BOOKCOMP, Inc. — John Wiley & Sons / Page 996 / 2nd Proofs / Heat Transfer Handbook / Bejan 996 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [996], (50) Lines: 1405 to 1421 ——— 4.10602pt PgVar ——— Normal Page PgEnds: T E X [996], (50) rates across a large substrate or PCB with an appropriately configured distribution plate or nozzle array, and the freedom to tailor the jet flow to the local cooling requirements, have made impingement cooling one of the most promising alternatives for the cooling of high-heat-flux components. Impingement cooling may involve a single jet or multiple jets directed at a single component or an array of electronic components. Circular orifices, slot-shaped ori- fices, or nozzles of various cross sections may form the jets. The axis of the impinging jet may be perpendicular or inclined to the surface of the component. Moreover, in the application of liquid jets, a distinction can be made between free jets, which are surrounded by ambient air and submerged jets, for which the volume surrounding the jet is filled with the working liquid. Whereas heat transfer associated with gas jets has been the subject of active research since the mid-1950s, jet impingement cooling with dielectric liquids is a far more recent development. Many of the pioneering studies in this field were reviewed by Bergles and Bar-Cohen (1990). More recent studies of heat transfer to free jets of dielectric liquids have been performed by Stevens and Webb (1989), Nonn et al. (1988), and Wang et al. (1990). Womac et al. (1990) ex- amined free as well as submerged liquid jets, while submerged jet impingement beat transfer was the subject of the investigations by Wadsworth and Mudawar (1990) and Mudawar and Wadsworth (1990). As a final distinction, jet impingement cooling of electronic components may involve forced convection alone or localized flow boiling, with or without net vapor generation. The discussion in this section is limited to single-phase forced convection. 13.5.2 Correlation Despite the complex behavior of the local heat transfer coefficient resulting from parametric variations in the impinging jet flow, it has been found possible to correlate the average heat transfer coefficient with a single expression, for both individual jets and arrays of jets impinging on isothermal surfaces. Based on earlier results by Schl ¨ under et al. (1970) and Krotzsch (1968), Martin (1977) proposed a relation to capture the effects of jet Reynolds number, nondimensional distance of separation (H/D), impinging area ratio (f ), Prandtl number (Pr), and fluid thermal conductivity on the jet Nusselt number: Nu D = 1 + H/D 0.6/ √ f 3 −0.05 f 1 −2.2 √ f 1 +0.2 [ (H/D) −6 ] √ f Re 0.667 D · Pr 0.42 (13.73) The range of validity for this correlation developed from extensive gas jet data, as well as some data for water and other, higher Prandtl number liquids, including some high-Schmidt-number mass transfer data, was given by Martin (1977) as 2 × 10 3 ≤ Re D ≤ 10 5 , 0.6 < Pr(Sc)<7(900), 0.004 ≤ f ≤ 0.04, and 2 ≤ H/D ≤ 12. Martin found this correlation to provide a predictive accuracy of 10 to 20% over the stated parametric range. The average Nu was also found to be nearly unaffected by the BOOKCOMP, Inc. — John Wiley & Sons / Page 997 / 2nd Proofs / Heat Transfer Handbook / Bejan JET IMPINGEMENT COOLING 997 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [997], (51) Lines: 1421 to 1439 ——— 0.56104pt PgVar ——— Normal Page PgEnds: T E X [997], (51) angle of inclination of the jet (Martin, 1977). It is to be noted that for jets produced by sharp-edged orifices, jet contraction immediately after the orifice exit must be taken into consideration in calculating the average velocity, jet diameter, and nozzle area ratio f . In applying the Martin correlation to the cooling of electronic components, con- stituting discrete heat sources on a large surface, it is necessary to alter the definition of the jet area ratio f . Recognizing that in this application, the