Efficient spreaders for cooling high-power computer chips

Applied Thermal Engineering 27 (2007) 1072–1088 www.elsevier.com/locate/apthermeng

Efficient spreaders for cooling high-power computer chips Mohamed S. El-Genk *, Hamed H. Saber, Jack L. Parker Institute for Space and Nuclear Power Studies and Chemical and Nuclear Engineering Department, The University of New Mexico, Albuquerque, NM 87131, United States Received 2 September 2005; accepted 12 July 2006 Available online 23 October 2006

Abstract Investigated is the performance of composite spreaders, consisting of a top layer of porous graphite (P0.4 mm), for enhanced cooling by nucleate boiling of FC-72 dielectric liquid, and a copper substrate (61.6 mm), for efficient spreading of the dissipated thermal power by the underling 10 · 10 mm or 15 · 15 mm high-power computer chips. The analysis assumes uniform thermal power dissipation by the chips and calculates the square surface area of the spreader, along with the spreading, boiling and total thermal resistances, the maximum chip temperature, and the removed thermal power from the spreader surface by saturation or subcooled nucleate boiling of FC-72 liquid. These performance parameters are determined as functions of the thickness of the copper substrate and the size of the underlying chip. When compared with those of copper and porous graphite spreaders of the same total thickness, 2.0 mm, the performance of the composite spreaders is superior for cooling high-power computer chips. When cooled by nucleate boiling of 30 K subcooled FC-72 liquid, the composite spreader removes 160.3 W and 98.4 W of dissipated thermal power by the underlying 10 · 10 mm and 15 · 15 mm chips, at total thermal resistances of 0.29 and 0.48 C/W. When the same spreader is cooled by saturation boiling of FC-72, the removed thermal power decreases to 85.6 W and 53.4 W, and the total thermal resistances also decrease to 0.12 and 0.20 C/W, respectively. Although the calculated surface temperatures of the chips are not uniform, the maximum temperatures are <71 C and the temperature differential across the chips is <8 C. For the same cooling condition, the calculated surface area of the copper spreaders, the total thermal resistance, and the maximum chip temperature are much higher, but the removed thermal powers from the surface of spreaders are much lower than with composite spreaders. The calculated surface areas of the porous graphite spreaders are smaller, the thermal powers removed from surface of these spreaders are much lower and both the total thermal resistance and the maximum chip temperature are higher than those with composite spreaders.  2006 Elsevier Ltd. All rights reserved. Keywords: Cooling high-power computer chips; Composite spreaders; Nucleate boiling of dielectric liquids

1. Introduction Adequate cooling is a major challenge to future development of faster and denser high-power computer chips. The ever-increasing thermal power dissipation by chips of more than 100 W, at an average heat flux that is approaching or exceeding 50 W/cm2 needs to be removed, while keeping the junctions or die temperatures below 85 C. The local heat flux at the hot spots on the surface of these chips could

*

Corresponding author. Tel.: +1 505 277 5442. E-mail address: [email protected] (M.S. El-Genk).

1359-4311/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.07.039

be as much as 100 W/cm2 [1,2]. Enhanced heat dissipation from the computer chips is achieved using efficient spreaders cooled by saturation or subcooled nucleate boiling of dielectric liquids, such as FC-72 and HFE-7100. The saturation temperature of these liquids, at an atmospheric pressure, are 56 C and 61 C, which help keep the die or junctions temperatures below 85 C. In addition to the high heat transfer coefficient, nucleate boiling reduces the nonuniformity in the chip surface temperature, hence decreasing the induced mechanical and thermal stresses. To take advantage of these attributes, the thermal power dissipated by the chips needs to spread to a larger surface area cooled by nucleate boiling.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

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Nomenclature A surface areas (m2) CHF critical heat flux (W/m2) h heat transfer coefficient (W/m2 K) L length (m or mm) NBHTC nucleate boiling heat transfer coefficient, hNB (W/m2 K) q surface heat flux (W/m2) Q thermal power dissipation or removed (W), Eq. (4) R thermal resistance (C/W) t thickness (m) T temperature (K) T average temperature, Eq. (3) x, y, and z Cartesian coordinates (Figs. 1 and 2) Greek symbols D dimensionless thickness (t/tsp) DTb (Tsp  Tb) (K)

Numerous experiments have investigated saturation and subcooled boiling of FC-72 and HFE-7100 liquids on smooth surfaces, such as copper and silicon, and surfaces with micro-fins, porous structure, and micro-porous coatings [3–23]. Significant increases in the nucleate boiling heat transfer coefficients of these liquids on micro-porous coatings and micro-finned surfaces and reductions in the surface temperature excursions prior to boiling incipience have been reported [3–23]. The very low surface tension and high wetting of dielectric liquids (12 m N/m and 13.6 m N/m for FC-72 and HFE-7100 at 20 C) cause these excursions in surface temperature. These liquids flood surface crevices and reduce the amount of trapped air, which delays boiling incipience until the surface temperature is large enough to initiate boiling. Temperature excursions prior to boiling incipience of as much as 35 K have been reported in pool boiling of dielectric liquids on smooth copper and silicon. Such temperature excursions are not desirable because they increase the junctions temperatures and hence, increase the failure frequency of the chips. Enhances in nucleate boiling for dielectric liquids, with no or little temperature excursions prior to boiling incipience, on micro-porous coatings, micro-finned and porous graphite surfaces have been reported [3–7,11,12,15–23]. On porous graphite, large increases in the nucleate boiling heat transfer coefficient and the critical heat flux (CHF) are measured with no temperature excursion prior to boiling incipience of either FC-72 or HFE-7100 [20–23]. Porous graphite has a high volume porosity of 60% with 95% of the enclosed pores and re-entrant type cavities interconnected. These pores and cavities entrap a large amount of air for stimulating nucleate boiling at very low surface superheats (DTsat < 1.0 K) [20–23]. The measured CHF of FC-72 on porous graphite varies from 27 W/cm2 in satu-

DTsat DTsub

surface superheat, (Tsp  Tsat) (K) liquid subcooling (Tsat  Tb)

