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46 CHAPTER 4 1959 Guide pipes (Hydraulic Paper HYD-55-2 ASME Transactions, .Vol. 55, No. 10, pp. 23-32, 1933). R. J. S. Pigott: The flow of fluids in closed conduits (Me chanical Engineering, Vol. 55, 1933, pp. 497-501 and p. 515). American Society of Mechanical Engineers: Fluid Meters, Their Selection and Installation (1933). A. D. MacLean: The Orifice Meter for Measurement of Flow of Gases and Liquids (Pittsburgh Equitable Meter Co., 1938). Edward S. Cole: Pitot tube practice (ASME Transactions, Vol. 57, 1935, pp. 281-294; with discussion Vol. 58, 1936, pp. 145-156). Edward S. Cole and E. Shaw Cole: Pitot tubes in large pipes {ASME Transactions, Vol. 61, 1939, pp. 465-473, with dis cussion pp. 473-475). C. W. Hubbard: Investigation of errors of pitot tubes (ASME Transactions, Vol. 61, 1939, pp. 477-497, with discus sion pp. 497-506). R. E. Sprenkle: Piping arrangements for acceptable flow meter accuracy (ASME Transactions, Vol. 67, 1945,. pp. 345357, with discussion pp. 357-360). CHAPTER 5 HEAT TRANSFER - Conduction, Convection, Radiation; Equations for Conduction, Convection, Rodiotion, and Combined Convection ond Radiation; Heat-Flow Resistance, in Series and Parallel; Practical Heat Transfer Problems; Periodic and Transient Heat Flow EAT is the form of energy that is transferred by vir in small tubes, or with viscous liquids such as heavy oil (low H tue of an existing temperature difference. The tem Reynolds numbers), the entire flow may be laminar. In these perature difference is the potential which causes the translatter cases there is no transition or eddy region. fer, the latter in turn being resisted by the thermal properties When the fluid currents are produced by sources external of the material combined in a single term known as the re to the heat transfer region, as for example by a pump, the sistance. Energy exchange associated with evaporation, described solid to fluid heat transfer is termed forced con condensation, etc., is treated elsewhere such as in the sec vection. In contrast, if the fluid currents are generated in tion Cooling Tower Theory in Chapter 40. 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 steadystate problems (temperature independent of time or a cyclic variable thereof) by means of several typical solutions of heat transfer systems. 3. Present concise summaries of available methods of analy sis for transient and periodic beat transfer problems. Further applications to specific systems will be found throughout The Guide. ternally, as a result of non-homogeneous densities arising from the temperature variations, the heat transfer is termed free convection. In the conduction and convection mechanisms, the trans fer of heat is associated with matter. For radiant heat trans fer, however, a change in energy form takes place, from in ternal energy at the source to electromagnetic energy for transmission, then back to internal energy at the receiver. The rate of heat transfer, corresponding to the three transfer mechanisms previously described, may be expressed by three rate equations. These are similar to Ohm's Law for electrical flow, the current flow through a resistance CONDUCTION, CONVECTION, AND RADIATION being proportional to the potential. The convection and radi ation flow rate expressions may be approximated by a po Thermal conduction is the term applied to the mechanism tential (temperature difference) and a resistance in order of heat transfer whereby the molecules of higher kinetic that heat transfer calculations may be effected more con energy transmit part of their energy to adjacent molecules veniently and rapidly. of lower kinetic energy by direct molecular action. Since the temperature is proportional to the average kinetic energy Thermal Conduction Equation 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, ther mal conduction is significant-in the region very close to a solid boundary or wall, where the flow is laminar and parallel with the wall surface, and where practically no cross cur rents exist in the direction of the heat transfer across the Equation 1 states symbolically that the thermal conduc tion per unit transfer area normal to the flow, q/A, Btu per (hour) (square foot), is proportional to the tempera ture gradient (dt)/(dL), Fahrenheit degrees per foot. The proportionality factor is termed the thermal conductioity, k, Btu per (hour) (square foot) (Fahrenheit degree per foot of thickness). solid fluid boundary. In solid bodies the significant mecha nism of heat transfer is always thermal conduction. In contrast to the thermal conduction mechanism, ther mal connection involves energy transfer by eddy mixing and The minus sign on the right side of the equation is intro diffusion1 in addition to conduction. This is shown sche duced to indicate positive transfer in the direction of de matically in Fig. 1 which exhibits transfer from a pipe wall creasing temperature. Fig. 2 shows the physical significance at surface temperature U to a colder fluid at a bulk tempera of the indicated quantities. ture tf . (Bulk temperature is that which would be attained It should be emphasised that the thermal conductivity if the fluid stream were drawn off at a certain section and used should be expressed in consistent units; either using mixed. It is therefore somewhat higher than the lowest the inch or foot throughout. temperature in the stream.) In the laminar sublayer, im Expressions of conductivity used in the heating field are mediately adjacent to the wall, the heat transfer occurs by usually inconsistent in this sense, in that it is customary to thermal conduction; in the transition region, which is called refer to the conductivity per square foot but for one inch of the buffer layer, eddy mixing as well as conduction effects are significant; in the eddy or turbulent region the major thickness. This custom has been adopted for the reason that wall thicknesses are usually expressed in inches, whereas fraction of the transfer occurs by eddy mixing. In most commercial equipment the main body of the fluid if expressed in feet, decimal or fractional thicknesses would result. When dealing with flat walls, no complication is in is in turbulent flow, and the laminar film exists at the solid volved in using the inconsistent expression of conductivity. walls only, as shown in Fig. 1. In cases of low-velocity flow However, where curved or spherical walls are concerned, 47