The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 66
Текст из файла (страница 66)
The Nusselt number (based on PCB spacing “b”) atthe top of the PCB is© 1999 by CRC Press LLC4-275Heat and Mass Transferé C2.78 ù+Nu L = ê0.4 úë Ra b Ra b û-0.5(4.8.49)C = 24 when heat transfer is from one side of the PCB, and C = 48 when from both sides.Nucleate Pool BoilingA number of investigators have tested small flush heat sources boiling in a pool of dielectric liquid.
Theheaters ranged from 4 ´ 4 mm to 12.7 ´ 12.7 mm. Typical saturated pool boiling data for FC-72 andFC-87 are shown in Figure 4.8.17. Note that a temperature overshoot up to 25°C has been regularlyobserved for silicon chips in dielectric liquid pools. To estimate the temperature excursion at boilingincipience (qi¢¢), the following approximation is recommendedæön2sDTex = Tsat ç p - pg ÷ - Tsat - C(qi¢¢)rbèø(4.8.50)whereéùcpC = mh fg êúbêë h fg Pr Csf úû1aéùaêúê g r - rg úëû(0.5)(4.8.51)with rb = 0.25 mm, Csf = 0.003, a = 0.33, and b = 1.7. (Note that n = 1/a = 3.)Park and Bergles (1988) determined the critical heat flux (CHF) as a function of size for flush heatersoperating in a saturated pool of R-113. For a 5-mm-wide heater, and for heater heights from 5 to 80mm, useqc¢¢sat152= 0.86 éê1 + *3.29 ùúqc¢¢zë Lû0.14(4.8.52)where the CHF prediction of Zuber, qc¢¢z = r0g.5 hfg[sg(rf – rg)]0.5, and L* = L[g(rf – rg)/s]0.5.For a 5-mm-high heater, and for heater widths from 2.5 to 70 mm, useqc¢¢sat52= 0.93éê1 + 1.02 ùúqc¢¢zë I û0.14(4.8.53)where the induced convection parameter is I = (rf Ws/m2)0.5.For flush 12.7 ´ 12.7 mm heaters in FC-72, test data yield qc¢¢sat / qc¢¢z » 1.45.
These subcooling datawere correlated by0.0643r f c p, f é r g ù= 1+ê úr g h fgqc¢¢satêë r f úûqc¢¢sub14DTsub(4.8.54)Single-Phase and Boiling Forced Convection in Channel FlowThe average Nusselt numbers for 12 flush 12.7 ´ 12.7 mm heaters (4 rows of 3 sources per row) operatingin FC-77 has been correlated by the following expression:© 1999 by CRC Press LLC4-276Section 4106Foil HeaterH = 4.6mm, W = 5.1mm1.1mm ProtrudingHeaterR-113Ts = 46.7 °CIncreasing PowerDecreasing Powerq", W2m105SingleFlushHeater104103110DTs, K100FIGURE 4.8.17 Typical pool boiling curve for small heater.(Nu L = C Re Dh)mPr 0.11(4.8.55)For row 1: C = 0.194 and m = 0.60; for row 2: C = 0.069 and m = 0.69; for row 3: C = 0.041 and m =0.74; and for row 4: C = 0.029 and m = 0.78.
All properties are determined at the inlet temperatureexcept for mh, which is evaluated at the heater temperature. Note that when heat sinks are employed,forced convection immersion cooling can support a heat flux of approximately 50 W/cm2.Test data have been obtained for a vertical column of ten 6.4 mm ´ 6.4 mm heaters, with subcooledR-113 flowing in the upward direction. In general, CHF occurred first at the last downstream elementin the array, and that CHF values of 100 W/cm2 were easily attained. The CHF data yielded the followingequation:æ rf öqc¢¢ = C5 We n Vr f h fg ç ÷è rg ø15 23æ LöçD ÷è hø1 23é c pf DTsub ùê1 +úh fg úûêë7 23é 0.021r f c pf DTsub ùê1 +úr g h fgêëúû(4.8.56)where the Weber number, We = rf V 2L/s.
Note that for We > 100, C5 = 0.125 and n = –8/23, and forWe < 10, C5 = 0.254 and n = –1/2.© 1999 by CRC Press LLC4-277Heat and Mass TransferImmersion Cooling Using JetsTwo modes have been studied. In the first, a dielectric liquid jet discharges into a miscible liquid andis said to be submerged; in the second, a liquid jet discharges into an immiscible gas (air) and is saidto be free.
In general, the average Nusselt number can be expressed as(Nu = f Re m , Pr n , L d , z d)(4.8.57)where L/d is the ratio of the chip length to orifice diameter, and z/d is the ratio of the jet to heat sourcedistance to the orifice diameter. A free jet is virtually unaffected by the orifice-to-chip distance, and asa consequence the (z/d) term drops out.Data for single-phase forced convection cooling with free jets are available for 2 ´ 2 and 3 ´ 3 heatsource arrays.
