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98 CHARTER ,5 1948 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 maybe 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 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 ba'ck 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. Fig. 1. Thermal Convection Conditions Fig. 2. Thermal Conduction in a Flat Slab 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 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, k, Btu per (hour) (square foot) (Fahrenheit degree per foot of thickness). A = _ kAL dA * dL (1) The minus sign on the right side of the equation is introduced toindicate 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 Fundamentals of Heat Transfer 99 v` inconsistent in this sense, in that .it is; customary to refer to the con ductivity per squarefoot but for one inch of thickness., This custom has been adopted for.^fne 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) (Fahrenheit degrees per one foot thickness) are used throughout. Conductivity values obtained from 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 ip Table 2 of Chapter 6, becomes 0.42 when Table 1. Approximate Unit Thermal Conductivities* Conductivity, k = Btu per (hr) (sq ft) (F deg per in.) Material ki Material k Air ______________ _ Aluminum____________ Cast-Iron______ . Copper . ____ ___ Glass. ................... 0.168 1416.0 720.0 336.0 2640.0 3.6--7.32 Lead____ _____ _ ____ Nickel________________ 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 Heat Transmission, 2nd edition, by W. H. McAdams-(McGraw-Hill Co., 1942) for addi tional valu es. 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, aU dimensions of thickness must be expressed in feet. Thermal Convection Equation = *c (. - if) (2) This rate equation states that the thermal convection per unit transfer area (dq)/(dA), Btu per (hour) (square foot) is proportional to the tem perature difference, (4 -- tt) 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), he, Btu per (hour) (square foot) (Fahrenheit degree). 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: i) (i) -*>" where 5c = heat transmission by convection, Btu per (square foot) (hour). C = a constant depending upon the shape of the surface. (2a)