Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 76
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— John Wiley & Sons / Page 496 / 2nd Proofs / Heat Transfer Handbook / Bejan[496], (58)(6.179)Lines: 2587 to 2605———1.927pt PgVar———Normal PagePgEnds: TEX[496], (58)HEAT TRANSFER FROM OBJECTS ON A SUBSTRATE123456789101112131415161718192021222324252627282930313233343536373839404142434445497where Ts,B is the surface temperature of block B and Tair,B is given by eq. (6.179).Again using the superposition principle, the heat flux at block B isqB = had,B Ts,B − Tair,B(6.180)Once θB/A is determined, it is straightforward to estimate qB (or Ts,B when qB isspecified) for any value of qA from eqs.
(6.179) and (6.180).Extension of this concept to a general case includes taking account of the contributions of all blocks upstream of block B in the equation for Tair,B :θB/(i,j ) q(i,j )(6.181)Tair,B = T0 +i,jwhere (i,j ) is the row and column index and the summation is performed for all thepackages upstream of block B.Although the foregoing concept looks convenient at first sight, it is a tedious andtime-consuming task to determine θB/(i,j ) . Except for a limited number of cases, therehave been few correlations that relate θB/(i,j ) to the geometrical and flow parameters.Moffat and Ortega (1988) summarized the work on this subject, and Anderson (1994)extended the concept to the case of conjugate heat transfer.The heat transfer data corresponding to the adiabatic heat transfer coefficient indownstream rows where the flow is fully developed were reported by Wirtz andDykshoorn (1984). The data were correlated by the equation[497], (59)NuP = 0.348Re0.6P[497], (59)(6.182)where the characteristic length for Nu and Re is the streamwise length of the block,P .6.6.5Plate Fin Heat SinksWhile the plate stack discussed in Section 4.2.1 allows bypass flow in two-dimensional domain, bypass flow around an actual heat sink is three-dimensional.
Numerical analysis of such flow is possible but very resource demanding. Ashiwake et al.(1983) developed a method that allows approximate but rapid estimation of the heatsink performance. In their formulation the bypass flow rate is estimated using thebalance between the dynamic pressure in front of the fin array and the flow resistancein the interfin passages. Although the validity of the modeling was well corroboratedby the experimental data, the method requires computations of the several pressurebalance and heat transfer correlations, and the task of developing a more conciseformulation of heat sink performance estimation remains.Presently, the performance estimation is largely in the realm of empirical art,although Ledezma et al.
(1996) and Bejan and Sciubba (1992) clearly show optimumspacings which agree with the theory. The heat sink is placed in a wind tunnel andthe thermal resistance is measured. The thermal resistance is defined asBOOKCOMP, Inc. — John Wiley & Sons / Page 497 / 2nd Proofs / Heat Transfer Handbook / BejanLines: 2605 to 2648———1.62717pt PgVar———Normal PagePgEnds: TEX498123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWS[498], (60)Lines: 2648 to 2664———0.06602pt PgVarFigure 6.26 Thermal resistance of plate-fin heat sinks. (From Matsushima and Yanagida,1993.)———Normal PagePgEnds: TEX[498], (60)QR=Tb − T 0(K/W)(6.183)where Q is the power input to the heater bonded to the bottom of the heat sink, Tb thetemperature at the bottom surface of the heat sink, and T0 the airflow temperature infront of the heat sink.
Figure 6.26 shows examples of thermal resistance data, whereU is the free stream velocity. All the data were obtained with aluminum heat sinkshaving a 22 mm × 22 mm base area. Of course, there is trade-off between the heattransfer performance and the cost of heat sink. Conventional extruded heat sinks (seeFig. 6.26) are at the lowest in the cost ranking but also in the performance ranking.The heat sink having 19 thin fins (0.15 mm thick) on the 22-mm span provides lowthermal resistance, particularly at high air velocities, but the manufacture of such aheat sink requires a costly process of bonding thin fins to the base.6.6.6Pin Fin Heat SinksAs electronic systems become compact, the path for cooling airflow is constrained.This means increased uncertainty in the direction of airflow in front of the heat sink.The performance of plate fin heat sinks degrades rapidly as the direction of air flowdeviates from the orientation of the fins.
The pin fin heat sink has a distinct advantageBOOKCOMP, Inc. — John Wiley & Sons / Page 498 / 2nd Proofs / Heat Transfer Handbook / BejanHEAT TRANSFER FROM OBJECTS ON A SUBSTRATE123456789101112131415161718192021222324252627282930313233343536373839404142434445499AirflowFanaL[499], (61)Figure 6.27 Pin-fin fan sink assembly.Lines: 2664 to 2687over the plate fin heat sink in that its performance is relatively insensitive to thedirection of the airflow.Figure 6.27 shows a scheme that exploits the advantage of pin fin heat sink to thefullest extent. A small axial fan is mounted above the fin heat sink, and air is blownfrom above to the heat sink. The airflow is longitudinal to those pins in the centralarea, and the pins in the perimeter are exposed to cross flow.