impingement area is usually equal to the component area, f can be expressed as f = nA jet A = 0.785D 2 n A (13.74) Womac (1989) found the Martin correlation to give reasonable agreement with his submerged jet data for small-diameter jets (< 3 mm) of water and FC-77. Two other studies of submerged jet impingement were conducted by Brdlik and Savin (1965) for air and by Sitharamayya and Raju (1969) for water. The correlations from these studies are plotted in Fig. 13.24 along with the Martin correlation for a specific condition of f = 0.008,H/D = 3, and Pr = 13.1, which falls well within the ranges of all three correlations. The maximum deviation of these correlations from the Martin correlation in this plot was 32%. The Martin correlation was chosen over these alternatives primarily because of the broad range of parameters in the database from which it was developed. Also, the Martin correlation generally falls below the other correlations, making it the most conservative choice. Although the Martin (1977) correlation does not explicitly address the effect of escaping crossflow at the perimeter of a chip or board, this behavior was investigated by Kraitshev and Schl ¨ under (1973) in mass transfer experiments using several con- figurations of circular jets with varying liquid escape paths. Kraitshev and Schl ¨ under Figure 13.24 Comparison of various submerged jet correlations. BOOKCOMP, Inc. — John Wiley & Sons / Page 998 / 2nd Proofs / Heat Transfer Handbook / Bejan 998 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [998], (52) Lines: 1439 to 1464 ——— 6.31302pt PgVar ——— Normal Page PgEnds: T E X [998], (52) (1973) found that for H/D < 3, the effects of acceleration of the crossflow offset losses due to interference with the jets and that at high values of H/D the heat trans- fer was unaffected. Only in an intermediate range of H/D, which varied with the configuration, was the heat transfer found to degrade in the outer regions of the array. 13.5.3 First-Order Trends The variation of the Nusselt number with each ofthe three primary factors influencing jet impingement in the range of the Martin correlation, eq. (13.73), is shown in Figs. 13.25 through 13.27, respectively. Examining these figures it may be seen that the Nusselt number increases steadily with the Reynolds number (Fig. 13.25) and decreases with the ratio of jet distance to jet diameter (Fig. 13.26). More surprisingly, the curves shown in Fig. 13.27 indicate that the Nusselt number reaches an asymptote in its dependence on the ratio of jet area to component area. Interestingly, Martin (1977) found that a nozzle/heater area ratio f of 0.0152 and a jet aspect ratio H/D of 5.43 yielded the highest average transfer coefficient for a specified pumping power per unit area. Returning to eq. (13.73), it may be observed that in the range of interest, the first term on the right side can be approximated as 1 + H/D 0.6/f 0.5 6 −0.05 H/D 0.6/f 0.5 −0.3 (13.75) Figure 13.25 Effect of Reynolds and Prantl numbers on heat transfer. BOOKCOMP, Inc. — John Wiley & Sons / Page 999 / 2nd Proofs / Heat Transfer Handbook / Bejan JET IMPINGEMENT COOLING 999 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [999], (53) Lines: 1464 to 1493 ——— 6.9471pt PgVar ——— Normal Page * PgEnds: Eject [999], (53) Figure 13.26 Effect of jet aspect ratio on heat transfer. and that the second term is not far different from 0.6f 0.5 . Reexpressing eq. (13.73) with these simplifications, the average heat transfer coefficient h is found to approx- imately equal Nu 0.5 H D −0.3 f 0.35 · Re 0.667 D · Pr 0.42 (13.76) This approximation falls within 30% of eq. (13.73) throughout the parametric range indicated but is within 10% H/D < 3. 