The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 31
Текст из файла (страница 31)
The first effect due to fluid property variations (or radiation) consists of two components: (1)distortion of velocity and temperature profiles at a given flow cross section due to fluid property variations— this effect is usually taken into account by the so-called property ratio method, with the correctionscheme of Equations (4.5.55) and (4.5.56) — and (2) variations in the fluid temperature along the axialand transverse directions in the exchanger depending upon the exchanger flow arrangement — this effectis referred to as the temperature effect.
The resultant axial changes in the overall mean heat transfercoefficient can be significant; the variations in Ulocal could be nonlinear, dependent upon the type of thefluid. The effect of varying Ulocal can be taken into account by evaluating Ulocal at a few points in theexchanger and subsequently integrating Ulocal values by the Simpson or Gauss method (Shah, 1993). Thetemperature effect can increase or decrease mean U slightly or significantly, depending upon the fluidsand applications. The length effect is important for developing laminar flows for which high heat transfercoefficients are obtained in the thermal entrance region.
However, in general it will have less impact onthe overall heat transfer coefficient because the other thermal resistances in series in an exchanger maybe controlling. The length effect reduces the overall heat transfer coefficient compared with the meanvalue calculated conventionally (assuming uniform mean heat transfer coefficient on each fluid side). Itis shown that this reduction is up to about 11% for the worst case (Shah, 1993).Shah and Pignotti (1997) have shown that the following are the specific number of baffles beyondwhich the influence of the finite number of baffles on the exchanger effectiveness is not significantlylarger than 2%: Nb ³ 10 for 1-1 TEMA E counterflow exchanger; Nb ³ 6 for 1-2 TEMA E exchangerfor NTUs £ 2, Rs £ 5; Nb ³ 9 for 1-2 TEMA J exchanger for NTUs £ 2, Rs £ 5; Nb ³ 5 for 1-2 TEMAG exchanger for NTUs £ 3, all Rs; Nb ³ 11 for 1-2 TEMA H exchanger for NTUs £ 3, all Rs. Variousshell-and-tube heat exchangers (such as TEMA E, G, H, J, etc.) are classified by the Tubular ExchangerManufacturers’ Association (TEMA, 1988).If any of the basic idealizations are not valid for a particular exchanger application, the best solutionis to work directly with either Equations 4.5.1 and 4.5.2 or their modified form by including a particulareffect, and to integrate them over a small exchanger segment numerically in which all of the idealizationsare valid.Fin Efficiency and Extended Surface Efficiency.Extended surfaces have fins attached to the primary surface on one or both sides of a two-fluid or amultifluid heat exchanger.
Fins can be of a variety of geometries — plain, wavy, or interrupted — andcan be attached to the inside, outside, or both sides of circular, flat, or oval tubes, or parting sheets. Finsare primarily used to increase the surface area (when the heat transfer coefficient on that fluid side isrelatively low) and consequently to increase the total rate of heat transfer. In addition, enhanced fingeometries also increase the heat transfer coefficient compared to that for a plain fin. Fins may also beused on the high heat transfer coefficient fluid side in a heat exchanger primarily for structural strengthpurposes (for example, for high-pressure water flow through a flat tube) or to provide a thorough mixingof a highly viscous liquid (such as for laminar oil flow in a flat or a round tube). Fins are attached tothe primary surface by brazing, soldering, welding, adhesive bonding, or mechanical expansion, or theyare extruded or integrally connected to the tubes.
Major categories of extended surface heat exchangersare plate-fin (Figures 4.5.2 to 4.5.4) and tube-fin (Figures 4.5.5 to 4.5.7) exchangers. Note that shelland-tube exchangers sometimes employ individually finned tubes — low finned tubes (similar to Figure4.5.5a but with low-height fins) (Shah, 1985).The concept of fin efficiency accounts for the reduction in temperature potential between the fin andthe ambient fluid due to conduction along the fin and convection from or to the fin surface dependingupon the fin cooling or heating situation. The fin efficiency is defined as the ratio of the actual heattransfer rate through the fin base divided by the maximum possible heat transfer rate through the fin© 1999 by CRC Press LLC4-134Section 4© 1999 by CRC Press LLCHeat and Mass Transfer4-135© 1999 by CRC Press LLC4-136Section 4© 1999 by CRC Press LLC4-137Heat and Mass TransferFIGURE 4.5.13 A flat fin over (a) an in-line and (b) staggered tube arrangement; the smallest representative segmentof the fin for (c) an in-line and (d) a staggered tube arrangement.base which would be obtained if the entire fin were at the base temperature (i.e., its material thermalconductivity were infinite).