Subscripts b FC-72 dielectric liquid bulk or pool Boil nucleate boiling Chip computer chip Cu copper in interface max maximum at the center of chip NB nucleate boiling PG porous graphite Sat saturation of FC-72 liquid in Albuquerque, NM sp spreader, or spreader top surface (Figs. 1 and 2) th thermal TOT total

ration boiling to 57 W/cm2 in 30 K subcooled boiling, compared to only 16.9 and 29.5 W/cm2 on smooth copper [21,23]. Results of HFE-7100 on porous graphite showed even much higher nucleate boiling heat fluxes than those of FC-72. For both liquids, depending on subcooling (630 K), nucleate boiling heat transfer coefficients on porous graphite can be 2–30 times higher than those on smooth copper [15,16,20–23]. These results suggest that a graphite spreader could facilitate removing the dissipated thermal power by highpower computer chips, while maintaining the junctions’ temperature <85 C. However, a concern with using porous graphite as a spreader is its anisotropic and relatively low thermal conductivity. At room temperature, the thermal conductivity of porous graphite is 245 W/m K out of plane and 70 W/m K in plane. Conversely, copper has a homogenous and higher thermal conductivity (375 W/ m2 K), but the nucleate boiling heat transfer coefficients of dielectric liquids on copper are significantly lower than on porous graphite. Furthermore, the large temperature excursions prior to boiling incipience on copper, and their absence on porous graphite, significantly increase the junctions’ temperature. To take advantage of the enhanced nucleate boiling of FC-72 on porous graphite and the excellent spreading quality of copper, this work proposes using composite spreaders that consist of a top layer of porous graphite (P0.4 mm thick) and a copper substrate (61.6 mm thick), to achieve better heat dissipation in computer chips. The performance of these spreaders for removing the thermal power dissipated by underlying 10 · 10 mm and 15 · 15 mm chips is investigated. The square surface areas of the spreaders, the removed thermal power from the spreader surface, the maximum surface temperatures of

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the chips, along with the spreading, boiling, and total thermal resistances of the spreaders are calculated. The performance results of the composite spreaders are compared with those of copper and porous graphite spreaders of the same total thickness, 2.0 mm, but different calculated surface areas. 2. Problem statement The present analysis assumes that the spreaders investigated in this paper (Fig. 1) are in good thermal contact with the underlying chips, using high thermal conductivity grease or other materials such as carbon black. With pressures of 0.46 and 0.69 MPa, the interfacial resistances of the carbon black, when used with a 10 · 10 mm chip, are 0.0528 and 0.0402 C/W, and 0.0235 and 0.0179 C/W with a 15 · 15 mm chip [24]. As shown in Figs. 1 and 2, the chip has a square surface area (LChip · LChip) and is centered below the spreader, which also has a square surface area (Lsp · Lsp). While the dimensions of the chips are part of the input to the analysis, the dimensions of the spreader surface are calculated, as detailed later. The analysis also assumes that the dissipation heat flux, qChip, from the top surface of the chip (0.5LChip 6 x 6 0.5LChip, 0.5LChip 6 y 6 0.5 and z = 0) is uniform. However, in actuality the heat dissipation by the chips is non-uniform with a peak heat flux 2–3 times the average heat flux [1,2]. In addition, the analysis assumes that both the bottom surface and the sides of the chips are thermally insulated, or adiabatic. As shown in Fig. 1, the top surface of the spreader (x, y, tsp) is cooled by either saturation or 10 K, 20 K, or 30 K subcooled nucleate boiling of FC-72 dielectric liquid (Figs. 2 and 3), subject to the following criterion: (a) The highest nucleate boiling heat flux at the center of the top surface of the spreader (0, 0, tsp) equals 90% of the measured CHF in the pool boiling experiments [21,23]. (b) The lowest nucleate boiling heat transfer coefficient at the edge of the spreader surface (y = x = ±0.5 Lsp, and z = tsp) corresponds to a surface superheat,

Fig. 2. Cross-sectional views of the composite spreader: (a) plane view, (b) elevation view.

DTsat, than is 1.0 K higher than measured at boiling incipience on porous graphite in the experiments [21,23]. Figs. 3 and 4 show the values of the nucleate boiling heat transfer coefficients, hNB, used in the present analysis for FC-72 on the surfaces of porous graphite and copper spreaders. The experimentally generated pool boiling curves in Albuquerque, New Mexico, where saturation temperature of FC-72 is only 52 C because of the high

35000

FC-72 Liquid on Porous Graphite ΔT =0K Sub ΔT = 10 K Sub ΔT = 20 K Sub ΔT = 30 K Sub

25000

2

NBHTC (W/m K)

30000

20000 15000 10000 5000 0

52

54

56

58

60

62

64

66

68

70

72

o

Surface Temperature ( C) Fig. 1. A schematic of the layout of the porous composite spreader for cooling high-power chips.

Fig. 3. Nucleate boiling heat transfer coefficient (NBHTC) of FC-72 liquid on porous graphite.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088 10000

2

NBHTC (W/m K)

8000

6000

4000

FC-72 Liquid on Copper Δ TSub = 0 K Δ TSub = 10 K Δ TSub = 20 K Δ TSub = 30 K

2000

0

60

62

64

66

68

70

72

74

76

78

T Cu ðx; y; tCu Þ ¼ T PG ðx; y; tCu Þ ¼ T in ðx; y; tCu Þ; dT Cu ð0 6 x 6 0:5LChip ; k Cu dz 0 6 y 6 0:5LChip ; 0Þ ¼ qChip ; dT Cu ðx P 0:5LChip ; y; 0Þ ¼ 0; k Cu dx dT Cu ðx; y P 0:5LChip ; 0Þ ¼ 0; k Cu dy dT Cu k Cu ðx ¼ 0:5Lsp ; y; zÞ ¼ 0; dx dT Cu ðx; y ¼ 0:5Lsp ; zÞ ¼ 0 k Cu dy

1075

ð2aÞ

o

Surface Temperature ( C) Fig. 4. Nucleate boiling heat transfer coefficient (NBHTC) of FC-72 liquid on copper.

local elevation [21,23], are used to generate the saturation and subcooled nucleate boiling heat transfer coefficients, hNB, curves in Figs. 3 and 4. Increasing the liquid subcooling increases the nucleate boiling heat fluxes [21,23] less than increasing the corresponding surface superheats, which decreases hNB (Figs. 3 and 4). The vertical lines in Fig. 3 indicate the values of hNB corresponding to 90% of the measured CHF values on porous graphite [21,23]. The saturation nucleate boiling heat transfer coefficient of FC-72 on porous graphite increases from a low of 20,000 W/m2 K, peaks at 33,000 W/m2 K when the spreader surface temperature, Tsp  58.5 C, then drops linearly with increasing surface temperature (Fig. 3). The values of hNB, or NBHTC, for 10, 20, and 30 K subcooled boiling of FC-72 liquid on porous graphite, peak at 16,800, 13,500, and 12,000 W/m2 K and surface temperatures of 62, 64.4, and 65.5 C (Fig. 3). The saturation and subcooled boiling values of hNB, or NBHTC, for FC-72 liquid on copper are much lower than on porous graphite (Fig. 4). The analysis solves the three-dimensional heat conduction equations in the copper substrate (x, y, and 0 6 z 6 tCu) and the top porous graphite layer (x, y, and tCu 6 z 6 tsp):     oT Cu oT Cu oT Cu oT Cu k Cu k Cu þ ox ox oy oy   oT Cu oT Cu k Cu þ ¼ 0 and oz oz     oT PG oT PG oT PG oT PG k PG ðxÞ k PG ðyÞ þ ox ox oy oy   oT PG oT PG k PG ðzÞ þ ¼ 0; oz oz

