The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 65
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Let’s try a sintered particle wickmade of copper with the following properties (see Table 4.8.5):d = 1.91 ´ 10–4 mrc,3 = 0.21d = 4.0 ´ 10–5 m (same as before)e = 0.48-4 2K=(1.91 ´ 10 )(0.48)= 2.07 ´ 10 -10 m 22150(1 - 0.48)ks = 400W(copper )mKk1 = 0.630keff =W(water)mK400[2(400) + 0.63 - 2(0.48) (400 - 0.63)]2(400) + 0.63 + 0.48(400 - 0.63)= 168 W mKAll other geometric and thermophysical properties are the same. The heat transfer limitations affectedby the change in wick structure are the capillary and boiling limitations.
The sintered metal wick producesa capillary limitation of(é (992.1) (0.07) 2.402 ´ 10 6Qc,max = ê6.5 ´ 10 -3êë) ùú éê (9.11 ´ 10 ) (2.07 ´ 10 ) ùú é-50.75úû êë-102úû êë 4.0 ´ 10-5+992.19.8(1.0)ùú0.07û(4.8.37)= 122 WThe boiling limitation for the sintered wick isQb,max =(4 p(0.75) (168)(313)(0.07) é11ù0.015 ö êë 2.0 ´ 10 -6 4.0 ´ 10 -5 úûæ62.402 ´ 10 (992.1) lnè 0.014 ø)(4.8.38)= 100 WThis design now meets all the specifications defined in the problem statement.Application of Heat PipesHeat pipes have been applied to a wide variety of thermal processes and technologies.
It would be animpossible task to list all the applications of heat pipes; therefore, only a few important industrialapplications are given in this section. In the aerospace industry, heat pipes have been used successfullyin controlling the temperature of vehicles, instruments, and space suits. Cryogenic heat pipes have beenapplied in (1) the electronics industry for cooling various devices (e.g., infrared sensors, parametricamplifiers) and (2) the medical field for cryogenic eye and tumor surgery.
Heat pipes have been employedto keep the Alaskan tundra frozen below the Alaskan pipeline. Other cooling applications include (1)turbine blades, generators, and motors; (2) nuclear and isotope reactors; and (3) heat collection fromexhaust gases, solar and geothermal energy.In general, heat pipes have advantages over many traditional heat-exchange devices when (1) heathas to be transferred isothermally over relatively short distances, (2) low weight is essential (the heatpipe is a passive pumping device and therefore does not require a pump), (3) fast thermal-response timesare required, and (4) low maintenance is mandatory.© 1999 by CRC Press LLC4-271Heat and Mass TransferDefining TermsCapillary force: The force caused by a curved vapor-liquid interface.
The interfacial curvature isdependent on the surface tension of the liquid, the contact angle between the liquid wick structure,the vapor pressure, and the liquid pressure.Effective thermal conductivity: The heat transfer rate divided by the temperature difference betweenthe evaporator and condenser outer surfaces.Heat transfer limitations: Limitations on the axial heat transfer capacity imposed by different physicalphenomena (i.e., vapor pressure, sonic, entrainment, capillary, and boiling limitations).Wettability: The ability of a liquid to spread itself over a surface. A wetting liquid spreads over a surfacewhereas a nonwetting liquid forms droplets on a surface.Wick: A porous material used to generate the capillary forces that circulate fluid in a heat pipe.ReferencesChi, S.W. 1976. Heat Pipe Theory and Practice, Hemisphere Publishing, Washington, D.C.Dunn, P.D.
and Reay, D.A. 1982. Heat Pipes, 3rd ed., Pergamon Press, Oxford, U.K.Gaugler, R.S. 1944. Heat Transfer Device. U.S. Patent No. 2350348.Grover, G.M. 1963. Evaporation-Condensation Heat Transfer Device. U.S. Patent No. 3229759.Peterson, G.P. 1994. An Introduction to Heat Pipes Modeling, Testing, and Applications, John Wiley &Sons, New York.Further InformationRecent developments in heat pipe research and technology can be found in the proceedings from anumber of technical conferences: (1) The International Heat Pipe Conference (2) The National HeatTransfer Conference, (3) The ASME Winter Annual Meeting, (4) The AIAA Thermophysics Conference.Books particularly useful for the design of heat pipes include (1) Heat Pipe Design Handbook byBrennan and Kroliczek available from B&K Engineering in Baltimore, M.D.
(2) The Heat Pipe byChisholm available from Mills and Boon Limited in London, England, and (3) Heat Pipes: Constructionand Application by Terpstra and Van Veen available from Elsevier Applied Science in New York, N.Y.An additional book particularly strong in heat pipe theory is The Principles of Heat Pipes byIvanovskii, Sorokin, and Yagodkin available from Clarendon Press in Oxford, England.Cooling Electronic EquipmentVincent W. AntonettiIntroductionIn electronic packages, the thermal resistances to heat transfer from heat source to heat sink are oftengrouped into an internal resistance and an external resistance. The internal thermal resistance Rint isconductive and exists between the chip and the module case:Rint =Tchip - TcasePchip(4.8.39)where Pchip is the chip power.The external thermal resistance Rext is primarily convective and exists between the surface of the caseof the module and some reference point, typically the temperature of the cooling fluid near the module.In a multichip module, the module power Pm is the sum of the individual chip powers, and the externalresistance is© 1999 by CRC Press LLC4-272Section 4Rext =Tcase - TcoolantPm(4.8.40)The internal and external resistances are related to the chip junction temperature Tj through the followingexpression:Tj = DTj -chip + Pchip Rint + Pm Rext + DTcoolant + Tcoolant in(4.8.41)Many factors are involved in determining the appropriate cooling mode to be used.