Recently, the schemehas become popular for cooling CPU chips in a constrained space.The work of Wirtz et al. (1997) provides a guide for the estimation of the performance of a pin fin heat sink/fan assembly. The dimensions of the pin fin heat sinkstested by Wirtz et al.
(1997) are as follows:Foot print area:L in Fig. 6.26:Dimensionless pin diameter:Dimensionless pin height:Fin pitch-to-diameter ratio:Number of pins on a row or a column:63.5 mm × 63.5 mm63.5 mmd/L = 0.05a/L = 0.157 − 0.629p/d = 2.71 − 1.46n = 8, 10, and 14The fan used in the experiment has overall dimensions of 52 mm × 52 mm ×10 mm, a 27-mm-diameter hub, and a 50-mm blade shroud diameter. The overallheat transfer coefficient U is defined asU=QAT ∆T(6.184)where Q is the heat transfer rate, AT the total surface area of the heat sink, and ∆Tthe temperature difference between the fin base and the incoming air. The Nusseltnumber is defined as Nu = U L/k, where k is the fluid thermal conductivity. TwoBOOKCOMP, Inc.
— John Wiley & Sons / Page 499 / 2nd Proofs / Heat Transfer Handbook / Bejan———-0.93945pt PgVar———Normal PagePgEnds: TEX[499], (61)500123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWStypes of correlations are proposed, one for a given pressure rise maintained by thefan, ∆p,0.574Nu = 7.12 × 10−4 C∆p a 0.223 p 1.72L(6.185)dwhere inC∆p =ρL2 ∆pµ25 × 106 < C∆p < 1.5 × 108µ is the dynamic viscosity of the air.The other correlation is for a given fan power PW :Nu = 3.2 × 10−6 CP0.520W a −0.205 p 0.89Ld(6.186)where[500], (62)Lines: 2687 to 2735CPW =ρLPWµ31011 < CPW < 1013———5.62617pt PgVar———Normal PageWirtz et al.
(1997) also reported on experimental results obtained with square and* PgEnds: PageBreakdiamond-shaped pins.[500], (62)6.7 TURBULENT JETSJets are employed in a wide variety of engineering devices. In cases where the jets arelocated far from solid walls, they are classified as free shear flows. In most cases, however, solid walls are present and affect the flow and heat transfer significantly. Theseflows can take many configurations. Some of the practically important cases for heattransfer include wall jets and jets impinging on solid surfaces as indicated in Fig.
6.28.Wall jets are frequently employed in turbomachinery applications and are notdiscussed here. Jet impingement on surfaces is of interest in materials packaging andelectronics cooling.6.7.1 Thermal Transport in Jet ImpingementDue to the thin thermal and hydrodynamic boundary layers formed on the impingement surface, the heat transfer coefficients associated with jet impingement are large,making these flows suitable for large heat flux cooling applications.
The relationshipfor impingement of a jet issuing from a nozzle at a uniform velocity and at ambienttemperature Te , with a surface at temperature Ts , can be written asq = h(Ts − Te )BOOKCOMP, Inc. — John Wiley & Sons / Page 500 / 2nd Proofs / Heat Transfer Handbook / Bejan(6.187)123456789101112131415161718192021222324252627282930313233343536373839404142434445BOOKCOMP, Inc.
— John Wiley & Sons / Page 501 / 2nd Proofs / Heat Transfer Handbook / BejanMain streamJet(a) Film cooling with tangential injectionPorous surface(b) Transpiration coolingFluid injectionNozzleNozzleplateTarget surface501(c) Unconfined jet impingementPlenumNozzleplateTarget surfacePlenumTarget surface(d) Confined jet impingement(e) Multiple confined jet impingementFigure 6.28 Several configurations of jet cooling arising in applications.[501], (63)Lines: 2735 to 2746———* 528.0pt PgVar———Normal Page* PgEnds: PageBreak[501], (63)502123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSThe impinging jet may be circular (round) or planar (rectangular or slot), based onits cross section.
It may be submerged (fluid discharged in the same ambient medium),or free surface (a liquid discharged into ambient gas). The flows in each of thesecases may be unconfined or partially confined. Moreover, in the case of multiple jets,interaction effects arise.6.7.2Submerged JetsA schematic of a single submerged circular or planar jet is seen in Fig. 6.29. Typically,the jet is turbulent at the nozzle exit and can be characterized by a nearly uniformaxial velocity profile. With increasing distance from the nozzle exit, the potential coreregion within which the uniform velocity profile persists shrinks as the jet interactswith the ambient.
Farther downstream, in the free jet region, the velocity profileis nonuniform across the entire jet cross section. The centerline velocity decreaseswith distance from the nozzle exit in this region. The effect of the impingementsurface is not felt in this region. The impingement surface influences the flow in[502], (64)Lines: 2746 to 2759———0.927pt PgVar———Normal PagePgEnds: TEX[502], (64)Figure 6.29 Transport regimes in a submerged circular unconfined jet impinging on a surface.BOOKCOMP, Inc.
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