13.5.4 Figures of Merit Recalling the definition of the jet Nusselt number, Nu = hD/ k, and substituting for the area ratio f from eq. (13.74), the heat transfer coefficient produced by impinging liquid jet(s) is found to be proportional to h ∝ kH −0.3 n A 0.35 · Re 0.67 D · Pr 0.42 (13.77) Or, expanding the Reynolds and Prandtl numbers yields h ∝ k 0.58 ρ 0.67 µ −0.25 n A 0.35 D 0.67 V 0.67 H 0.3 (13.78) BOOKCOMP, Inc. — John Wiley & Sons / Page 1000 / 2nd Proofs / Heat Transfer Handbook / Bejan 1000 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1000], (54) Lines: 1493 to 1505 ——— 0.04701pt PgVar ——— Normal Page PgEnds: T E X [1000], (54) Figure 13.27 Effect of jet area/heater area ratio on heat transfer. The first term on the right-hand side in eq. (13.78) represents a fluid figure of merit for submerged-jet heat transfer, the second term constitutes a thermal figure of merit for the jet plate, and the third the operating conditions of an impingement cooling system. Clearly, to maximize the jet heat transfer rate, it is desirable to choose a fluid with high thermal conductivity and density but relatively low viscosity. To the accuracy of the approximations used to derive eq. (13.78) (and especially in the low-f range), the thermally preferred jet plate would contain many large-diameter nozzles per component. Due to the strong dependence of the heat transfer rate on the jet Reynolds number, maximization of the heat transfer coefficient also requires increasing the fluid velocity at the nozzle and decreasing the distance of separation between the nozzle and the component. Alternatively, if a fluid has been selected and if the jet Reynolds number is to remain constant, a higher heat transfer coefficient can be obtained only by increasing n/A or decreasing H . 13.5.5 General Considerations for Thermal–Fluid Design Although the thermal relations discussed in Section 13.5.4 can be used to establish the gross feasibility of submerged jet impingement cooling for high-power chips, successful implementation of this thermal management technique requires consider- ation of system-level issues and design trade-offs (Maddox and Bar-Cohen, 1991). The minimization of life-cycle costs is a crucial element in electronic systems, and consequently, attention must be devoted to the “consumed” fluid flow rate, pressure drop, and pumping power as well as to the limitations imposed by manufacturing tolerances and costs. The gross impact of these considerations on the design of im- pinging jet cooling systems can be seen with the aid of eq. (13.78). BOOKCOMP, Inc. — John Wiley & Sons / Page 1001 / 2nd Proofs / Heat Transfer Handbook / Bejan JET IMPINGEMENT COOLING 1001 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1001], (55) Lines: 1505 to 1517 ——— 0.0pt PgVar ——— Normal Page * PgEnds: Eject [1001], (55) The nozzle pressure drop and hence plenum pressure required to achieve a spec- ified jet velocity has direct bearing on the choice and cost of the coolant circulation system and the structural design, as well as cost, of the jet plate. Since eqs. (13.73) and (13.78) show the jet heat transfer coefficient to increase with velocity to the 0.67 power while nozzle pressure losses generally depend on the square of the velocity, concern about the plenum operating pressure would lead the designer to choose the lowest possible jet velocity. Examination of the approximate relation for the jet heat transfer coefficient, eq. (13.78), suggests that to maintain high heat transfer rates at low jet velocities would necessitate increasing the number of nozzles (n/A), increasing the diameter of each nozzle (D), or decreasing the spacing between the nozzle exit and the component (H ). The minimum value of H is likely to be determined by the precision of assembly and deflection under pressure of the jet plate and thus it will benefit from reduced operat- ing pressure. Because the maximum heattransfer rates are approached asymptotically as the total jet area increases to approximately 4% of the component area (see Fig. 13.27), there is coupling between the number of jets and the jet diameter. The heat transfer rate can thus be improved by increasing both jet diameter and the number of jets up to this value, but if operating near the maximum rate, the jet