The heat sources were 12.7 ´ 12.7 mm and the cooling fluid was FC-77. Each heat sourcewas cooled either by a single jet or by a 2 ´ 2 or 3 ´ 3 array of jets per source. For all the configurationstested, the average Nusselt number was correlated by a single expression:LNu L = 3.84æ 0.008 n + 1ö Re1 2 Pr 1 3èød(4.8.58)where fluid properties are to be evaluated at an average of the heat source and jet inlet temperatures.Data for single-phase forced convection using submerged jets are available for a 5 ´ 5 mm verticalheat source cooled by a 1.0-mm-diameter submerged jet of R-113. The Nusselt number at the stagnationpoint was correlated byNu d = 1.29Re1d 2 Pr 0.4(4.8.59)Also note that the performance of a submerged liquid jet should be approximately equivalent to gas jetimpingement.Data for two-phase forced convection using free jets have been collected for a single 12.7 ´ 12.7 mmheat source cooled by either a single jet or a 2 ´ 2 or 3 ´ 3 array of jets.
The jet diameter, velocity, andjet-to-source distance were varied. The CHF data was correlated byqc¢¢ = 0.0742 We-0.365æ rg öVr f h fg ç ÷è rf ø0.2390.118éær öæ c pf DTsub ö ùê1 + 0.952ç f ÷ç h÷ úúêrg øèèøûfgë1.414(4.8.60)Experimental evidence in two-phase forced convection using submerged jets indicates that (1) thetemperature overshoot at incipient boiling was very small compared with pool or forced boiling; (2) theboiling curves at various velocities merge to a single curve and that this curve coincides approximatelywith an upward extrapolation of the pool boiling curve; (3) the CHF varies as the cube of the jet velocity;(4) the CHF is greatly improved by increasing the subcooling; and (5) powers in excess of 20 W (5 ´5-mm chip) could be accommodated within a 85°C chip temperature.© 1999 by CRC Press LLC4-278Section 4Defining TermsExternal thermal resistance: The thermal resistance from a convenient reference point on the outsideof the electronic package to the local ambient.Internal thermal resistance: The thermal resistance from the device junction inside an electronicpackage to a convenient reference point on the outside surface of the package.Immersion cooling: Concerns applications where the coolant is in direct physical contact with theelectronic components.ReferencesAntonetti, V.W.
1993. Cooling electronic equipment — section 517, Heat Transfer and Fluid Flow DataBooks, Kreith, F., Ed., Genium Publishing, Schenectady, NY.Antonetti, V.W. and Simons, R.E. 1985. Bibliography of heat transfer in electronic equipment, IEEETrans. Components, Hybrids, Manuf. Tech., CHMT-8(2), 289–295.Park, K.A. and Bergles, A.E. 1988. Effects of size of simulated microelectron chips on boiling andcritical heat flux, J. Heat Transfer, 110, 728–734.Simons, R.E. 1988. Bibliography of heat transfer in electronic equipment, in Advances in ThermalModeling of Electronic Components and Systems, Vol.
1, Bar-Cohen, A. and Kraus, A.D., Eds.,Hemisphere Publishing, New York, 413–441.Simons, R.E. 1990. Bibliography of heat transfer in electronic equipment, in Advances in ThermalModeling of Electronic Components and Systems, Vol. 2, Bar-Cohen, A. and Kraus, A.D., Eds.,ASME Press, New York, 343–412.Sparrow, E.M., Niethammer, J.E., and Chaboki, A. 1982. Heat transfer and pressure-drop characteristicsof arrays of rectangular modules in electronic equipment, Int. J. Heat Mass Transfer, 25, 961–973.Sparrow, E.M., Yanezmoreno, A.A., and Otis, D.R.
1984. Convective heat transfer response to heightdifferences in an array of block-like electronic components, Int. J. Heat Mass Transfer, 27,469–473.© 1999 by CRC Press LLC4-279Heat and Mass Transfer4.9 Non-Newtonian Fluids — Heat TransferThomas F. Irvine, Jr., and Massimo CapobianchiIntroductionThe general characteristics of non-Newtonian fluids are described in Section 3.9 and will not be repeatedhere.
Topics to be included in this section are laminar and turbulent heat transfer in fully developed ductflow, and laminar free convection heat transfer in vertical channels and plates and several other commongeometries.For non-Newtonian flows, except for certain classes of fluids which exhibit a slip phenomenon atsolid boundaries, the boundary condition is taken as no-slip or zero velocity at all solid surfaces. Forheat transfer analyses, however, the situation is more complicated because there are many different waysto heat a wall, which in turn affects the type of thermal boundary conditions.In general, the rate of heat transfer from a surface, or the temperature difference between the walland the fluid, is calculated using the equation qc = hcAqDT.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
