BOOKCOMP, Inc. — John Wiley & Sons / Page 1006 / 2nd Proofs / Heat Transfer Handbook / Bejan 1006 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 [1006], (60) Lines: 1635 to 1651 ——— 5.7pt PgVar ——— Normal Page PgEnds: T E X [1006], (60) In all 12 heat sinks studied, the vertical–vertical orientation, that is, a vertically oriented base with vertical fins and channels, yielded the highest heat transfer coef- ficients most often. However, in a relatively large number of situations, the thermal performance of the vertical–vertical arrays was indistinguishable from that attained by a vertical base plate with fins rotated 30° from the axis, a horizontal base plate, and a base plate inclined 60° from the horizontal with unrotated fins. On the other hand, vetical–horizontal orientation, that is, the base plate vertical and the fins rotated 90° from the axis, led to the lowest heat dissipation rates. For the unrotated fins, the low- est heat transfer coefficients were almost always found to occur at a base plate angle of 30° from the horizontal. The use of smoke revealed a relatively complex three- dimensional flow pattern around the heat sinks, with very substantial inflow from the direction of the fin tips when the base plate was strongly inclined and when the heat sinks were in the vertical base–horizontal fins orientation. The influence of the spacing z between the fins for short and long base plates was examined by comparing pairs of heat sinks that differed only in geometric parameters, z (fin arrays 1 and 4, 2 and 5, 3 and 6, 7 and 10, 8 and 11, and 9 and 12 in Table 13.15). Bilitzky (1986) observed that in nearly all the configurations and operating conditions examined, the highest heat transfer coefficients were attained with the larger fin spacing. However, the improvement in the heat transfer coefficient was not always sufficient to compensate for the loss of wetted fin surface area. Moreover, for the horizontal base plate configurations as well as for the vertical base with horizontal fins, the total array dissipation appeared not to depend on this parameter. 13.7 PHASE-CHANGE PHENOMENA 13.7.1 Heat Pipes and Vapor Chambers Among the various available cooling techniques, the use of heat pipe technology is increasing rapidly, especially in portable computers. Heat pipes can provide a low- thermal-resistance path for heat transfer within electronic equipment, linking a high- power component with a remotely placed heat sink or cold plate, without adding substantial weight to the system. A heat pipe is a thermal transport device that uses phase-change processes and vapor diffusion to transfer large quantities of heat over substantial distances, with no moving parts and at nearly a constant temperature. A heat pipe is composed of a sealed slender tube containing a wick structure, which lines the inner surface, saturated by a small amount of fluid (such as water), as shown in Fig. 13.30. It is composed of three sections: the evaporator section at one end, where heat is absorbed and the fluid is vaporized; a condenser section at the other end, where the vapor is condensed and heat is rejected; and the adiabatic section, in between, where the vapor and the liquid phases of the fluid flow in opposite directions through the core and the wick, respectively, and in which no significant heat transfer occurs between the fluid and the surrounding medium. The evaporation and condensation processes yield extremely high heat transfer coefficients, and only a modest pressure difference is required to transport the vapor BOOKCOMP, Inc. — John Wiley & Sons / Page 1007 / 2nd Proofs / Heat Transfer Handbook / Bejan PHASE-CHANGE PHENOMENA 1007 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 [1007], (61) Lines: 1651 to 1657 ——— 0.097pt PgVar ——— Normal Page PgEnds: T E X [1007], (61) Figure 13.30 Longitudinal cross section of a heat pipe. from the evaporator to the condenser end of the heat pipe. However, very careful wick design and assembly is required to ensure that capillary forces, in the wick structure, will be successful in pumping the liquid back to the evaporator. Unfortunately, even modest accumulations of noncondensable gas in the vapor space, especially in the region adjacent to the condenser, can lead to severe deterioration in heat pipe perfor- mance, often in just a few weeks or months of operation. Contamination and trapping of air and/or other noncondensable gases, during the fabrication process, as well as gas leakage and/or generation due to material incompatibilities, can all contribute to such a loss of heat pipe performance. Due to the small axial gradient in vapor pressure, required to propel the vapor from the evaporator to the condenser, and the strong dependence of vapor pressure on temperature embodied in the Clausius–Clapeyron equation (Dunn and Reay, 1994), even a modest internal temperature difference is