diameter is inversely related to the square root of n/A. In the use of liquid jets, the operating costs are often dominated by the pumping power, or product of total volumetric flow rate and pressure drop, needed to provide a specified heat removal rate. The pumping power can easily be shown to vary with D 2 V 3 n/A. Examining this dependence in light of the approximate heat transfer coefficient relation, eq. (13.78), it is again clear that reduced costs are associated with low liquid velocity and a relatively large total nozzle area. These results suggest that optimum performance, based on system level as well as thermal considerations, and as represented by the average heat transfer coefficient, would be achieved by designing jet impingement systems to provide approximately 4% jet-to-component area ratios and operate at relatively low jet velocities. Improved surface coverage, more uniform heat removal capability, and decreased vulnerability to blockage of a single (or a few) nozzles would appear to be favored by the use of a relatively large number of jets per component, allowing reduction in the diameter of individual jets. Alternatively, the cost of manufacturing and the probability of nozzle blockage can be expected to increase for small-diameter nozzles and thus place a lower practical limit on this parameter. Given the approximate nature of eq. (13.78), these relationships must be viewed as indicative rather than definitive, and the complete Martin correlation [eq. (13.73)] should be used for any detailed exploration of these trends. 13.5.6 Impingement on Heat Sinks El Sheikh and Garimella (2000) carried out extensive research on jet impingement cooling of electronic components and derived heat transfer correlations for impinge- ment-cooled pin-fin heat sinks. Results were presented in terms of Nu base , based on the heat sink footprint area, and on Nu HS , based on the total heat sink surface area: BOOKCOMP, Inc. — John Wiley & Sons / Page 1002 / 2nd Proofs / Heat Transfer Handbook / Bejan 1002 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1002], (56) Lines: 1517 to 1536 ——— -2.60796pt PgVar ——— Normal Page PgEnds: T E X [1002], (56) Nu base = 3.361Re 0.724 · Pr 0.4 D d −0.689 S d −0.210 (13.79) Nu HS = 1.92Re 0.716 · Pr 0.4 A HS A d −0.689 D d 0.678 S d −0.181 (13.80) These equations are valid for 2000 ≤ Re ≤ 23000,S/d = 2 and 3. The term D refers to the jet diameter and d refers to the pin diameter. 13.6 NATURAL CONVECTION HEAT SINKS Despite the decades-long rise in component heat dissipation, the inherent simplicity and reliability of buoyantly driven flow continues to make the use of natural con- vection heat sinks the cooling technology of choice for a large number of electronic applications. An understanding of natural convection heat transfer from isothermal, parallel-plate channels provides the theoretical underpinning for the conceptual de- sign of natural convection cooled plate-fin heat sinks. However, detailed design and optimization of such fin structures requires an appreciation for the distinct character- istics of such phenomena as buoyancy-induced fluid flow in the interfin channels and conductive heat flow in the plate fins. The presence of the heat sink base, or prime surface area, along one edge of the parallel-plate channel, contrasting with the open edge at the tip of the fins, introduces an inherent asymmetry in the flow field. The resulting three-dimensional flow pattern generally involves some inflow from (and possibly outflow through) the open edge. For relatively small fin spacings with long and low fins, this edge flow may result in a significant decrease in the air temperature between the fins and alter the performance of such heat sinks dramatically. For larger fin spacings, especially with wide, thick fins, the edge flow may well be negligible. Thus, Sparrow and Bahrami (1980), who studied 7.6-cm-wide vertically oriented isothermal plates, found the edge flow to have a negligible effect on the heat