Document b5OYJ1LGy9z8dLjLGqjZDzp7O

ioo ,CHAPTER 5 1946-Guide In most commercial equipment the main body of the fluid is in turbu lent flow, and the laminar film exists at the solid wails only, as shown in Fig. 1. But in cases of low-velocity flow in small tubes, or with viscous liquids such as heavy oil (low Reynolds numbers), the entire flow may be laminar. In these latter cases there is no transition or eddy region. When the fluid currents are induced by sources external to the heat transfer region, as for example a pump, the described solid to fluid heat transfer is termed forced convection. In contrast, if the fluid currents are internally generated, as a result of non-homogeneous densities arising from the temperature variations, the heat transfer is termedfree convection. In the conduction and convection mechanisms heat is transferred as internal energy, i.e., the random molecular kinetic energy associated with the material temperature. For radiant heat transfer, however, a change in energy form takes place from internal energy at the source to electro magnetic energy for transmission, then back to internal energy at the receiver. Since radiant energy exhibits characteristic wave lengths, the Fig. 1. Thermal Convection Conditions Fig. 2. Thermal Conduction in a Flat Slab solution of thermal radiation problems is in many respects similar to the solution of problems in the field of illumination. The rate, of thermal current flow (i.e., rate of heat transfer), corre sponding 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 being proportional to the potential difference. Thermal Conduction Equation Equation 1 states symbolically that the thermal conduction current per unit transfer area normal1 to the flow, (dq)/(dA), Btu per (hour) (square foot), is proportional to the temperature gradient (dt)/(dL), degrees Fahrenheit per foot. The proportionality factor is termed the thermal conductivity, k, Btu per (hour) (square foot) (degrees Fahrenheit per foot of thickness). Al___kJL dA dL (1). The minus sign on the right side of the equation is introduced to indicate positive current flow in the direction of decreasing temperature. Fig. 2 shows the physical significance of indicated quantities. It should be emphasized that the thermal conductivity Used should be expressed in consistent units; either using the inch or foot throughout. ' Fundamentals of Heat Transfer 101 Expressions of conductivity' used in the heating field are usually inconsistent in this sense, in that it is customary to refer to the con ductivity per square foot but for one inch of thickness. This custom has been adopted for the reason that wall thicknesses are usually expressed in inches, whereas if expressed in feet, decimal or fractional thicknesses would result. When, dealing with flat walls no complication is involved in using the inconsistent expression of conductivity. However, when curved or spherical walls are considered, considerable complication is involved. Therefore, in this discussion the consistent units of con ductivity expressed in Btu per (hour) (square foot) (degrees Fahrenheit per one foot thickness) are used throughout. Conductivity values obtainedfrom Chapter 6 or Table 1 in this chapter, which are expressed in inconsistent units, must therefore be converted for use in the calculations of this chapter by dividing by 12. As an example, the conductivity of brick, expressed in inconsistent units as 5.0 in Table 2 of Chapter 6, becomes 0.42 when Table 1. Approximate Unit Thermal Conductivities.3 Conductivity, k = Btu per (hr) (sq ft) (deg F per in.) Material k Material k Air. Aluminum...'........... . .. Brass (70 -- 30) ........ Cast-Iron........ -........... Copper......................... Glass.--..... :..................... 0.168 1416.0. ' 720.0 336.0 2640.0. 3.6--7.32 Nickel........... ............... Soil................................ Steel, mild............. :..... Water,.liquid............... 240.0 408.0 2.4--12.0 312.0 ! 4.08 aThern^l conductivities depend to some extent on temperature. The above magnitudes are approxi mate only. Refer to Heat Transmission, by W. H. McAdams (McGraw-Hill Co., 1942) for additional values. used in the calculations of this chapter. Also, it should be emphasized that in order to make the calculations and applications consistent in this chapter, all dimensions of thickness must be expressed in feet. Thermal Convection Equation ! = he ((.. - tt) ' (2) This rate equation states that the thermal convection current per unit transfer area (dq)/(dA), Btu per (hour) (square foot) is proportional to the temperature difference, (ts -- k) which is the temperature of the surface less that of the fluid. The particular fluid temperature to use for a given system will be noted under the discussion of that system. The proportionality factor is termed the unit convection conductance (some times called the film coefficient for convection), hc, Btu per (hour) (square foot) (degree' Fahrenheit). These convection conditions are illustrated in Fig.,1. The heat transmission by free or natural convection for objects sur rounded by air can be conveniently expressed as in Equation 2a: where ^ - ) U )f t(1 \ o.t / i \ o.ui ..... (2a) ffc = heat transmission by convection, Btu per (square foot) (hour). 1 C -- a constant depending upon the surface shape.