sufficient to effect considerable thermal transport. Moreoever, since much of the working volume of a heat pipe is occupied by vapor, such heat pipes may weigh just a few grams. Indeed, a simple heat pipe with water as the working fluid may have an effective axial thermal conductivity on the order of 100,000 W/m ·K, compared with about 400 W/m ·K for copper. For example, a 0.6-cm-diameter 15-cm-long horizontal cylindrical heat pipe, with water as the working fluid can transfer 300 W at just a 2- to 3-K temperature difference between the evaporator end and the condenser end of the pipe. However, the resistance to heat flow in the radial direction, or perpendicular to the heat pipe surface, is often far higher than in the axial direction. The relatively low thermal conductivity of the commonly used wick materials, the high porosity of the wick, and the use of low-thermal-conductivity working fluids all combine to impede the flow of heat from the heat pipe wall to the liquid–vapor interface. Moreoever, the interface thermal resistance between the heat pipe and the microelectronic device, heat sink, cold plate, and/or other elements in the thermal path frequently poses a substantial thermal resistance that may well govern the cooling capability of the heat pipe. Although most heat pipes are cylindrical in shape, they can be manufactured in a variety of shapes, involving right-angle bends, S-turns, or spirals. Heat pipes can also BOOKCOMP, Inc. — John Wiley & Sons / Page 1008 / 2nd Proofs / Heat Transfer Handbook / Bejan 1008 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 [1008], (62) Lines: 1657 to 1691 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [1008], (62) be made in a flat configuration, with a minimum thickness that currently is close to 0.3 cm (Zorbil et al., 1988). Flat heat pipes, attached directly to the back surface of a PCB, have been used successfully for cooling high-power boards in avionic applications, in which heat must be conducted to the edges of the board, which are attached to an air- or water-cooled, cold plate. When the ultimate heat sink is the ambient air, cooling fins are usually attached to the condenser end of the heat pipe, to increase the heat transfer area and reduce the convective resistance. Recent years have seen growing interest in a special category of flat heat pipes, popularly known as vapor chambers. Vapor chambers differ from traditional cylin- drical heat pipes in relying on two-dimensional rather than one-dimensional flow of vapor andliquidinthe chamber core and in the wick, respectively. Vapor chambers are used in the base of a heat sink for enhanced lateral spreading of heat from a high-heat- flux component. Although the high lateral thermal conductivity of the vapor chambers is most advantageous in this regard, the relatively low axial conductivity of the vapor chamber, often due to the low thermal conductivity of the wick, high wick porosity, and low fluid conductivity, can compromise the effectiveness of a poorly designed vapor chamber. Recently, Chesser et al. (2000) provided a simplified scheme to pre- dict the capillary limits of a vapor chamber and suggested ways in which this same analysis could also be used to predict the temperature variations in the flowing vapor. Alternative Designs Murthy et al. (2000) presented a micromachined thermo- syphon design to be used as heat spreader. The thermosyphon included a central evap- orator section, with integrated fins for cooling along the edges and a microfabricated three-dimensional copper structure for enhancing boiling heat transfer. Zeng et al. (2000) have proposed a two-phase cooling design based on the use of an electroki- netic (EK) pump delivering 0.05 to 10 mL/min of electroosmotic flow for the cooling of microelectronic devices in the range 1 to 200 W. Such pumps have no moving parts and are expected to develop pressure heads in excess of 1 atm, substantially above values reported for other micropumps. 13.7.2 Immersion Cooling Thermal control of operational electronic components by direct immersion in low- boiling-point dielectric liquids dates back to the late 1940s. In the mid-1980s use of immersion cooling for the Cray 2 and ETA-10 supercomputers, as well as substantial research on jet impingement and spray cooling, led to renewed interest in this technol- ogy. Due to elimination of the solid-to-solid interface resistance, immersion cooling is well suited to the cooling of advanced, high-heat-flux electronic components now under development. Table 13.16 lists the thermophysical properties for some of the most commonly used dielectric liquids. It is clear from the data in this table that these fluids have higher thermal conductivities, densities, and specific heats than air and that, conse- quently, use of these fluids can be expected to offer substantial improvements relative to conventional air