ð1aÞ

and T PG ðx; y; tsp Þ ¼ T sp ðx; y; tsp Þ; dT PG ðx ¼ 0:5Lsp ; y; zÞ ¼ 0; k PG ðxÞ dx dT PG ðx; y ¼ 0:5Lsp ; zÞ ¼ 0: k PG ðyÞ dy

The interface temperature between the copper substrate and the top graphite layer, Tin(x, y, tCu), is calculated from the energy balance at the interface: k Cu

dT Cu dT PG ðx; y; tCu Þ ¼ k PG ðzÞ ðx; y; tCu Þ: dz dz

ð3aÞ

Similarly, the spreader surface temperature, Tsp(x, y, tsp), is calculated from the energy balance: k PG ðzÞ

dT PG ðx; y; tsp Þ ¼ hNB ðx; y; tsp Þ½T sp  T b : dz

ð3bÞ

The values of hNB in Eq. (3b) are obtained from the curves in Figs. 3 and 4, as a function of the spreader surface temperature, Tsp. Eqs. (1a) and (1b) are solved numerically using the ANSYS, finite element commercial software, subject to the boundary conditions in Eqs. (2a)–(3b). The 3-D temperature fields in the copper substrate and the porous graphite top layer of the composite spreader, the surface area of the spreader, ðAsp ¼ L2sp Þ, and the dissipated thermal power by the underling chip, ðQChip ¼ qChip L2Chip Þ, removed from the spreader surface, are calculated. In the case of either copper or porous graphite spreaders, the applicable heat conduction equations, (1a) or (1b), are solved subject to the following boundary conditions (Figs. 1 and 2):

ð1bÞ

subject to the following boundary conditions (Figs. 1 and 2):

ð2bÞ

T Cu ðx; y; tsp Þ ¼ T sp ðx; y; tsp Þ; dT Cu k Cu ð0 6 x 6 0:5LChip ; dz 0 6 y 6 0:5LChip ; 0Þ ¼ qChip ;

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M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

dT Cu ðx P 0:5LChip ; y; 0Þ ¼ 0; dx dT Cu k Cu ðx; y P 0:5LChip ; 0Þ ¼ 0; dy

where

k Cu

dT Cu ðx ¼ 0:5Lsp ; y; zÞ ¼ 0; k Cu dx dT Cu k Cu ðx; y ¼ 0:5Lsp ; zÞ ¼ 0: dy

Rsp ðx ¼ yÞ ¼ ðT max  T sp ðx ¼ yÞÞ=Qsp ðx ¼ yÞ; ð4aÞ

The total thermal resistance, RTOT, based on the calculated total surface area of the spreader, is: RTOT ðx ¼ y ¼ Lsp Þ ¼ Rsp ðx ¼ y ¼ Lsp Þ þ RBoil ðx ¼ y ¼ Lsp Þ; ð6aÞ

or,

where

T PG ðx; y; tsp Þ ¼ T sp ðx; y; tsp Þ;

Rsp ðx ¼ y ¼ Lsp Þ ¼ ðT max  T sp ðx ¼ y ¼ Lsp ÞÞ=Qsp ðx ¼ y ¼ Lsp Þ;

dT PG ð0 6 x 6 0:5LChip ; dz 0 6 y 6 0:5LChip ; 0Þ ¼ qChip ;

k PG ðzÞ

¼ ðT sp ðx ¼ y ¼ Lsp Þ  T b Þ=Qsp ðx ¼ y ¼ Lsp Þ:

In addition to calculating the surface area of the spreader, the present thermal analysis calculates the spreading, boiling, and total thermal resistances, along with the twodimensional temperature distribution on the surface of the underlying 10 · 10 mm and 15 · 15 mm chips. The analysis varied the thickness of the top porous graphite layer of the composite spreaders from 0.4 mm (DPG = tPG/tsp = 0.2) to 1.5 mm (DPG = 0.75). The performance results of copper (DPG = 0.0), porous graphite (DPG = 1.0), and composite spreaders (0.75 6 DPG P 0.2) of the same total thickness, 2.0 mm, are compared and discussed in the next section. The maximum surface temperatures at the centerline of the underlying chips, Tmax, are calculated as a function of the thickness of the top porous graphite layer (or copper substrate) in the composite spreaders. The calculated values are compared with those using copper and porous graphite spreaders, subject to the same nucleate boiling cooling conditions at the top surface of the spreaders (Figs. 3 and 4). The calculated thermal resistance in the present analysis excludes the contact resistance between the spreader and the underlying chip, which depends on the selected interface material in the assembly process, and is outside the scope of this work. Thus, the local thermal resistance is calculated as the sum of the spreading resistance of the dissipated thermal power by the underling chip, Rsp, and the nucleate boiling resistance at the surface of the spreader, RBoil, as ð5aÞ

Power Dissipation (W)

dT PG ðx ¼ 0:5Lsp ; y; zÞ ¼ 0; dx dT PG k PG ðyÞ ðx; y ¼ 0:5Lsp ; zÞ ¼ 0: dy

These definitions and the layouts in Figs. 1 and 2 of the composite spreader on the chip are consistent with typical packaging terminology and arrangement [25–27]. The

120

15 mm x 15 mm Chip

(a) Copper Spreader Saturation ΔT = 30 K Sub

100 80 60 40

10 mm x 10 mm Chip

20 0 0

2

4

6

8

10

12

14

16

18

20

22

18

20

22

20

22

100

Power Dissipation (W)

ð4bÞ

k PG ðxÞ

Rth ðx ¼ yÞ ¼ Rsp ðx ¼ yÞ þ RBoil ðx ¼ yÞ;

ð6bÞ

RBoil ðx ¼ y ¼ Lsp Þ

(b) Composite Spreader 10 mm x 10 mm Chip

80

0.2 0.5

ΔT

60

= 30 K Sub 1.0 0.2

40 0.5 Δ

20 Saturation

PG

= 1.0

0 180

Power Dissipation (W)

dT PG ðx P 0:5LChip ; y; 0Þ ¼ 0; k PG ðxÞ dx dT PG k PG ðyÞ ðx; y P 0:5LChip ; 0Þ ¼ 0; dy

ð5bÞ

RBoil ðx ¼ yÞ ¼ ðT sp ðx ¼ yÞ  T b Þ=Qsp ðx ¼ yÞ;

0

2

4

6

8

10

12

(c) Composite Spreader 15 mm x 15 mm Chip

160 140 100

ΔT

Sub

80

= 30 K

60

0.5

40

Saturation

20 0

16

0.2 0.5

1.0

120

14

0

2

4

6

8

10

Δ

0.2

= 1.0 PG

12

14

16

18

Distance Along Spreader Surface (mm) Fig. 5. Lateral distributions of removed thermal power with copper and composite spreaders.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

0

0

ð7Þ The removed local thermal power from the surface of the spreader, Qsp, is determined from the calculated local heat flux on the spreader surface, qsp(x 0 , y 0 ), as Z y¼x Z x Qsp ðx ¼ yÞ ¼ qsp ðx0 ; y 0 Þ dx0 dy 0 : ð8Þ 0

0

0.4

0.4

0.3

(a) Copper Spreader

Saturation

o

To confirm the accuracy of the ANSYS calculations, the performed overall energy balance calculated the total rate of heat removal from the surface of the spreader, Qsp(x = y = Lsp), and compared it with the thermal power dissipation by the underlying chip, QChip. The difference was less than 0.1%.

