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ScienceDirect Energy Procedia 110 (2017) 256 – 261

1st International Conference on Energy and Power, ICEP2016, 14-16 December 2016, RMIT University, Melbourne, Australia

An investigation into the effective thermal conductivity of vapour chamber heat spreaders Jason Velardoa*, Randeep Singhb, Ashwin Datea, Abhijit Datea a

School of Engineering, RMIT University, Bundoora, Victoria, 3083, Australia b Fujikura Ltd., Japan

Abstract Vapour chambers are a promising solution to thermal spreading issues associated with high heat flux devices. This paper presents a numerical investigation into vapour chamber heat spreaders using the concept of effective thermal conductivity. A 2D axisymmetric model was built and thermal performance was analysed through variation in effective thermal conductivity. The vapour chamber had more even temperature distributions and lower spreading resistances than an equivalent copper spreader. At a larger radius the superiority over copper was less distinct as only a 7% reduction in spreading resistance was observed compared to 20% reduction at a smaller radius. The effective thermal conductivity was identified as the limiting factor for this case and thus further advances are required to improve the spreading performance of vapour chambers. ©©2017 by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license 2017Published The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 1st International Conference on Energy and Power. Peer-review under responsibility of the organizing committee of the 1st International Conference on Energy and Power. Keywords: vapour chamber; heat spreader; high heat flux; effective thermal conductivity

1. Introduction Two phase heat transfer devices have been used in the past to cope with demand for more effective heat transfer from high flux heat sources. Such devices include heat pipes and more recently vapour chambers (also referred to as a flat plate heat pipe). The vapour chamber acts as a transformer which spreads heat to a larger sink area. It does this

* Corresponding author. Tel.: +6-141-315-8795. E-mail address: [email protected]

1876-6102 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 1st International Conference on Energy and Power. doi:10.1016/j.egypro.2017.03.136

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Jason Velardo et al. / Energy Procedia 110 (2017) 256 – 261

more efficiently than an equivalent copper spreader thus has been the focus of much research recently. Nomenclature h H k keff q" Q r R Rsp T z

heat transfer coefficient, W/m2.K thickness of spreader, cm thermal conductivity, W/m.K effective thermal conductivity, W/m.K heat flux, W/cm2 heat, W radial direction outer radius of spreader, cm spreading thermal resistance, oC/W temperature, oC height direction

The operating principle of phase change heat transfer devices is shown schematically for a vapour chamber in Fig. 1. Heat is absorbed in the evaporator which causes the working fluid to vaporise and travel to the condenser where it condenses into a liquid, releasing the absorbed heat. The working fluid is commonly returned to the evaporator via a wick structure. The main difference between a heat pipe and vapour chamber is that for a heat pipe, heat is transferred axially from the evaporator, whereas for a vapour chamber, heat is transferred mostly radially from the evaporator as seen in Fig. 1. This is owing to the design of the vapour chamber, which is often two parallel plates with a heat source located centrally on one plate. Hence they are often used for heat spreading. Heat Sink/Condenser

Wick

Container

Heat Source/Evaporator

Liquid

Vapour

Fig. 1. Working principle of vapour chamber. A high heat flux input can be spread to a lower heat flux output with vapour chambers.

Vapour chambers have recently been subject to much research, with particular focus on experimental work [1-3]. They have also been investigated numerically through computational fluid dynamics (CFD) models [4-6]. Such CFD models have taken into account fluid modelling of the internal processes of the vapour chamber. An alternative approach is one where an effective thermal conductivity of the vapour chamber is used. Chen et al. explored this is their work [7]. The effective thermal conductivity was based on previous experimental work and analytical relations developed therein [8, 9]. They suggested the effective thermal conductivity of a vapour chamber was at least 435.6 W/m.K when an isotropic approach was considered and this was strongly dependent on heat source size. An effective thermal conductivity of 557.9 W/m.K was reported when a larger heat source was used. The authors claimed an orthotropic method was better which resulted in effective radial thermal conductivity at least 23.5 times greater than effective axial thermal conductivity. Wang & Wang [10] proposed an empirical formula to determine the effective thermal conductivity. Buckingham Π theorem was used to correlate variables and experimental data to determine constants. The authors suggested that the effective axial thermal conductivity was much smaller than in the radial direction. An isotropic value as high as 910 W/m.K was reported. This was again dependent on the size of the vapour chamber. Other work has aimed at determining the effective thermal conductivity of the vapour space inside the vapour