If the componentjunction temperature is constrained to approximately 85°C, Table 4.8.6 may be used to make a preliminary selection of the cooling mode. Extended surfaces can often be used to increase the allowable heatfluxes.TABLE 4.8.6Maximum Component Heat Flux for Various Cooling ModesCooling ModeW/cm2Free convection airForced convection airImpingement airFree convection immersionForced convection immersionPool boilingForced convection boilingJet immersion (single phase)Boiling jet immersion0.050.51.01.050201004090Free Convection Air Cooling of Vertical Printed Circuit BoardsData have been collected from rack-mounted simulated printed circuit boards (PCBs) (see Figure 4.8.15)and from several actual electronic systems at AT&T Bell Laboratories.
Results indicated that existingparallel plate correlations for symmetric isoflux plates (separated by distance “b”) could be adapted toPCB conditions. Specifically, for Rab < 10 use the equation corresponding to the fully developed laminarboundary layer condition:Nu b = 0.144 Ra b0.5(4.8.42)For 10 < Rab < 1000, useé 482.5 ùNu b = ê+0.4 úRaRab ûë b-0.5(4.8.43)whereRa b =gbc p r2 b 5 q ¢¢mkLFor Ra > 1000, the expression for an isolated plate in infinite media is recommended:Nu b = 0.524 Ra b0.2© 1999 by CRC Press LLC(4.8.44)4-273Heat and Mass TransferaLbFIGURE 4.8.15 Typical PCB array.In the previous three expressions air properties are evaluated at the average of the module case andambient temperatures.The PCB spacing bmax for a given power dissipation which yields the lowest PCB component casetemperatures (or which maximizes the rate of heat transfer while maintaining PCB temperatures belowthe maximum allowable) occurs when the developing boundary layers from adjacent PCBs do notinterfere, i.e., so the isolated plate condition is approached as follows: If heat is transferred from bothsides of the PCB, let Raab = 17,000 and the recommended PCB spacing is bmax = 7.02x–0.2.
If heat istransferred from only one side of the PCB, let Raab = 5400 and the recommended PCB spacing is bmax= 5.58x–0.2. In both casesx=gbr2 Prq ¢¢m 2 kL(4.8.45)Forced Convection Air Cooling of Vertical PCBsSparrow et al. (1982, 1984) studied vertical arrays with simulated modules of uniform size, which was4 modules wide by 17 module rows deep in the flow direction; the modules were 26.7 mm square and10 mm high; the space between modules was 6.67 mm, and the distance from the top of the module tothe adjoining card Hc = 16.7 mm.
The Nusselt number as a function of module row position for a fullypopulated array may be determined from Figure 4.8.16. Correction factors to the fully developed Nusseltnumbers for the effect of missing modules and the presence of modules whose height differs from othersin the array are presented in the cited references.In actual electronic packages, conditions differ from the relatively ideal setups in laboratories becausein real packages the flow is disturbed by the PCB supporting hardware and may extend the entry regioneffect.Data from actual computer hardware with PCBs containing a 6 ´ 4 array of 28 mm modules (4 inthe flow direction) were used to develop the following expressions:{ [Nu x = C Re Dh 1 + x ( Dh )© 1999 by CRC Press LLC-0.836]}m(4.8.46)4-274Section 4100Re = 7000Re = 3700Re = 2000Nusselt Number8060402000246Row Number810FIGURE 4.8.16 Nusselt number for fully populated array of modules.For Re < 2000, C = 0.072 and m = 0.70, and for 2000 < Re < 10,000, C = 0.056 and m = 1.02, wherex is the distance in the flow direction.
Because the array was only 4 modules deep, all the modules onthe PCB were in the entry region.Tests have been conducted on a 9 ´ 7 array of 25-mm-square by 6.4-mm-high blocks cooled by a 3´ 3 array of air jets directed normal to the face of each block. The spent flow exited along the channelformed by the orifice plate and the heat transfer surfaces. Test results were correlated by the relation:N d = 0.213( z d )-0.376Re 0d.743(4.8.47)where d is the jet orifice diameter, s is the orifice-to-orifice spacing, and z is the distance from the orificeoutlet to the face of the module.Immersion CoolingThe highly inert perfluorinated liquids, called FC coolants by the 3M Company, are frequently used inimmersion cooling applications. FC coolants are available with boiling points from 30 to 172°C atatmospheric pressure.
FC-75 are FC-77 with boiling points of 100°C are often used in single-phaseapplications, while FC-72 and FC-87, with boiling points of 56 and 30°C, respectively, are used insystems involving phase change.Data exist for free convection immersion cooling of a 3 ´ 3 array of simulated chips mounted on avertical wall in an enclosure filled with FC-75. Each heat source was 8 mm high by 24 mm wide by 6mm thick. With the Nusselt and modified Rayleigh numbers based on the heater height, L, the best fitto the data isNu L = 0.279Ra 0b.224(4.8.48)Air cooling expressions have been modified to make them applicable to free convection immersioncooling of vertical PCB arrays with FC coolants.
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