Spreading Resistance ( C/W)

0

The calculated thermal power dissipated by the underlying chips, removed from the spreader surface, and the calculated surface areas of the copper, composite and porous graphite spreaders are presented in Fig. 5a–c. The x-axis indicates the distance along the spreader surface measured from its center (x = y = 0). The calculated surface areas of the spreaders change with their composition, copper in Fig. 5a and both porous graphite (DPG = 1.0) and composite spreaders (DPG = 0.5 and 0.2) in Fig. 5b and c. Fig. 5a shows that the dissipated powers by the underlying chips, removed from the surface of the copper spreaders, increase markedly with increasing subcooling of FC-72 liquid and to a lesser extent with increasing the size of the underlying chip. The liquid subcooling negligibly affects the surface areas of the copper spreaders. The total dissipated thermal power by 10 · 10 mm chip and removed by 30 K subcooled

Spreading Resistance ( C/W)

0

3. Results and discussion

Spreading Resistance ( C/W)

spreader’s local average surface temperature, T sp , is determined from the calculated local values, Tsp(x 0 , y 0 ), in the analysis as Z y¼xZ x Z y¼x Z x 0 0 0 0 T sp ðx ¼ yÞ ¼ T sp ðx ; y Þ dx dy dx0 dy 0 :

1077

(a) Copper Spreader ΔT = 30 K Sub

o

Chip Temperature ( C)

74 72

Saturation

70 68

10 mm x 10 mm Chip 66

0

1

2

3

4

6

7

8

69 Δ

67

PG

15 mm x 15 mm Chip 0.1

0.5 0.2

63 61

1.0 0.5 0.2

59 57

1

2

3

4

6

7

8

(c) Composite Spreader 15 mm x 15 mm Chip

69

o

Chip Temperature ( C)

5

67

Δ

65

PG

= 1.0 0.5

0.2

63 61

1.0

59

0.5

0.2

57

Δ

0.3

1

2

3

4

5

6

7

Distance Along Chip Surface (mm) Fig. 6. Lateral distributions of the chips surface temperatures.

10

12

8

PG

14

16

18

20

22

= 1.0 0 .5

0.2

0.2

0.1 4

6

8

10

12

14

16

18

20

22

(c) Composite Spreader, 15 x 15 mm Chip

0.2 Δ

PG

= 1.0

0 .5

0.1 2

55 0

8

o

0

6

(b) Composite Spreader, 10 x 10 mm Chip

2

55 71

4

o

= 1.0

65

= 30 K

0.2

2

(b) Composite Spreader 10 mm x 10 mm Chip

o

Chip Temperature ( C)

5

Sub

10 mm x 10 mm Chip

15 mm x 15 mm Chip 64 71

ΔT

0.3

4

6

8

10

12

14

0 .2

16

18

20

22

Distance Along Spreader Surface (mm) Fig. 7. Lateral distributions of the spreading resistances of dissipated thermal powers.

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M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

o

Boiling Resistatce ( C/W)

nucleate boiling of FC-72 from the calculated copper spreader surface (37 · 37 mm) is 83.5 W (Fig. 5a). When cooled with saturation nucleate boiling, the calculated surface area of the copper spreader increases slightly, but the removed power dissipation decreases significantly to 54.6 W. Similarly, for the 15 · 15 mm chip, the calculated surface area of the copper spreader is 41.2 · 41.2 mm and the dissipated thermal power by the underlying chip, removed from the spreader surface by 30 K subcooled nucleate boiling, is 121 W. The dissipated power decreases to 78.4 W, while the calculated surface area increases slightly to 43 · 43 mm, when the surface of the copper spreader is cooled by saturation nucleate boiling of FC-72 liquid (Fig. 5a). The dissipated thermal powers by the underlying chips, removed by saturation nucleate boiling from the surface of the composite spreaders, are much lower than when the spreaders are cooled by subcooled nucleate boiling. However, the calculated surface areas of the composite spreaders are smaller when cooled by subcooled nucleate boiling

(Figs. 5b and c). These figures show that increasing the size of the underlying chip increases the removed total thermal power dissipation from, and the calculated surface areas of, the composite spreaders. The removed thermal power dissipation and the calculated surface areas of these spreaders also increase as the thickness of the copper substrate increases or the thickness of the top graphite layer decreases. The calculated surface areas of the composite spreaders for the 15 · 15 mm chip are larger than those for the 10 · 10 mm chip (Figs. 5b and c), but much smaller than those of the copper spreaders for the same total thermal power dissipation (Fig. 4a). The calculated surface areas of the porous graphite spreaders (DPG = 1.0) are the smallest and the removed thermal power dissipation by the underlying chip is the lowest. This is because the low in-plane thermal conductivity of porous graphite limits the spreading of the dissipated power by the underlying chip, despite the higher nucleate boiling heat transfer coefficient at the surface of the spreader (Fig. 3). The copper substrate improves the spreading efficiency, increasing the

2.0 (a) Copper Spreader Saturation 1.5

71

Δ TSub = 30 K

61

10 x 10 mm Chip

59

4

6

8

10

12

14

16

18

20

57

22

0

2.0

1.5

Δ

PG

Δ

PG

o

= 0.5 = 0.2

1.0 ΔT

0.5

Sub

= 30 K Saturation

0 2

4

6

8

10

12

14

16

18

20

22

2.0

6

8

60

Δ

58

10

12

14

16

18

2

4

6

8

10

12

14

16

18

20

22

(c) Composite Spreader, 15 x 15 mm Chip PG

22

Distance Along Spreader Surface (mm) Fig. 8. Lateral distributions of the boiling resistances on spreaders surface.