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chamber, rather than considering the entire unit a bulk material. The majority of this research has focused on heat pipes where the vapour flows inside a circular cross section, unlike the case in a vapour chamber. Cao and Gao suggested the effective thermal conductivity of vapour can be 100 times higher than that of copper based on experimental results [11]. Prasher combined analytical relations with experimental data and found the effective vapour thermal conductivity to be 267,154 W/m.K [12]. Borgmeyer and Ma suggested that effective thermal conductivity of 6000 W/m.K was attainable with heat pipes [9]. In this work a numerical investigation into the influence of effective thermal conductivity on vapour chamber heat spreaders will be undertaken and comparisons will be made to equivalent copper heat spreaders. This is expected to be useful for future design and thermal analysis of vapour chamber heat spreaders. 2. Numerical method and procedure A numerical model was developed to solve the steady 2D axisymmetric governing heat conduction equation without heat generation, shown with Equation 1:

1 w § wT · w § wT · ¸ ¨ kr ¸ ¨ k r wr © wr ¹ wz © wz ¹

0

(1)

Finite difference modelling was utilised with second order approximations for each of the nodes. The thermal conductivity, k, was constant in the above equation, however varied between simulations as explored in Table 1. The boundary conditions and mathematical descriptions of these are shown in Fig. 2. wT k

wz

h(TH Tf )

ൌ

z H

Convection

ൌ

Adiabatic

Symmetry

k

wT wr

k

0 r 0

ͲǡͲ Heat Flux

wT k wz

ൌ

q" z 0

0 r R

ൌ

Adiabatic

wT k wz

wT wr

0 z 0

Fig. 2. The numerical model with boundary conditions.

Heat flux was applied through a small section on the bottom surface (z=0) of the spreader. The radius of the heat source, rhs, was equal to 1 cm. The input flux, q”, varied from 10, 20 and 30 W/cm2. The remainder of the bottom surface was adiabatic. The radius of the spreader, R, varied from 4 to 8 cm. The surface on the outer radius (r=R) was adiabatic and all heat left the model through the top convective surface (z=H). For these models it was assumed that forced convection was present, thus the external heat transfer coefficient, h, was set to 200 W/m2.K. The ambient temperature was set to 20oC. The centre of the model (r=0) was the line of symmetry. The thermal conductivity, k, for the copper models were 400 W/m.K. For the vapour chamber models this was set to the effective thermal conductivity, keff. From the previous literature review the following table is presented. Table 1. The effective thermal conductivities reported in the literature. Effective Thermal Conductivity, keff [W/m.K]

Note

Bulk

Treating the entire vapour chamber as one medium.

435.6 - 557.9

For vapour chamber. Lower value corresponds to small area heat source and larger value to large area heat source.

Reference

[7]

259


350 - 910

For vapour chamber. Lower value corresponds to large area heat source and larger value to small area heat source.

[10]

6000

For a heat pipe

[9]

Vapour Space

Treating the vapour space as a different medium.

267,154

For a flat plate heat pipe (heat source not centrally located)

[12]

40,000

For a heat pipe

[11]

According to the data from Chen et al. [7] presented in Table 1, the effective thermal conductivity was dependent on the ratio of heat source size to vapour chamber size. For the vapour chambers simulated here, effective thermal conductivity of 490 and 430 W/m.K was chosen for the 4 and 8 cm radius spreader, respectively. This was consistent in magnitude with the data from Wang & Wang [10]. A theoretical check on this is provided in Appendix A. Using effective thermal conductivity means that only Equation 1 was solved with given boundary conditions. The equations of continuity and momentum are not solved thus this is significantly less demanding computationally. 3. Results and discussion The results from the model are shown in the following figures. The temperature distributions and trends observed agree well with theoretical results and experimental data [5, 6, 13] providing validation of the models accuracy. The temperature distribution on the top surface (z=H) of the model has been plotted for r=4 cm in Fig. 3.