cooling. However, the table also indicates that due to the inferiority of the thermophysical properties to those of water, the thermal performance afforded BOOKCOMP, Inc. — John Wiley & Sons / Page 1009 / 2nd Proofs / Heat Transfer Handbook / Bejan PHASE-CHANGE PHENOMENA 1009 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 [1009], (63) Lines: 1691 to 1713 ——— 0.75417pt PgVar ——— Normal Page PgEnds: T E X [1009], (63) TABLE 13.16 Thermophysical Properties of Typical Dielectric Coolants Property FC-87 L-1402 FC-72 FC-84 R-113 Boiling point (°C) 30 51 52 83 48 Liquid density (kg/m 3 ) 1633 1635 1592 1575 1511 Vapor density (kg/m 3 ) 11.58 11.25 12.68 13.28 7.40 Dynamic viscosity (N · m/s 2 ) 4.2 × 10 −4 5.2 × 10 −4 4.5 × 10 −4 4.2 × 10 −4 5.0 × 10 −4 Specific heat (J/kg ·K) 1088 1059 1088 1130 979 Thermal conductivity (W/m · K) 0.0551 0.0596 0.0545 0.0535 0.0702 Prandtl number 8.3 9.2 9.0 8.9 7.0 Heat of vaporization (J/kg) 87,927 104,675 87,927 79,553 146,824 Surface tension (N/m) 8.9 × 10 −3 1.1 × 10 −2 8.5 × 10 −3 7.7 × 10 −3 1.5 × 10 −3 Source: Danielson et al. (1987). by these fluids is significantly lower than that expected from the use of water as a coolant. Immersion cooling systems can be classified as passive or active. Passive systems are those in which no pumping devices are used to circulate the coolant. In such systems, heat transfer from the hot component to the coolant may occur due to natural convection or pool boiling. In an active system, on the other hand, the heat transfer from the immersed component is governed by forced convection and/or by flow boiling to the fluid actively circulated by a pump. As seen from Table 13.16, the Prandtl number for most commonly used dielectric fluids is very high. In addition, the length scales of electronic components are usually smaller than those used to establish the free- and forced-convection correlations listed in Table 13.4. The effect of length scale is much more pronounced on the natural convection heat transfer coefficient. Park and Bergles (1988) provided a correlation accounting for the effect of heater length on the natural convection heat transfer coefficient from vertically oriented heaters immersed in dielectric fluids: Nu = a · Ra b ∗ (13.81) where a = 0.906 1.0 + 0.0111 (W/W ∞ ) 3.965 0.2745 (13.82) b = 0.184 1.0 + 2.64 ×10 −5 (W/W ∞ ) 9.248 −0.0362 (13.83) Although eq. (13.81) was developed from measurements taken on vertically oriented heaters, it predicts natural convection on horizontal silicon chips quite well. The importance of substrate conduction on natural convection heat transfer from a package to a dielectric coolant has been addressed by Sathe and Joshi (1992) and by BOOKCOMP, Inc. — John Wiley & Sons / Page 1010 / 2nd Proofs / Heat Transfer Handbook / Bejan 1010 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 [1010], (64) Lines: 1713 to 1722 ——— 2.25099pt PgVar ——— Normal Page PgEnds: T E X [1010], (64) Wroblewski and Joshi (1992). Both numerical studies found that a significant portion of the heat was conducted from the power-dissipating component into the substrate and then convected to the surrounding coolant. Sathe and Joshi (1992) also found that natural convection liquid cooling was preferable to natural convection air cooling only if the ratio of the package thermal conductivity to the fluid thermal conductivity was less than 1. Due to the large liquid densities and the flow rates commonly encountered in active immersion cooling methods, the liquid flow regime is usually transitional or turbulent. The equations listed in Table 13.4 can be used to obtain fairly accurate estimates of forced-convection heat transfer coefficients on electronic components being cooled by flowing dielectric coolants. Although single-phase natural or forced convection of the dielectric coolants can be used for cooling of electronics, the high heat transfer efficiency of nucleate boiling makes this phase-change process a highly attractive mode of heat transfer. Once boiling is initiated on the component very large changes in component heat dissipation can be accommodated with a very small change in component temperature. This is clear from the steep slope of the pool boiling curve for FC-72 shown in Fig. 13.31. Most commonly used electronic cooling fluids have rather large air solubilities and very low surface tension. Consequently, prolonged exposure of any surface to these fluids allows the fluid to dissolve air out of the microscopic surface cavities. In the Figure 13.31 Nucleate pool boiling curve for FC-72 on a horizontal silicon chip. (From Watwe et al., 1997.) BOOKCOMP, Inc. — John Wiley & Sons / Page 1011 / 2nd Proofs / Heat Transfer Handbook / Bejan PHASE-CHANGE PHENOMENA 1011 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 [1011], (65) Lines: 1722 to 1747 ——— 0.42209pt PgVar ——— Normal Page PgEnds: T E X [1011], (65) absence of these air-filled