transfer coefficient for values of the Elenbaas number greater than 10, but to produce deviations of up to 30% in the equivalent Nusselt number when the Elenbaas number was less than 4. Heat flow in extended surfaces must result in a temperature gradient at the fin base. When heat flow is from the base to the ambient, the temperature decreases along the fin, and the average fin surface temperature excess is typically between 50 and 90% of the base temperature excess. As a consequence of the anisothermality of the fin surface, exact analytic determination of the heat sink capability requires a combined (or conjugate) solution of the fluid flow in the channel and heat flow in the fin. Due to the complexity of such a conjugate analysis, especially in the presence of three- dimensional flow effects, the thermal performance of heat sinks is frequently based on empirical results. In recent years, extensive use has also been made of detailed numerical solutions to quantify heat sink performance. Alternatively, a satisfactory estimate of heat sink capability can generally be obtained by decoupling the flow and temperature fields and using an average heat transfer coefficient, along with an BOOKCOMP, Inc. — John Wiley & Sons / Page 1003 / 2nd Proofs / Heat Transfer Handbook / Bejan NATURAL CONVECTION HEAT SINKS 1003 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1003], (57) Lines: 1536 to 1565 ——— -0.073pt PgVar ——— Normal Page PgEnds: T E X [1003], (57) average fin surface temperature, to calculate the thermal transport from the fins to the ambient air. 13.6.1 Empirical Results Starner and McManus (1963)were perhaps the first toinvestigate in detail the thermal performance of natural convection heat sinks as a function of the geometry (spacing and height) and angle of base plate orientation (vertical, horizontal, and 45°). Their configuration, with the present terminology, is shown in Fig. 13.28. For a base surface area of 254 mm × 127 mm, supporting 14 and 17 1.02-mm fins (with the cases sum- marized in Table 13.13), Starner and McManus found that the measured heat transfer coefficients for the vertical orientation were generally lower than the values expected for parallel-plate channels. The inclined orientation (45°) resulted in an additional 5 to 20% reduction in the heat transfer coefficient. Results for the horizontal orientation showed a strong contribution from three-dimensional flow. Welling and Wooldridge (1965) performed an extensive study of heat transfer from vertical arrays of 2- to 3-mm-thick fins attached to an identical 203 mm × 66.3 mm base (the individual cases are summarized in Table 13.14). Their results revealed that in the range 0.6 < El < 100, associated with 4.8- to 19-mm spacings and fin heights from 6.3 to 19 mm, the heat transfer coefficients along the total wetted surface were lower than attained by an isolated flat plate but generally above those associated with parallel-plate flow. This behavior was explained in terms of the competing effects of channel flow, serving to preheat the air, and inflow from the open edge, serving to mix the heated air with the cooler ambient fluid. In this study it was observed for the first time that for any given interfin spacing there is an optimum fin height b beyond which thermal performance per unit surface area deteriorates. A similar study of upward- and downward-facing fin arrays on a horizontal base was reported by Jones and Smith Figure 13.28 Geometric parameters for Starner and McManus (1963) fin arrays. BOOKCOMP, Inc. — John Wiley & Sons / Page 1004 / 2nd Proofs / Heat Transfer Handbook / Bejan 1004 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1004], (58) Lines: 1565 to 1635 ——— 0.2251pt PgVar ——— Normal Page PgEnds: T E X [1004], (58) TABLE 13.13 Geometric Parameters for Starner and McManus (1963) Fin Arrays LW b Z δ Array N in. mm in. mm in. mm in. mm in. mm 1 17 10.0 254 5.0 127 0.5 12.7 0.25 6.35 0.04 1.016 2 17 10.0 254 5.0 127 1.5 38.1 0.25 6.35 0.04 1.016 3 17 