T(z=H) for q"=20 W/cm2


94

57

Copper 93

Vapour Chamber

56

55

54

Temperature, T [oC]

Temperature, T [o C]

Copper

Vapour Chamber

92 91 90 89 88 87

53 0

1

2 3 Radial position, r [cm]

4

0

1


4

Fig. 3. Surface temperature distributions for the 4 cm radius heat spreader (copper and vapour chamber).

There was a more even temperature distribution on the surface on the vapour chamber due to its higher effective thermal conductivity. As a result, its spreading resistance (Equation 2) was found to be 20% lower than the equivalent copper spreader.

R sp

Ths Tts Q

(2)

Where Rsp is the spreading resistance [oC/W], Ths is the average temperature [oC] of the heat source (z=0), Tts is the average temperature [oC] of the top surface (z=H) and Q is the heat transfer rate [W]. The spreading thermal resistance for each spreader has been summarised in Table 2. Table 2. Calculated spreading resistance. Copper

o

Rsp [ C/W]

Vapour Chamber

r = 4 cm

r = 8 cm

r = 4 cm

r = 8 cm

0.0626

0.0988

0.0511

0.0920

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From Table 2 the spreading resistance is a function of both material and heat spreader radius. This has also been documented in the literature [13]. For the larger radius heat spreader (r=8 cm) the improvement in spreading resistance by using a vapour chamber is only 7% compared to 20% for the small radius heat spreader. This suggested that the radius of the heat spreader was the limiting factor for this scenario. This was further explored by considering two heat spreaders of radius 8 cm; one with unchanged keff of 430 W/m.K and the second with keff of 1000 W/m.K (see Appendix A). The temperature distributions are shown for these cases in Fig. 4.


T(z=H) for q"=20 W/cm2 45


430 W/m.K

43 42 41 40 39 38


1000 W/m.K

44

37 36

0

2


8

57 56 55 54 53 52 51 50 49 48 47 46 45 44

1000 W/m.K 430 W/m.K

0

2


8

Fig. 4. Surface temperature distributions for the 8 cm radius vapour chamber heat spreader with keff = 430 and 1000 W/m.K.

It was observed in Fig. 4 that increasing the effective thermal conductivity from 430 to 1000 W/m.K had a profound effect on the temperature distribution on the top surface of the spreader. The central temperature (r=0) dropped by 4oC at q”=20 W/cm2 and 6oC at q”=30 W/cm2. Further the spreading resistance dropped from 0.0920 oC/W to 0.0399 o C/W as reported in Table 3. This suggested that to fully benefit from larger radius heat spreaders, higher conductivity materials needed to be used. That is, using a vapour chamber may not have as many thermal benefits unless its effective thermal conductivity is sufficiently greater than copper. As has been mentioned in this work, effective thermal conductivities for vapour chambers tend to be larger than copper, however as there is only little literature on this, and for only limited cases, this should be explored more in the future. Table 3. The spreading resistance of vapour chambers (r=8cm). Vapour Chamber

keff = 430 W/m.K

keff = 1000 W/m.K

Rsp [oC/W]

0.0920

0.0399

Thus increasing effective thermal conductivity is paramount to reducing spreading resistance of vapour chambers, particularly at large spreader sizes. Such improvements may be found in using wicks with larger effective thermal conductivity, enhancing the evaporation and condensation processes, and reduced vapour pressure losses. 4. Conclusion A numerical investigation into thermal spreading of vapour chambers was carried out via a 2D axisymmetric finite difference model with effective thermal conductivity. A 4 cm radius vapour chamber was found to have 20% lower spreading resistance compared to copper. However when the radius was increased to 8 cm, the improvement of the vapour chamber was only 7%. This was linked to the geometric constraints of the spreader and the chosen value for effective thermal conductivity. Using larger conductivity which more closely aligned with theory and experimental data for heat pipes saw a significant improvement in the performance of the large radius vapour chamber. This suggested that further work is required to explore the effective thermal conductivity relationship and to improve it for vapour chambers so that spreading performance can be maximized.