surface cavities, boiling cannot be initiated on the surface of the silicon. Thus with increasing component heat flux the die temperature increases rapidly, while heat transfer from the component occurs primarily via natural convec- tion, as shown in Fig. 13.31. When the temperature difference between the component surface and the bulk coolant is sufficiently large, boiling may be initiated, causing a rapid decrease in the component temperature. The initial increase in component temperature followed by the temperature drop subsequent to the onset of boiling is termed incipience overshoot. Such a thermal shock is rather undesirable in the design of an immersion cooled system due to component reliability considerations. Although it is very difficult to predict incipience overshoot, You et al. (1990) have presented a comprehensive investigation of the parameters that affect nucleate boiling incipience for the highly wetting dielectric coolants. Bar-Cohen and Simon (1986) have proposed the following equation to obtain and engineering estimate of the incipience temperature excursion ∆T ex : ∆T ex ≤ 2T s σ l h fv 4 × 10 6 1 ρ f − 1 ρ l ρ f ρ f − ρ v − 0.003 q h 2 fv C 3 p µ f σ f g(ρ f − ρ v ) 1/3 · Pr 1.7 (13.84) Once nucleate boiling initiates on the component, the relationship between the com- ponent heat flux and its temperature rise above that of the coolant saturation temper- ature is given by the Rohsenow (1951) correlation: q = µ f h fg g(ρ f − ρ g ) σ C sf a · Pr 1.7 f · h fg (T w − T sat ) n (13.85) Watwe et al. (1997) determined that values of a and n in eq. (1.52) were 0.0075 and 7.5, respectively, for fluorocarbon FC-72 boiling on a 1-cm 2 silicon chip. Danielson et al. (1987) have reported values of a ranging from 0.003 to 0.0093 and values of n ranging from 4 to 8 for nucleate boiling of FC-72. Watwe et al. (1997) have also shown that eq. (13.85) can be used to predict the boiling heat transfer characteristics accurately at elevated ambient pressure or under subcooled liquid conditions. Flow boiling in channels occurs due to bubble generation at the channel walls. Depending on the fluid velocity, channel orientation with respect to gravity and hy- drodynamic effects due to vapor and liquid density differences, several different flow regimes can be identified. Following initiation of boiling, the heat transfer coefficient at the wall increases significantly while the vapor bubbles are carried away by the flowing liquid. This is the bubbly flow regime. With increasing vapor volume frac- tion, individual bubbles coalesce to form large vapor slugs. This constitutes the slug flow regime. At very high heat flux levels, the rate of vapor generation is so high that the indi- vidual bubbles coalesce into large vapor mushrooms. These large vapor mushrooms depart from the heated surface periodically due to hydrodynamic instabilities caused BOOKCOMP, Inc. — John Wiley & Sons / Page 1012 / 2nd Proofs / Heat Transfer Handbook / Bejan 1012 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 [1012], (66) Lines: 1747 to 1791 ——— 0.5102pt PgVar ——— Custom Page (-10.0pt) PgEnds: T E X [1012], (66) by density differences between the vapor and liquid flow. If the surface of the heater cannot be rewetted following the cyclic departure of these vapor mushrooms, the sur- face temperature is expected to rise rapidly and cause the heater to melt or burnout. The heat flux at which such a dryout/burnout phenomenon occurs is called critical heat flux (CHF). It is extremely essential to ensure that the critical heat flux con- dition does not occur on an immersion-cooled electronic component to ensure its functionality and reliability. Watwe et al. (1997) extended the classical Kutateladze (1951)–Zuber (1959) Haramura-Katto (1983) model of the pool boiling critical heat flux to propose the equation CHF = π 24 h fg ρ g σ f g(ρ f − ρ g ) 1/4 δ ρ s C s k s δ ρ s C s k s + 0.1 × 1.3014 − 0.01507L ) 1 + 0.03 ρ f ρ g 0.75 C pf h fg (T sat − T bulk ) (13.86) where L = L g(ρ f − ρ g ) σ f (13.87) and δ is the heater thickness. Equation (13.86) is a composite equation that includes effects such as heater size, heater thermophysical properties, system pressure, and bulk liquid subcooling (temperature difference between the saturation temperature and bulk liquid temperature can be used to estimate critical heat flux during pool boiling of dielectric coolants). Lee and Simon (1989) proposed the following equation to compute the critical heat flux on heater lengths ranging from 0.25 to 3 mm for flow velocities from 1 to 17 m/s and subcooling ranging from 13 to 68°C: CHF = ρ v h fv U 0.04 ρ f ρ v 0.99 σ f ρ f U 2 L 0.33 1 + 3.03 ρ f ρ v 0.78 C p ∆T sub h fv 0.42 (13.88) Most practical immersion cooling systems operate in a closed loop, where the vapor of the dielectric liquid is condensed and returned to the electronic enclosure. Two such systems are shown