65, No. 10, 7-22, 1933; Discussion, idem., 55. No. 10, 23-32, 1933). [G] The Flow of Fluids in Closed Conduits, by R. J. S. Pigott (Mechanical Engi neering 55, 1933, 497-501, 515). [H] Fluid Meters, Their Theory and Application (American Society of Mechanical Engineers, 4th edition, 1937). [I] Fluid Meters, Their Selection and Installation (American Society of Meckanicai Engineers, 1933). [J] The Orifice Meter for Measurement of Flow of Gases and Liquids, by Allen D. MacLean (Pittsburgh Equitable Meter Co., 1938). [K] Flow Measurement (American Society of Mechanical Engineers, 1940). [L] Pitot Tube Practice, by Edward S. Cole (A.S.M.E. Transactions 57,1935,281-294; Discussion, idem. 58, 1936, 146-156). [M] Pitot Tubes in Large Pipes, by Edward S. Cole and E. Shaw Cole (A.S.M.E. Transactions, 61, 1939, 465-473; Discussion, idem. 61, 1939, 473-475). [N] Investigation of Errors of Pitot Tubes, by C. W. Hubbard (A.S.M.E. Trans actions, 61, 477-497; Discussion, idem. 61, 1939, 497-506). [O] Piping Arrangements for Acceptable Flowmeter Accuracy, by R. E. Sprenkle (A .S.M.E. Transactions, 67, 345-357, .1945; Discussion, idem. 67, 357-360, 1945). . Chapter 5 FUNDAME3VTALS OF HEAT TRANSFER Conduction, Convection, Radiation, Combined Convection.and Radiation, HeatFlow Resistance, Practical Heat Transfer. Problems, Unit.Conductances for. Convection Plow Systems, Radiation Factors or .Eniissivities, Solutions for Steady-State Conduction Problems HEAT is that form of energy that is transferred by virtue of an existing. temperature difference. The temperature difference is.the potential which causes the transfer, the latter in. turn being resisted by the thermal properties of the material combined in a single term known as the resis tance. Energy exchange associated with evaporation, condensation, etc. is treated elsewhere such as in the section on cooling tower design in Chapter 37. The objectives of this chapter are to: 1. Describe the mechanisms and present the rate equations for the different modes of heat transfer. 2. Illustrate the application of the basic concepts to steady-state problems (tempera ture independent of-time or a cyclic variable thereof) by means of several typical solutions of heat transfer systems. Further applications to specific systems will be found throughout The . Guide. CONDUCTION, CONVECTION AND RADIATION Thermal conduction is the term applied to the mechanism of heat trans fer whereby the'molecules of higher kinetic energy transmit part of their energy to adjacent molecules of lower kinetic energy by direct molecular action. Since the temperature is proportional to the average kinetic energy of. the molecules, thermal transfer will occur in the direction of decreasing temperature,. The motion of the molecules is random; there is no net material flow associated with the conduction mechanism. In the case of flowing fluids,' thermal conduction is significant in the region very close to a solid boundary or wall, for in this region the.flpw is laminar, parallel, with the wall surface, and there are practically no cross currents in the direction of the heat transfer across the solid fluid boundary. In solid bodies the significant mechanism of heat transfer is. always thermal conduction. ' Contrasted to the thermal conduction mechanism, thermal convection involves energy transfer by eddy mixing and diffusion 1 in addition to conduction. : This is shown schematically in Fig. 1 which exhibits transfer from a pipe wall at surface temperature 4' to a colder fluid at a bulk temperature k- (Bulk temperature is that which would be attained if the fluid stream were drawn off at a certain section and mixed. It is therefore slightly higher than the lowest temperature in the stream). In the laminar sublayer, immediately adjacent to the wall, the heat transfer occurs by thermalconduction; in the transition region, which is called the buffer layer, eddy mixing as well as conduction effects are significant; 'in the eddy or. turbulent region the major fraction of the transfer occurs by eddy mixing. ............. . In- most commercial equipment the main body of the fluid is in turbu-. lent flow, and the laminar film exists at the solid walls only, as shown in 97