= 1.0

1.0 0.2 0.5 0.2 0.5

54

20

22

52

56

Saturation 8

20

= 1.0 0.5 0.2

58

= 30 K Sub

6

18

PG

Δ

ΔT

4

16

1.0 0.5 0.2

54

60

2

14

56

62

= 0.2 PG

1.0

0

12

62

64

Δ PG = 0.5

0.5

10

(b) Composite Spreader, 10 x 10 mm Chip

64

0

Δ

4

66

(c) Composite Spreader, 15 x 15 mm Chip Δ = 1.0 PG

1.5

2

66

(b) Composite Spreader, 10 x 10 mm Chip = 1.0 Δ PG

Surface Temperature ( C)

o

Boiling Resistatce ( C/ W)

= 30 K

63

0.5

2

o

Sub

Saturation

65

15 x 15 mm Chip

0

Boiling Resistatce ( C/ W)

ΔT

15 x 15 mm Chip

67

10 x 10 mm Chip 1.0

(a) Copper Spreader

69

52 0

2

4

6

8

10

12

14

16

18

20

22

Distance Along Spreader Surface (mm) Fig. 9. Lateral distributions of the spreaders surface temperatures.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

removed thermal power dissipation by the underlying chips as well as the calculated surface area of the composite spreaders. The removed total thermal power dissipated by a 10 · 10 mm chip is 100 W and 53.6 W, when the copper substrate in the composite spreader is 1.6 mm thick (or DPG = 0.2), and the spreader is cooled by 30 K subcooled and saturation nucleate boiling of FC-72 liquid, respectively. The removed total thermal power dissipation decreases to only 57.3 W and 29.6 W, respectively, for a porous graphite spreader (DPG = 1.0). The total thermal power dissipated by a 15 · 15 mm chip and removed from the surface of a composite spreader having a 1.6 mm thick copper substrate (DPG = 0.2) is 160.4 W and 85.3 W, when the surface of this composite spreader is cooled by 30 K subcooled and saturation nucleate boiling of FC-72, respectively (Fig. 5c). For these total thermal power dissipation and cooling conditions, the cal-

(a) Copper Spreader Saturation 1.5

ΔT

10 x 10 mm Chip

Sub

= 30 K

o

3.1. Chip surface temperature The calculated maximum surface temperature, as well as the temperature differentials across the surface of the 10 · 10 mm and 15 · 15 mm chips, when using copper spreaders, are shown in Fig. 6a and composite spreaders in Fig. 6b and c. When cooling the spreader surface with subcooled nucleate boiling of FC-72 liquid, the maximum surface temperature of, and the temperature differentials across, the surface of the underlying chips are the highest. With composite spreaders, the maximum surface temperatures of the underling chips (Fig. 6b and c) are 3.5–8 C lower than those with copper spreaders (Fig. 6a). With copper spreaders cooled by 30 K subcooled and saturation nucleate boiling of FC-72 liquid, the calculated maximum surface temperatures of the 10 · 10 mm chip are 74.6 and

15 x 15 mm Chip

1.0

18 (a) 10 x 10 mm Chip 16

0.5 2

0

Thermal Resistance ( C/W)

culated spreader surface measures 28.6 · 28.6 mm and 32.6 · 32.6 mm, respectively. Note that the removed total thermal power dissipation from the surface of the spreaders in Fig. 5a–c approaches zero at the termination point, which correspond to the centerline of the spreaders (Figs. 1 and 2).

Spreader Area (cm )

o

Thermal Resistance ( C/W)

2.0

2.0

2

4

6

8

10

12

14

16

18

20

22

(b) Composite Spreader 10 x 10 mm Chip Δ = 1.0 PG

1.5

1.0

Δ

PG

Δ

= 0.2 PG

= 0.5

ΔT

Sub

0.5

14 12

Saturation

10

ΔT

Sub

ΔT

Sub

ΔT

Sub

0.2 0.3 0.5

8 6

= 10 K = 20 K = 30 K

0.75 Δ

= 30 K

2 0.1

Saturation 2

4

6

8

10

12

14

16

18

20

0.5

ΔT

Sub

Δ

PG

Δ

PG

Δ

= 0.2 PG

= 1.0 = 0.5

= 30 K

6

8

10

12

14

16

0.6

0.7

0.8

0.9

16 14 12 0.2 0.3 0.5

10 8

0.75

0 4

0.5

Copper Spreader

18

6

Saturation 2

0.4

2

Spreader Area (cm )

1.0

0.3

= 1.0

(b) 15 x 15 mm Chip

20

22

(c) Composite Spreader 15 x 15 mm Chip 1.5

0.2

PG

22

2.0

o

Copper Spreader

4

0

Theraml Resistance ( C/W)

1079

18

20

22

Distance Along Spreader Surface (mm) Fig. 10. Lateral distribution of the total thermal resistances for removing dissipated thermal powers by underlying chips.

Δ

PG

= 1.0

4 0.1

0.2

0.3

0.4

0.5

o

Total Thermal Resistance ( C/W) Fig. 11. Effects of material properties and subcooling of FC-72 liquid on spreaders surface areas and the total thermal resistances.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

(a) The composite spreaders not only have small surface areas but also reduce the maximum chip temperatures. (b) Cooling the surface of the spreaders with subcooled nucleate boiling of FC-72 liquid, increases the maximum surface temperature of, and temperature differential across, the underlying chips. This is because the subcooled NBHTCs of FC-72 liquid are lower than those for saturation nucleate boiling (Figs. 3 and 4). (c) The copper spreaders cause the highest maximum surface temperatures of, and the temperature differentials across, the underling chips, as the NBHTCs of FC-72 liquid on copper are much lower than on porous graphite (Figs. 3 and 4). (d) The superior performance of the composite spreaders is due in part to the high NBHTCs of FC-72 on porous graphite and to the efficient spreading of the dissipated thermal power by underlying chips in the copper substrate.

.0

75 (a) 10 x 10 mm Chip Copper Spreader 74 73 Saturation 72 ΔT = 10 K Sub 71 ΔT = 20 K Sub 70 ΔT = 30 K Sub 69 68 67 66 65 0.5 .3 0 2 64 0. 63 62 61 60 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 75 (b) 15 x 15 mm Chip 74 Copper Spreader 73 72 71 70 69 68 67 0 1. 66 = 75 65 Δ PG 0. 5 0. 3 64 0. 63 0.2 62 61 60 55 65 75 85 95 105 115 125 135 145 155 165

surface areas of the copper spreaders. The calculated differences in performance are summarized as follows:

=1

Fig. 12. Effects of material properties and subcooling of FC-72 liquid on chip maximum temperature and the total thermal power dissipation.