Since most of the real fins are “thin”, they are treated as one-dimensional(1-D) with standard idealizations used for the analysis (Huang and Shah, 1992). This 1-D fin efficiencyis a function of the fin geometry, fin material thermal conductivity, heat transfer coefficient at the finsurface, and the fin tip boundary condition; it is not a function of the fin base or fin tip temperature,ambient temperature, and heat flux at the fin base or fin tip in general. Fin efficiency formulas for somecommon fins are presented in Table 4.5.5 (Shah, 1985). Huang and Shah (1992) also discuss the influenceon hf if any of the basic idealizations used in the fin analysis are violated.The fin efficiency for flat fins (Figure 4.5.5b) is obtained by a sector method (Shah, 1985).
In thismethod, the rectangular or hexagonal fin around the tube (Figures 4.5.7a and b) or its smallest symmetrical section is divided into n sectors (Figure 4.5.13). Each sector is then considered as a circular finwith the radius re,i equal to the length of the centerline of the sector. The fin efficiency of each sector issubsequently computed using the circular fin formula of Table 4.5.5. The fin efficiency hf for the wholefin is then the surface area weighted average of hf,i of each sector.nåhhf =f ,iA f ,ii =1(4.5.22)nåAf ,ii =1Since the heat flow seeks the path of least thermal resistance, actual hf will be equal to or higher thanthat calculated by Equation (4.5.22); hence, Equation (4.5.22) yields a somewhat conservative value of hf .The hf values of Table 4.5.5 or Equation (4.5.22) are not valid in general when the fin is thick, whenit is subject to variable heat transfer coefficients or variable ambient fluid temperature, or when it has atemperature depression at the fin base.
See Huang and Shah (1992) for details. For a thin rectangularfin of constant cross section, the fin efficiency as presented in Table 4.5.5 is given by© 1999 by CRC Press LLC4-138TABLE 4.5.5Section 4Fin Efficiency Expressions for Plate-Fin and Tube-Fin Geometries of Uniform Fin ThicknessFin Efficiency FormulaGeometryé 2h ædi öùmi = êç1 + ÷ úl f øúê k f di èëû12E1 =tanh(mi l 1 )m i l1i = 1, 2hf = E1bl1 = - d 1 d 1 = d f2hA1 (T0 - Ta )hf =sinh( m1l1 )m1l1+ qeéT - Ta ùcosh( m1l1 ) êhA1 (T0 - Ta ) + qe 0úT1 - Ta úûêëhf = E1l1 =hf =ld1 = d f2E1l1 + E2 l21l1 + l2 1 + m12 E1 E2 l1l2d1 = d fd2 = d3 = d f + dsl1 = b - d f +ds2l 2 = l3 =pf2ìa(ml ) - bfor F > 0.6 + 2.257 r *eïh j = í tanh Ffor F £ 0.6 + 2.257 r *ïî F( )( )( )a = r*-0.246( )F = mle r *-0.445-0.445exp ( 0.13 mle -1.3863)for r * £ 2ì0.9107 + 0.0893r *b=í**î0.9706 + 0.17125 ln r for r > 2æ 2h öm=ç÷è kfd f øhj =le = l j +df2r* =dedotanh( mle )mleé 2hm=êêë k f d f© 1999 by CRC Press LLC12d f öùæç1 + w ÷ úèø úû12le = l j +df2lf =(de- do )24-139Heat and Mass Transferhf =tanh(ml)ml(4.5.23)where m = [2h(1 + df lf )/kf df ]1/2.
For a thick rectangular fin of constant cross section, the fin efficiency(a counterpart of Equation (4.5.23) is given by (Huang and Shah, 1992)+ 12hf =(Bi )[12( )tanh K Bi +KBi](4.5.24)where Bi+ = Bi/(1 + Bi/4), Bi = (hdf /2kf )1/2, K = 2l/df . Equation (4.5.23) is accurate (within 0.3%) fora “thick” rectangular fin having hf > 80%; otherwise, use Equation (4.5.24) for a thick fin.In an extended-surface heat exchanger, heat transfer takes place from both the fins (hf < 100%) andthe primary surface (hf = 100%). In that case, the total heat transfer rate is evaluated through a conceptof extended surface efficiency ho defined asho =ApA+ hfAfA= 1-AfA(1 - h )f(4.5.25)where Af is the fin surface area, Ap is the primary surface area, and A = Af + Ap. In Equation 4.5.25, heattransfer coefficients over the finned and unfinned surfaces are idealized to be equal.
Note that ho ³ hfand ho is always required for the determination of thermal resistances of Equation (4.5.5) in heatexchanger analysis.Pressure Drop Analysis.Usually a fan, blower, or pump is used to flow fluid through individual sides of a heat exchanger. Dueto potential initial and operating high cost, low fluid pumping power requirement is highly desired forgases and viscous liquids.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
