Document dDQ0dDN4o1Y9827gqx4eg6wyQ

50 CHAPTER 5 1960 Guide considerable complication is involved. Therefore, in this discussion the consistent units of conductivity expressed in Btu per (hew) (square foot) (Fahrenheit degrees per one foot thickness) ate used throughout. Conductivity values obtained from Chapter $ or Table t in this chapter, must therefore he eonverted for use in the calculations of this chapter by dividing by IS. As an example, the conductivity of brick listed as 5.0 in Table 4 of Chapter 9, becomes 0.42 when used in the calculations of fchta chapter. Also, it should be emphasised that in order to make the calculations and applications con sistent in this chapter, all dimensions of thickness must be expressed in feet. Fig. 1 .... Thermal Convection Conditions Thermo! Convection Equation ~ - Ml. - hi (2) This rate equation states that the thermal convection per unit transfer ares (q/A), Btu per (hour) (square foot) is proportional to the temperature difference (f, -- </) 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 thermal convective con ductance (sometimes called the film coefficient for convec tion), hc, Btu per (hour) (square foot) (Fahrenheit degree). Fig. I shows the conditions associated with convection. The heat transmission by free or natural convection for objects surrounded by air can be conveniently expressed as in Equation 3: <3> uhere q -- * heat transmission by convection, Btu per (square foot) (hour). Table 1 .... Approximate Unit Thermal Conductivities* Conductivity, k Btu per (dr) (sq ft) (F dog per fiv) Material k Material k Lead................. 240.0 Brass (70 - 30) .. Cast-Iron............. Copper................. Glass..................... 720.0 SoU................... 336.0 Steel, mild.... 2640.0 Water, liquid.. 3.6-7.32 2.4-12.0 312.0 4.08 * Tberms] eoodoctiritiet depesd to toatc extent oa temperetam. The rime aeenitadea ere eppraximrie only, fte&r to Chapter 0, asd Reference < Ice nd<tttoari drift. B * a constant depending upon the shape of the sur face. 2> -- diameter of pipe or circular duet or height of ver tical wall, inches. (Effect of diameter or height becomes constant at 24 in.) Too " average of wall surface and surrounding air tem perature, Fahrenheit degrees absolute. t, -- tf -- temperature excess between wall surface and sur rounding sir, Fahrenheit degrees. For horizontal cylinders, the value of B =* 1.02 has been well established by various investigations. For vertical plates, the value of B *= 1.39 has been fairly well established. Suggested values* of B for horizontal plates warmer than the surrounding air are 1.79 when facing upward, and 0.89 when facing downward. Problems in either forced convection or natural convec tion may be solved by the simple first-power equation if the convection coefficient is expressed as a unit conductance: ) where q b heat transmission by convection, Btu per hour. A = surface area, square feet, f, -- f, ~ temperature difference between the surface and the fluid, Fahrenheit degrees. A, ft* unit convective conductance, from Table 2, Btu per (square foot) (hour) (Fahrenheit degree tem perature difference). Fig. 2 .... Thermal Conduction in a Rat Slab Thermal Radiation Equation The relation given by Equation 5 is applicable to systems in which radiant exchange takes place between the surfaces of solids, as schematically shown in Fig. 3. qt - oAiFaFm(Ti* - TV) (5) Gaseous and luminous radiation are not considered in tJiia discussion. Equation 5 states that the net radiation per unit transfer area of surface 1, q,/A Btu per (hour) (square foot), which sees surface 2 through a non-absorbing medium, is proportional to the difference of the fourth powers of the absolute surface temperatures (7V TV). The proportion ality factor (<rFaF%) may be conveniently separated into three parts (excepting in some problems involving interreflections, where it is not possible to divide the product (Fj.Fs) into separate terms): a > the Stefan-Boltzmann radiation constant = 1730 X 10"M Btu per (hour) (square foot) (Fahrenheit degree abso lute temperature to the fourth power). Heat Transfer 51 -Cmo Table 2 . :. Approximate Unit Conductances for Thermal Convection for Several Row Systems Expronod in Convenient Empirical Fora SyxtM Hoot Troitifar Equation and /ft Liaitt of Appficofioo Forced Convection 1 Ref. 3 W J o Longitudinal flow in' ' ^ --grsl v y 1 a circular cylinder.^ General Equation hj> ~ - 0.0225 /{lX~?jy * /C^V4* f-=-J /OG\ wAere t > 4.4D and {--J > 2200 2 Ref: 3 Same as Case l.fc Equation for Air 1, * 5.4 X 10~<(77)*-* -- where x > *Af> and 1--J > 2200 3 Ref. 3 Same as Case l.b 4r ** 13.5(//)*-M Equation for Liquid Water (32-400 F) where x > 4.40 and > 2200 4 Ref. 4 v^yj single cylinder. General Equation h,D /DOV * /ewA** -~ft=0.26f -- j f-=l DG where 1000 < < 50,000 5 Ref. 4 Same as Case 4. 6 Ref. 4 Same as Case 4. Equation for Air Kw^ooC - Q.2H(T/)I M -ff. IF* where 1000 < -- < 50,000 ft ~ Equation for Liquid Water (32-400 F) It.- 34.0(i,)' " where 1000 > -- > 50,000 7 Ref. 3 j J 8 Ref. 3 Same as Case 7. 9 Ref. 3 Same as Case 7. General Equation (Turbulent Flow) 7Flow along a flat plate. t5 - 00296 ( )" (t)'" **" (7) > 500'00 and A 1.254,, Equation for Air (Turbulent Flow) K. - 0.5I(r,)* ` Jjjirr" tnherc and > 500,000 " 1.254,, General Equation (Laminar Flow) For ^ < 500,000 and A*(.wru,| 24,, 10 Ref. 3 Same as Case 7. Equation for Air (Laminar Flow) 0.0562(7-,)' For ^ < 500,000