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Appendix A. Theoretical check of effective thermal conductivity of vapour chambers A check has been undertaken on the reported values for effective thermal conductivity of vapour chambers in the literature. It was assumed that a 6 mm thick vapour chamber was a sandwich structure composed of copper walls and effective vapour (Fig. 5) then its effective thermal conductivity was found assuming series heat conduction. kvap

Q

kcu Q

x3 x2 x1

Fig. 5. The schematic for series heat conduction through a sandwich structure of copper and effective vapour.

If the thicknesses x1, x2 and x3 are assumed to be equal to 1, 4 and 1 mm, respectively and the thermal conductivity of the copper (kcu) and effective vapour (kvap) are assumed to be 400 and 40,000 W/m.K [11], respectively, the following equation can be used to determine the effective thermal conductivity of this combination.

k eff

x1 x 2 x3 x x1 x 2 3 k Cu k vap kCu

(3)

Substituting in known parameters resulted in effective thermal conductivity of 1176 W/m.K which was in the same order of magnitude as observed from experimental results. Further, if 267,154 W/m.K [12] was used for vapour thermal conductivity, then the resulting value for effective thermal conductivity only increased to 1196 W/m.K which suggested that copper and geometrical constraints were the limiting factors. References [1] Boukhanouf, R., et al., Experimental investigation of a flat plate heat pipe performance using IR thermal imaging camera. Applied Thermal Engineering, 2006. 26(17–18): p. 2148-2156. [2] Naphon, P., S. Wiriyasart, and S. Wongwises, Thermal cooling enhancement techniques for electronic components. International Communications in Heat and Mass Transfer, 2015. 61(0): p. 140-145. [3] Tsai, M.-C., S.-W. Kang, and K. Vieira de Paiva, Experimental studies of thermal resistance in a vapor chamber heat spreader. Applied Thermal Engineering, 2013. 56(1–2): p. 38-44. [4] Koito, Y., et al., Numerical analysis and experimental verification on thermal fluid phenomena in a vapor chamber. Applied Thermal Engineering, 2006. 26(14–15): p. 1669-1676. [5] Koito, Y., et al., Fundamental Experiments and Numerical Analyses on Heat Transfer Characteristics of a Vapor Chamber (Effect of Heat Source Size). JSME International Journal Series B Fluids and Thermal Engineering, 2006. 49(4): p. 1233-1240. [6] Carbajal, G., et al., Thermal response of a flat heat pipe sandwich structure to a localized heat flux. International Journal of Heat and Mass Transfer, 2006. 49(21): p. 4070-4081. [7] Chen, Y.-S., et al., Numerical simulation of a heat sink embedded with a vapor chamber and calculation of effective thermal conductivity of a vapor chamber. Applied Thermal Engineering, 2009. 29(13): p. 2655-2664. [8] Chen, Y.-S., et al., Investigations of the Thermal Spreading Effects of Rectangular Conduction Plates and Vapor Chamber. Journal of Electronic Packaging, 2006. 129(3): p. 348-355. [9] Borgmeyer, B.V. and H.B. Ma, Heat-spreading analysis of a heat sink base embedded with a heat pipe. Frontiers of Energy and Power Engineering in China, 2010. 4(2): p. 143-148. [10] Wang, J.C. and R.T. Wang, A NOVEL FORMULA FOR EFFECTIVE THERMAL CONDUCTIVITY OF VAPOR CHAMBER. Experimental Techniques, 2011. 35(5): p. 35-40. [11] Cao, Y., et al. Experiments and analyses of flat miniature heat pipes. in Energy Conversion Engineering Conference, 1996. IECEC 96., Proceedings of the 31st Intersociety. 1996. [12] Prasher, R.S., A Simplified Conduction Based Modeling Scheme for Design Sensitivity Study of Thermal Solution Utilizing Heat Pipe and Vapor Chamber Technology. Journal of Electronic Packaging, 2003. 125(3): p. 378-385. [13] Song, S., V. Au, and K.P. Moran. Constriction/spreading resistance model for electronics packaging. in Proceedings of the 4th ASME/JSME thermal engineering joint conference. 1995.