10.0 254 5.0 127 0.25 6.35 0.25 6.35 0.04 1.016 4 14 10.0 254 5.0 127 1.0 25.4 0.313 7.95 0.04 1.016 (1970). The Welling and Woldridge (1965) data formed the basis for the Van de Pol and Tierney (1973) correlation discussed later in this chapter. In 1986, Bilitzky completed a comprehensive investigation of natural convection heat transfer from multiple heat sink geometries that differed primarily in fin height and spacing. The heat sinks were operated at different heat dissipations as well as different angles of inclination and orientation. Twelve distinct heat sinks and a flat plate were tested in a room within which extraneous convection had been suppressed. The range of angles is indicated in Fig. 13.29. The base was first kept vertical, while the fins were rotated through four different positions (90°, 60°, 30°, and 0°). Then the base was tilted backward toward the horizontal orientation through four different positions (90°, 60°, 30°, and 0°). Six of the heat sinks used bases 144 mm long × 115 mm wide to support plate fins, nominally 2 mm in thickness and 6 to 13.8 mm apart, ranging in height from 8.6 to 25.5 mm. Six additional heat sinks, with identical fin geometries, were supported on bases 280 mm long and 115 mm wide. The geometric parameters of the 12 heat sinks were selected to span the base and fin dimensions encountered in electronics cooling applications and are summarized in Table 13.15. TABLE 13.14 Geometric Parameters for Welling and Wooldridge (1965) Fin Arrays LW b Z δ Array N in. mm in. mm in. mm in. mm in. mm 1 4 8.0 203.2 2.61 66.3 0.75 19.05 0.75 19.05 0.09 2.29 2 6 8.0 203.2 2.61 66.3 0.75 19.05 0.414 10.52 0.09 2.29 3 8 8.0 203.2 2.61 66.3 0.75 19.05 0.27 6.86 0.09 2.29 4 10 8.0 203.2 2.61 66.3 0.75 19.05 0.19 4.83 0.09 2.29 5 4 8.0 203.2 2.61 66.3 0.5 12.7 0.75 19.05 0.09 2.29 6 6 8.0 203.2 2.61 66.3 0.5 12.7 0.414 10.52 0.09 2.29 7 8 8.0 203.2 2.61 66.3 0.5 12.7 0.27 6.86 0.09 2.29 8 10 8.0 203.2 2.61 66.3 0.5 12.7 0.19 4.83 0.09 2.29 9 4 8.0 203.2 2.61 66.3 0.25 6.35 0.75 19.05 0.09 2.29 10 6 8.0 203.2 2.61 66.3 0.25 6.35 0.414 10.52 0.09 2.29 11 8 8.0 203.2 2.61 66.3 0.25 6.35 0.27 6.86 0.09 2.29 12 10 8.0 203.2 2.61 66.3 0.25 6.35 0.19 4.83 0.09 2.29 13 0 8.0 203.2 2.61 66.3 0.00 0.00 2.61 66.3 0.00 0.00 BOOKCOMP, Inc. — John Wiley & Sons / Page 1005 / 2nd Proofs / Heat Transfer Handbook / Bejan NATURAL CONVECTION HEAT SINKS 1005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1005], (59) Lines: 1635 to 1635 ——— * 55.13504pt PgVar ——— Normal Page PgEnds: T E X [1005], (59) Figure 13.29 Geometry and orientation of Bilitzky (1986) fin arrays. TABLE 13.15 Geometric Parameters for Bilitzky (1986) Fin Arrays LW b Z δ Array in. mm in. mm in. mm in. mm in. mm 1 5.67 144 4.53 115 1.004 25.5 0.236 6.0 0.075 1.9 2 5.67 144 4.53 115 0.677 17.2 0.232 5.9 0.079 2.0 3 5.67 144 4.53 115 0.339 8.6 0.228 5.8 0.083 2.1 4 5.67 144 4.53 115 1.004 25.5 0.547 13.9 0.075 1.9 5 5.67 144 4.53 115 0.677 17.2 0.543 13.8 0.079 2.0 6 5.67 144 4.53 115 0.339 8.6 0.539 13.7 0.083 2.1 7 11.02 280 4.53 115 1.004 25.5 0.236 6.0 0.075 1.9 8 11.02 280 4.53 115 0.669 17.0 0.232 5.9 0.079 2.0 9 11.02 280 4.53 115 0.335 8.5 0.228 5.8 0.083 2.1 10 11.02 280 4.53 115 1.004 25.5 0.547 13.9 0.075 1.9 11 11.02 280 4.53 115 0.669 17.0 0.543 13.8 0.079 2.0 12 11.02 280 4.53 115 0.335 8.5 0.539 13.7 0.083 2.1 . BOOKCOMP, Inc. — John Wiley & Sons / Page 996 / 2nd Proofs / Heat Transfer Handbook / Bejan 996 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [996],. correlations. BOOKCOMP, Inc. — John Wiley & Sons / Page 998 / 2nd Proofs / Heat Transfer Handbook / Bejan 998 HEAT TRANSFER IN ELECTRONIC EQUIPMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [998],. + H/D 0.6/f 0.5 6 −0.05 H/D 0.6/f 0.5 −0.3 (13.75) Figure 13.25 Effect of Reynolds and Prantl numbers on heat transfer. BOOKCOMP, Inc. — John Wiley & Sons / Page 999 / 2nd Proofs / Heat Transfer Handbook / Bejan JET IMPINGEMENT COOLING 999 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [999],