in Fig. 13.32a and b. In Fig. 13.32a a “remote” condenser, external to the electronic enclosure and cooled by water, air, or other fluid, condenses the vapor leaving the enclosure and directs the condensate back to the enclosure for reuse. In the configuration represented by Fig. 13.32b, the condenser is located in the vapor BOOKCOMP, Inc. — John Wiley & Sons / Page 1013 / 2nd Proofs / Heat Transfer Handbook / Bejan PHASE-CHANGE PHENOMENA 1013 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 [1013], (67) Lines: 1791 to 1791 ——— * 43.927pt PgVar ——— Custom Page (-10.0pt) PgEnds: T E X [1013], (67) Figure 13.32 Two closed-loop immersion cooling systems. BOOKCOMP, Inc. — John Wiley & Sons / Page 1014 / 2nd Proofs / Heat Transfer Handbook / Bejan 1014 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 [1014], (68) Lines: 1791 to 1793 ——— 0.097pt PgVar ——— Normal Page PgEnds: T E X [1014], (68) Figure 13.33 Submerged condenser immersion cooling systems. space above the liquid—producing a more compact immersion module design—and the condensate drips back into the liquid. As discussed previously, due to the high solubility of air in the perfluorinated fluorocarbons, often used as immersion cooling liquids, it is not uncommon for vapor space condensers to be affected adversely by a buildup of noncondensable gas. BOOKCOMP, Inc. — John Wiley & Sons / Page 1015 / 2nd Proofs / Heat Transfer Handbook / Bejan PHASE-CHANGE PHENOMENA 1015 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 [1015], (69) Lines: 1793 to 1825 ——— -0.50587pt PgVar ——— Normal Page * PgEnds: Eject [1015], (69) Such difficulties can be avoided by submerging the condenser (i.e., heat exchanger tubes) in the liquid, as shown in Fig. 13.33a. The circulating water through the tubes absorbs the heat from the dielectric liquid, thus subcooling the liquid. Any vapor bubbles generated by boiling on the component surfaces collapse and condense in the subcooled liquid. As a further modification of this approach, it is possible to use the side and top walls of the liquid-filled enclosure to serve as the submerged condenser, which can then be externally air- or liquid-cooled, as shown in Fig. 13.33b. Nelson et al. (1994), Kitching et al. (1995), and Geisler et al. (1996) have performed empirical studies on the cooling capabilities of “passive immersion cooled multichip modules” based on the concepts discussed above. Nelson et al. (1994) showed that the overall thermal performance of these modules was not affected by the presence of uneven chip power densities. The maximum power that can be dissipated from such modules depends on the nucleate pool boiling critical heat flux on the power-dissipating component as well as the condensation limit of the condenser. The thermal behavior of the module can be plotted on performance maps where the lower bound marked is determined by natural convection heat transfer on both heater and condenser sections. The natural convection correlation by Park and Bergles (1988) and those listed in Table 13.4 can be used to estimate the lower bound. Once pool boiling is initiated on the heaters, one of the following two scenarios determines the cooling limit: 1. The maximum power dissipation from the module can be limited by the occur- rence of the critical heat flux condition on the heater. Geisler et al. (1996) have shown that it may be possible to raise the critical heat flux limit by reducing the module-to- ambient thermal resistance, thereby increasing the subcooling of the coolant inside the module. The Watwe et al. (1997) correlation [see eq. (13.86)] can be used to compute the critical heat flux limit. 2. The maximum power dissipation from the module can also be limited if the condenser is unable to condense the volume of vapor generated at the heater. The uncondensed vapor will occupy the near wall regions of the condenser, thereby dra- matically reducing the condenser efficiency. The condensation limit on an unfinned flat plate condenser can be computed using the following correlation proposed by Gerstmann and Griffith (1966): Nu = 0.81Ra 0.193 for 10 10 > Ra > 10 8 (13.89) 0.69Ra 0.20 for 10 8 > Ra > 10 6 (13.90) where the Nusselt number Nu and the Rayleigh number Ra are defined as follows: Nu = h k f σ f g(ρ f − ρ v ) cos θ 1/2 (13.91) Ra = g cos θρ f (ρ f − ρ v )h fv kµ∆T σ f g(ρ f − ρ v ) cos θ 3/2 (13.92) . BOOKCOMP, Inc. — John Wiley & Sons / Page 1006 / 2nd Proofs / Heat Transfer Handbook / Bejan 1006 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 [1006],. can also BOOKCOMP, Inc. — John Wiley & Sons / Page 1008 / 2nd Proofs / Heat Transfer Handbook / Bejan 1008 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 [1008],. the natural convection heat transfer coefficient. Park and Bergles (1988) provided a correlation accounting for the effect of heater length on the natural convection heat transfer coefficient from