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96 CHAPTERS 1951 Guide 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 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 produced by sources external to the heat transfer region, as for example by a pump, the described solid to fluid heat transfer is termed forced convection. In contrast, if the fluid currents are generated internally, 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 transfer of heat is associated with matter. For radiant heat transfer, however, a change in Heat Transfer 97 Evoressions-of.conductivity used in the heating field are usually incon- ft in this sense,- -in that it is customary to refer to the conductivity S1S (ruare fool but for one inch of thickness. This custom has been adopted Per fuergason that wall thicknesses are usually expressed in inches, whereas fexDressed 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, where curved or spherical walls are concerned considerable complication is involved. Therefore, in this discussion'the consistent units of conductivity expressed in Btu per (hour) (sauare foot) (Fahrenheit degrees per one foot thickness) are used throughout. Conductivity values obtained from. Chapter 9 or Table 1 in this chapter, must therefore be converted for use in the calculations of this chapter by dividing bv '18- As an example, the conductivity of brick listed as 5.0 in Table 2 of Chapter 9, becomes 0.42 when used in the calculations of this chapter. Fig. 1. Thermal Convection Conditions energy form takes place, from internal energy at the source to electromag netic energy for transmission, then back to internal energy at the. receiver. The rate of heat transfer, corresponding to the three transfer mech anisms 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. The. convection and radiation flow rate expressions may be approximated by a potential (tem perature difference) and a resistance in order that heat transfer calculations may be effected more conveniently and rapidly. Thermal Conduction Equation . Equation 1 states symbolically that the thermal conduction per unit transfer area normal to the flow, q/A, Btu per (hour) (square foot), is proportional to the temperature gradient (dt)/(dL), Fahrenheit degrees per foot. The proportionality factor is termed the thermal conductivity, k, Btu per (hour) (square foot) (Fahrenheit degree per foot of thickness). The minus sign on the right side of the equation is introduced to indicate positive transfer in the direction of decreasing temperature. Fig. 2 shows the physical significance of the indicated quantities. It should be emphasized that the thermal conductivity used should be expressed in consistent units; either using the inch or foot throughout. Fig. 2. Thermal Conduction in a Flat Slab 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. 7= A - <<> (2) This rate equation states that the thermal convection per unit transfer area {q/A)t Btu per (hour) (square foot) is proportional to the tem- Table 1. Approximate Unit Thermal Conductivities* Conductivityt k = Btu per (hr) (sqft) (F deg per in.) Material Air Aluminum Brass (70 - 30) Cast-Iron CoDper.... Glass. k 0.168 1416.0 720.0 336.0 2640.0 , 3.6--7.32 Material SoiL ......... ............. Steel, mild_______ _ Water, liquid.............. * 240.0 408.0 2.4--12.0 312.0 4.08 * Thermal conductivities depend to some extent on temperature. The above magnitudes are approxi mate only. Refer to Chapter 9, and Reference 4 for additional data.