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102 CHAPTERS 1949 Guide. 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 heat is transferred as internal energy, i.e., the random molecular kinetic energy associated with Fundamentals of Heat Transfer k, Btu per (hour) (square foot). (Fahrenheit d^ree 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 indicated quantities. It should be emphasized that the thermal conductivity used should be expressed in consistent units; either using the inch or foot throughout. Expressions of conductivity used in the heating field are usually incon sistent in this sense, in that it is customary to refer to the conductivity per squarefoot 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 Fia.l. Thermal Convection Conditions 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. The rate of heat transfer, corresponding to the three transfer mech anisms previously described, may be expressed by three rate equations. Table 1. Approximate Unit Thermal Conductivities* Conductivity, k = Btu per (hr) (tsqfl) (F deg per in.) Material Air___ _.... Aluminum..;____ . ' ; , Brass (70 - 30) Cast-Iron_____ Cooper Glass. k 0.168 1416.0 720.0 336.0 2640.0 3.0-7.32 Material Nickel. .*....... Soil Water, liquid_______ k 240.0 408.0 2.4--rl2.0 312.0 4.08 Thermal conductivities depend to some extent on temperature. The above magnitudes are approxi mate only. Refer to Heat Transrmssion. 2nd edition, by W. H. McAdams (McGraw-Hill Co.. 1942) foraddi- tionai values. . 'These are similar to Ohm's Lawfor 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 per unit transfer area normal to the flow, (dq)/(dA), 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, Fig. 2. Thermal Conduction in a Flat Slab expression of conductivity. However,, when curved or spherical walls are considered, considerable complication is involved. Therefore, in this discussion the consistent units of conductivity expressed in Btu per (hour) (square foot),.(Fahrenheit degrees per one foot thickness) are used throughout. Conductivity values obtained from Chapter 6 or Table 1 in this chapter, must therefore be converted for use in the calculations of this chapter by dividing by IF. As an example, the conductivity of brick listed as 5.0 in Table. 2 of Chapter 6, becomes 0.42 when 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 ^- = K(t,-td dA (2) This rate equation states that the thermal convection per unit transfer area (dg)/(dA), Btu per (hour) (square foot) is proportional to the tem perature difference (t,--li) 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 propor tionality factor is termed the unit convection conductance (sometimes called the film coefficient''for convection), hc, Btu per (hour) . (square, foot): (Fahrenheit degree). These convection conditions are illustrated in Fig. 1.