10 x 10 mm Chip 10

Saturation ΔT

Sub

0

= 30 K

2

4

6

8

10

12

14

16

18

20

22

18

20

22

18

20

22

(b) Composite Spreader, 10 x 10 mm Chip

Power Dissipation (W)

PG

0.7 5

Δ

Total Power Disspation (W)

15 x 15 mm Chip

(a) Copper Spreader

100

1

100 ΔT

Sub

0.5 0.2

1.0

= 30 K

0.5 Δ

10

PG

0.2

= 1.0

Saturation

1 0

2

4

6

8

10

12

14

16

(c) Composite Spreader, 15 x 15 mm Chip

Power Dissipation (W)

o

Chip Maximum Temperature ( C)

o

Chip Maximum Temperature ( C)

71.5 C (Fig. 6a). These temperatures are slightly lower for the 15 · 15 mm chip; 73.8 and 71 C, respectively. The composite spreaders (0.75 6 DPG P 0.2) are better than the porous graphite spreaders (DPG = 1.0), and the latter are better than the copper spreaders for lowering the maximum surface temperatures of, and the temperature differentials across, the underlying chips. When the composite spreaders are cooled by saturation nucleate boiling, the calculated maximum surface temperature of, and the temperature differential across, the 10 · 10 mm chip are 62– 62.4 C and <6 C Fig. 6b. When these spreaders are cooled with 30 K subcooled nucleate boiling of FC-72 liquid, the calculated maximum surface temperatures of the chip increase to 69–69.8 C, and the calculated temperature differentials across the chip also increased. These temperatures are close to those calculated of the 15 · 15 mm chip (Fig. 6c) using the same spreaders. In summary, the performance of the composite spreaders (Figs. 1 and 2) is superior to that of copper and porous graphite spreaders for achieving better cooling of the chips, using the same cooling conditions at the spreader surface. They not only increase the total thermal power dissipated by the underlying chips, removed from the surface of the spreaders, but also the composite spreaders have smaller

Power Dissipation (W)

1080

1.0

100 ΔT

0.5 0.2

= 30 K Sub

0.5 0.2 Δ

= 1.0

Saturation

10

1

PG

0

2

4

6

8

10

12

14

16

Distance Along Spreader Surface (mm) Fig. 13. Lateral distributions of the thermal power dissipation removed by spreaders.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

3.2. Spreading resistance The calculated local spreading resistances, Rth, (Eq. (5a)) for removing the thermal powers dissipated by 10 · 10 mm and 15 · 15 mm underling chips are lowest near the edges of spreaders and equal to the total spreading resistances, RTOT (Eq. (6b)). The total spreading resistances with copper spreaders for 10 · 10 mm and 15 · 15 mm chips are 0.18 and 0.113 C/W (Fig. 7a). With porous graphite spreaders, the spreading resistances are much higher, but those with the composite spreaders are lower, than with copper spreaders, at the same cooling conditions of the spreaders. The spreading resistances decrease faster with distance along the spreader surface, when cooled with subcooled nucleate boiling of FC-72 (Fig. 7b and c). For a 10 · 10 mm chip (Fig. 7b), the total spreading resistances of porous graphite spreaders (DPG = 1.0) cooled by saturation and subcooled nucleate boiling of FC-liquid are 0.25 and 0.22 C/W. These values decrease to 0.14 and 0.13 C/W for the composite spreader (DPG = 0.2), which are smaller than those of the copper spreader in Fig. 7a (0.18 C/W) with the same chip size. With the larger 15 · 15 mm chip, the total thermal spreading resistances, RTOT, of the porous graphite (DPG = 1.0) and the compos-

(a) ΔPG = 1.0

Removed Thermal Power (%)

90

3.3. Boiling resistance and spreader surface temperature The calculated local boiling resistances of FC-72 liquid, RBoil (Eq. (5b)), on copper, porous graphite, and composite spreaders with 10 · 10 mm and 15 · 15 mm underlying chips are shown in Fig. 8a–c. The boiling resistances depend on the size of the underlying chip, the composition and material properties of the spreaders, and the subcooling of the boiling FC-72 liquid on the surface of the spreaders. For the porous graphite (DPG = 1.0) and composite (DPG = 0.2) spreaders cooled by 30 K subcooled and saturation nucleate boiling of FC-72 liquid, the calculated total boiling resistances (Eq. (6b)) with a 10 · 10 mm underlying chip are 0.35 and 0.05 C/W, respectively (Fig. 8b). They are 0.24 and 0.03 C/W with a 15 · 15 mm chip (Fig. 8c). The total boiling resistances on the composite spreaders decrease as the thickness of the top porous graphite layer decreases or the thickness of the copper substrate increases.

(c) ΔPG = 0.2

90

10 x10 mm Chip

80

15 x15 mm Chip

80 70

70 60

15 mm x15 mm Chip

60

50

50

40

40

30

30

20

Saturation

10

ΔT

0

10 x10 mm Chip

20 = 30 K 10 Sub

0 10 20 30 40 50 60 70 80 90 100

0

0 10 20 30 40 50 60 70 80 90 100

100

100

Removed Thermal Power (%)

ite spreaders (DPG = 0.2) are the lowest, 0.09–0.11 C/W and 0.07–0.08 C/W, respectively. The spreading resistances of the porous graphite are only slightly lower, but those of the composite spreaders are 10–20% lower than those of the copper spreaders (Fig. 7a and c).

100

100

(b) ΔPG = 0.5

90

(d) Copper Spreader 15 x15 mm Chip

90 80

80

10 x10 mm Chip

70

70

60

60

50

50

10 x10 mm Chip

40

40

15 x15 mm Chip

30

30

20

20

10

10 0

0 0

10 20 30 40 50 60 70 80 90 100

Spreader Surface Area (%)

1081

0

10 20 30 40 50 60 70 80 90 100

Spreader Surface Area (%)

Fig. 14. Fractions of removed thermal power dissipation from the surface of spreaders.

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M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

This is because copper efficiently spreads the thermal power dissipated by the underlying chips, hence decreasing the local nucleate boiling heat flux and the corresponding surface temperature of the porous graphite top layer. In addition, cooling the spreaders surface with saturation nucleate boiling results in much lower boiling resistances than with 30 K subcooled boiling, because the saturation NBHTCs of FC-72 liquid are much higher than the subcooled NBHTCs (Figs. 3 and 4). When cooled by saturation nucleate boiling, the surface temperatures of the spreaders are much lower than when cooled by 30 K subcooled nucleate boiling (Fig. 9a–c). Not only the calculated surface areas of, but also the boiling resistances on the copper spreaders are significantly higher (Fig. 8a) than on the porous graphite of the composite spreaders (Fig. 8b and c). When the copper spreaders are cooled by 30 K subcooled and by saturation nucleate boiling of FC-72 liquid, the calculated total boiling resistances are 0.47 and 0.2 C/W with a 10 · 10 mm chip and

0.34 and 0.14 C/W with a 15 · 15 mm underlying chip (Fig. 8a). For the same cooling conditions of the spreader surface, the surface temperatures of the copper spreaders (Fig. 9a) are several degrees higher than those of the porous graphite or the composite spreaders (Fig. 9b and c). Saturation nucleate boiling for removing the thermal power dissipated by the underlying chip from the surface of the spreader decreases the maximum temperatures at the center of the spreader surfaces. The calculated surface temperatures of the copper spreaders cooled with saturation nucleate boiling are lower near the center, but increase with distance along the spreader surface, exceeding those of the spreaders cooled with 30 K subcooled nucleate boiling in the outer part of the spreader surface (Fig. 9a). Everywhere on the surface of the composite spreaders cooled by saturation nucleate boiling, the surface temperatures are always lower than those cooled with 30 K subcooled nucleate boiling (Fig. 9b and c). On average, cooling the composite spreaders surface with saturation,

Fig. 15. Calculated temperature contours on bottom surfaces of composite and porous graphite spreaders with 15 · 15 mm chips.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

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instead of 30 K subcooled, nucleate boiling of FC-72 liquid lowers the maximum surface temperatures of the spreaders by 5.5 K. The size of the underlying chips and the thickness of the top porous graphite layer of the composite spreaders (or of the copper substrate) seems to have very little effect on the calculated values and the lateral distribution of the surface temperatures of the spreaders, but changes the calculated surface areas (Fig. 9b and c).

c). The total thermal resistances also decrease as the size of the underlying chip increases. For the same chip size, the calculated surface areas and total thermal resistances of the copper spreaders (Fig. 10a) are the highest, followed by those of the composite spreaders, then of the porous graphite spreaders (Fig. 10b and c). The total thermal resistances are those indicated by the last data points at the edge of the spreaders in Fig. 10a–c.

3.4. Total thermal resistance

3.5. Surface areas of spreaders

Fig. 10a–c plot the calculated total thermal resistances (Eq. (6a)) for cooling underlying 10 · 10 mm and 15 · 15 mm chips using copper (DPG = 0), porous graphite (DPG = 1.0) and composite spreaders (0.75 6 DPG P 0.2). These thermal resistances are the sum of the spreading and the boiling resistances (Eq. (6b)). The total thermal resistances at the centerline of the total spreaders are the highest and decrease almost exponentially with distance along the spreader surface. The total thermal resistances with the spreaders cooled with saturation nucleate boiling are always lower than when the spreaders are cooled using subcooled nucleate boiling of FC-72 liquid. Decreasing the thickness of the top porous graphite layer (or increasing the thickness of the copper substrate) decreases the total thermal resistance with the composite spreaders (Fig. 10b and

Fig. 11a and b compare the calculated surface areas of the spreaders, versus the total thermal resistances, for removing the thermal powers dissipated by underlying 10 · 10 mm and 15 · 15 mm chips using copper (DPG = 0), porous graphite (DPG = 1.0) and composite spreaders (0.75 6 DPG P 0.2). The surface areas of the copper spreaders are much larger than those of the porous graphite (DPG = 1.0) and the composite spreaders (0.75 6 DPG P 0.2). The surface areas of the copper spreaders are highest when cooled by 10 K subcooled nucleate boiling, but the total resistances consistently increase with increased liquid subcooling. The effect of the subcooling of FC-72 liquid on the surface areas and total thermal resistances of the porous graphite and composite spreaders is different from that on those of the copper spreaders. Increasing the

Fig. 16. Calculated temperature contours on bottom surfaces of copper spreaders with 15 · 15 mm chips.

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liquid subcooling and reducing the thickness of the top porous graphite layer decreases the total thermal resistances, but increases the surface areas of the composite spreaders (Fig. 11a and b). These figures also show that the differences in the calculated surface areas and the total thermal resistances with porous graphite and composite spreaders, cooled with 20 K and 30 subcooled nucleate boiling, are either small or negligible. 3.6. Chip maximum surface temperature Fig. 12a and b plot the calculated maximum surface temperatures of the underlying chips as functions of the dissipated thermal powers removed from the surface of the copper, porous graphite and composite spreaders. With porous graphite and composite spreaders, the maximum surface temperatures of the chips are lower than with copper spreaders, but both increase with increasing subcooling

of FC-72 liquid at the surface of the spreaders. Increasing the thickness of the copper substrate in the composite spreaders decreases the maximum surface temperature of the underlying chips. For a 10 · 10 mm chip with a composite spreader (DPG = 0.2) cooled with 30 K subcooled FC-72 liquid, the dissipated thermal power by the underlying chip, removed from the spreader surface, is 98.4 W and the chip maximum temperature is 69.5 C. For the same liquid subcooling on a copper spreader, the removed total thermal power dissipation for the same 10 · 10 mm chip is only 83.9 W and the chip maximum temperature (74.6 C) is 5.1 C higher (Fig. 11a). For the large 15 · 15 mm chip with a composite spreader (DPG = 0.2) cooled by 30 K subcooled nucleate boiling, the dissipated thermal power by the underlying chip, removed from the spreader surface, is 160.3 W and the chip maximum temperature is only 69 C (Fig. 12b). With the same cooling conditions, the removed thermal power by a copper sprea-

Fig. 17. Calculated temperature contours on surfaces of composite and porous graphite spreaders on 15 · 15 mm chips.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

der and dissipated from the same 15 · 15 mm chip is 121.8 W and the chip maximum temperature is 73.9 C (Fig. 12b). 3.7. Dissipation thermal power and temperature contours Fig. 13a–c plot the dissipated thermal power by the underlying chips and removed by nucleate boiling from the surfaces of the copper, porous graphite and composite spreaders, with distance along the spreaders surface. The origin of the x-axis coincides with the center of the square surface of the spreaders. The dissipated thermal powers by the underlying chips are removed from less than 50% of the calculated surface area of the spreaders. For example, 80–86% and 76–80% of the total dissipated powers by the underlying 15 · 15 mm and 10 · 10 mm chips are removed from the inner 50% of the surface areas of the copper spreaders (Fig. 14). Fig. 15a and b present the calculated temperature contours on the bottom surface of the composite spreader (DPG = 0.2) cooled with saturation and 30 K subcooled boiling of FC-72 liquid, respectively. Fig. 15c and d presents the calculated temperature contours on the bottom surface of a porous graphite spreader, subject to the same nucleate boiling cooling conditions. All the temperature contours in these figures are for the spreaders with an

1085

underlying 15 · 15 mm chip. The chips are coolest when cooling the surfaces of the spreaders with saturation nucleate boiling of FC-72 liquid. The calculated maximum surface temperatures of, and the temperature differentials across the underling chip are 62.1 to 62.8 C and <5 C, (Fig. 15a and c). The calculated total thermal resistances (Eq. (6a)) of 0.12 and 0.128 C/W for these 15 · 15 mm chips with composite and porous graphite spreaders are the smallest (Fig. 15a and c). On the other hand, the total thermal power dissipated by the chip and removed from surface of these spreaders of 85.6 W and 59.4 W are the lowest. Fig. 16a–c show the calculated temperature contours on the bottom surfaces of the copper spreaders on top of 15 · 15 mm and 10 · 10 mm chips. The surface areas of these spreaders with the large chip (Fig. 16a and b) are only slightly larger than those with a 10 · 10 mm underlying chip (Fig. 16c and d). When the copper spreaders are cooled by saturation nucleate boiling of FC-72 the maximum surface temperatures of the large and small chips (70.6 C) are almost the same (Fig. 16a and c), but 3– 4 C higher than those of the chips with copper spreaders cooled by 30 K subcooled nucleate boiling of FC-72 liquid (Fig. 16b and d). For the same nucleate boiling cooling and dimensions of the underlying chips, with porous graphite or composite spreaders the chip maximum surface

Fig. 18. Calculated temperature contours on surfaces of copper spreaders with 15 · 15 mm chips.

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Fig. 19. Temperature contours at the mid-section of composite and porous graphite spreaders on top of 10 · 10 mm and 15 · 15 mm chips.

temperatures are several degrees lower than those of the same chips but with copper spreaders (Figs. 15 and 16). Fig. 17a–d show the calculated temperature contours on the top surface of the composite (DPG = 0.2) and the porous graphite (DPG = 1.0) spreaders cooled with saturation nucleate boiling (Fig. 17a and c) and 30 K subcooled (Fig. 17b and d) nucleate boiling of FC-72 liquid. The temperature contours in Fig. 17a–d correspond to those in Fig. 15a–d on the bottom surfaces of these spreaders, with 15 · 15 mm chips. The maximum surface temperatures of the spreaders are on average <5.4 C and 2.2 C lower than those of the underlying chips. The calculated maximum surface temperatures of the copper spreaders are on average 5.0 K and 8.5 lower than those of the underlying chips. Fig. 18a–d present the calculated temperature contours on the top surface of the copper spreaders (DPG = 0) cooled with saturation nucleate boiling and 30 K subcooled (Fig. 17b and d) nucleate boiling of FC-72 liquid, with 10 · 10 mm and 15 · 15 mm underlying chips. Fig. 19a and b present the calculated temperature contours at the mid-section of porous graphite spreaders cooled with saturation and 30 K subcooled boiling of FC-72 liquid, and with 15 · 15 mm underlying chip. Those with 10 mm · 10 mm underlying chip are shown in Fig. 19e and f. With a composite spreader cooled with 30 K subcooled nucleate boiling of FC-72, the dissipated thermal power by the underlying 15 · 15 mm chip, removed from the surface of the spreader, is 160.3 W and the total thermal resistance is 0.29 C/W (Fig. 19b), compared to 118.6 W and 0.412 C/W with a porous graphite spreader (Fig. 19d). The corresponding values with 10 · 10 mm underlying chip are 98.4 W and 0.48 C/W. Similar results are shown in Fig. 19c, d, g and h for 15 · 15 mm and 10 · 10 mm chips with porous graphite spreaders cooled

with saturation and 30 K subcooled nucleate boiling of FC-72 liquid. 4. Summary and conclusions This paper investigated the performance of composite spreaders made up of a top layer of porous graphite (0.2 6 DPG 6 0.75) and a copper substrate for achieving better cooling of underlying 10 · 10 mm and 15 · 15 mm computer chips. The calculated performance results of the composite spreaders are compared with those of copper (DPG = 0) and porous graphite (DPG = 1.0) spreaders of the same total thickness, 2.0 mm, at the same cooling conditions on the spreader surface. The top surfaces of the spreaders are cooled with either saturation or 10, 20 K, and 30 K subcooled nucleate boiling of FC-72 dielectric liquid. The 3-D steady state heat conduction equations in the spreader layers are solved using ANSYS, finite element analysis software, assuming uniform heat dissipation by the underlying chips and adiabatic sides and bottom surface of the spreaders. The excellent agreement between the calculated total thermal powers removed from the surface of the spreaders, and those dissipated by the underlying computer chips, confirmed the accuracy of the calculations. These calculations include the surface areas of the spreaders, the total and local surface temperature and the removed thermal power from the surface of the spreaders, along with the spreading, boiling, and total thermal resistances, and the maximum temperature of, and temperature distribution across, the chips and spreader surfaces. The values of these performance parameters are calculated as functions of the chip size, subcooling of the FC-72 liquid, and the thickness of top porous graphite layer (or of the copper substrate) in the composite spreaders.

M.S. El-Genk et al. / Applied Thermal Engineering 27 (2007) 1072–1088

In the present analysis, the local nucleate boiling heat transfer coefficient at the centerline of the spreader surface is assumed equal to that measured at 90% of the Critical Heat Flux (CHF) in recent pool boiling experiments of FC-72 dielectric liquid on porous graphite and on smooth copper. In addition, the nucleate boiling heat transfer coefficient at the edge of the spreader surface is that corresponding to 1.0 K higher surface temperature, than measured at boiling incipience in these experiments. Results indicate that composite spreaders are superior to both copper and porous graphite spreaders, increasing the removed total thermal power dissipated by the underlying chips, at lower maximum chip surface temperature and total thermal resistance. Cooling the spreaders with subcooled nucleate boiling increases the removed total thermal power dissipated by the underlying chips and decreases the calculated surface area of the spreaders, but increases the chips maximum surface temperatures and the total thermal resistance. For 15 · 15 mm and 10 · 10 mm chips the total thermal power dissipation, removed by composite spreaders (DPG = 0.2) cooled by 30 K subcooled nucleate boiling of FC-72 liquid is 160.3 W and 98.4 W, at total thermal resistances of 0.29 and 0.48 C/W. When cooled by saturation nucleate boiling of FC-72 liquid, however, the total thermal power dissipation removed from the surface of the composite spreader is 85.6 W and 53.4 W at total thermal resistances of 0.12 and 0.20 C/W. For the same nucleate boiling cooling condition at the surface of the spreader, the thermal powers dissipated by underlying chips, removed from the surface of a porous graphite spreader (DPG = 1.0), are much lower, and the total thermal resistances are much higher than those with composite spreader. The chip maximum surface temperatures are highest with copper spreaders and lowest with composite spreaders (DPG = 0.2). In addition, the thermal powers from the surface of the composite spreaders are the highest and increase with increased subcooling of the FC-72 dielectric liquid. The chip maximum temperatures decrease very little, but the removed thermal powers from the surface of the spreaders increase significantly with increasing the size of underlying chip from 10 · 10 mm to 15 · 15 mm. With composite spreaders cooled with saturation nucleate boiling of FC-72 liquid, the total thermal powers dissipation by the underlying chips, and removed from the surface of spreaders, are higher than those removed from the surface of copper spreaders. In conclusion, the composite spreaders investigated in this paper are an attractive option for better cooling of high-power computer chips, at relatively lower chip maximum surface temperatures. References [1] ITRS, International Technology Roadmap for Semiconductors, 2004. [2] J.U. Knickerbocker et al., An advanced multichip module (MCM) for high-performance UNIX servers, IBM Journal of Research and Development 46 (6) (2002) 779–804.

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