A Paraetric Study of Microorous Metal Matrix-Phase hange Material oosite Heat Sreaders for Transient Theral Alications Srilakshi Linganeni, Mehdi Asheghi, Kenneth E. Goodson Deartent of Mechanical Engineering, 44 Escondido Mall Stanford University Stanford, A, USA, 9435 Eail: sril@stanford.edu ABSTRAT Metal-PM (Phase hange Material) coosite heat sreaders offer a cobination of high effective theral conductivity and high density heat storage caability that are desirable for transient theral anageent alications, esecially in obile and wearable electronic devices. In this study, we roose fabrication of icroorous etal atrix (MMM)-PM coosite heat sreaders through electrodeosition of etal over a telate of PM icrocasules that result in coosites with etal volue fraction of ~.6. Effective theral conductivity of these coosites equal 74 W/. K and 44 W/. K for coer atrix and aluinu atrix resectively. Order of agnitude analysis for tie resonse and theral energy storage utilization erfored on etal-pm coosites, as a function of etal volue fraction, shows that the otial etal volue fraction range is.-.5 for the best theral erforance of etal-pm coosite heat sreaders. Furtherore, the teerature resonse of the MMM-PM coosite heat sreaders to a heat inut showed that the use of PM within a etal atrix can hold the device skin teerature below the ergonoic liit for long durations of tie without sacrificing the tie resonse. KEY WORDS: oosite heat sreader, transient cooling, icroorous etal atrix, hase change aterial, effective theral conductivity NOMENLATURE k Theral conductivity (W/. K) f Volue fraction c P Secific heat caacity (J/ kg. K) P Voluetric heat caacity (J/ 3. K) ΔH Latent heat of fusion of PM (J/kg) d Length of the heat sreader () b Breadth of the heat sreader () h Height of the heat sreader () t Tie (sec) U Storage caacity utilized (J) MMM Microorous etal atrix MM Microorous coer atrix MAM Microorous aluinu atrix PM Phase change aterial Greek Sybols: ρ Density (kg/ 3 ) α Theral diffusivity ( / s) Subscrits: e l s 1 INTRODUTION Metal Phase change aterial Effective roerty PM in liquid state PM in solid State Electronic ackaging in 3D integrated circuits and ortable electronic devices ose new theral challenges that can be addressed by the develoent of novel aterials [1]. Theral anageent in obile and wearable electronic devices is a two-ronged roble with stringent requireents on both junction teerature (allowed axiu of 85 o to 1 o for device erforance) and device skin teerature (ergonoic liit of 4 o to 45 o deending on the aterial of the enclosure []). The roble has becoe ore intense in the recent years due to the increased functionality and rolonged usage of these devices. Due to the sall for factors in such devices, we are liited to coact theral technologies such as iezoelectric actuators and synthetic jets [, 3] that rovide active cooling in confined saces. However, to ensure low ower budget for theral anageent (for rolonged battery life), effective assive solutions are ost attractive. The use of hase change aterials (PMs) in theral technologies rovide a roising solution to this roble, where the latent heat for hase transition is used for transient theral cooling. PMs rovide both high energy storage density and sall teerature gradients during the release and storage cycles [5]. Of the various PMs, coercial araffin waxes are aong the least exensive aterial candidates, are cheically inert, and undergo negligible subcooling. In the ast decade, several researchers have extensively studied PM-based heat sinks with a wide variety of configurations for theral anageent in electronic devices. Wang et al., showed that the orientation of the device has a liited effect on the theral erforance of PM-based heat sinks [6], which akes the attractive for ortable electronic cooling as
well. However, the low theral conductivity of PMs results in high theral resistance for heat conduction and slow theral resonse of these systes. This severely liits their alications, articularly for theral anageent in obile and wearable electronics where short tie resonse of the theral solution is desirable. To alleviate the roble, etallic fillers, etal atrix structures, and finned tubes are traditionally used to enhance the theral conductivity of the coosite. Vadwala used coer foa (with coer volue fraction of 5%) to enhance the theral conductivity of araffin wax and exerientally deonstrated.5 ties ore PM utilization coared to the sales without the coer foa, while reducing the energy storage caacity by less than 5% [7]. In this work, we roose high theral conductivity coosite heat sreaders with theral energy storage caabilities fabricated by electrodeosition of etal over a telate of sherical icrocasules ade fro PMs for transient assive cooling alications. We call the coosites fabricated in this fashion icroorous etal atrix (MMM)- PM coosites. In addition, we study the effective theral roerties and tie resonse of etal-pm coosite heat sreaders at various etal volue fractions to deterine otial coosition for the coosites and coare the results to the coosition of MMM-PM coosite heat sreaders. STRUTURE OF THE MMM-PM OMPOSITES The MMM-PM coosites roosed in this work can be fabricated through electrodeosition of etal [8] over a telate of sherical icrocasules of PMs. Heat sreaders fabricated using this ethod are free standing with PM sealed within the etal atrix. When electrodeosition is used to grow etal around the PM icrocasule telate, the etal is deosited around each of the icrocasules, resulting in an otial geoetry for heat transfer fro the highly conductive etal to the oorly conductive PM aterial. This is due to the axiized etal-pm surface contact area for a given icrocasule diaeter. The size of the icrocasules can vary fro sub-icron to a few hundred icrons deending on the ethod eloyed to synthesize the [9], [1]. One of the any ethods studied extensively in literature, including dro casting, sin coating, electrostatic deosition, and self-assebly, can be used to for icrocasule telates, where the icrocasules arrange theselves in a hexagonal close acked (HP) structure in every ethod. This results in a acking fraction of ~.74, the highest acking fraction ossible for sherical icrocasules of equal diaeters. Higher acking fractions can be achieved if a variation in article size is resent. The acking fraction is, however, indeendent of the diaeter of the sheres; it is only the noralized diaeter distribution and the effectiveness of the ethod used to reare the icrocasule telate that ultiately affects the acking fraction. When the above-entioned ethod is used for fabrication of the coosites, the volue fraction of PM in the resulting coosite will be equal to the acking fraction of the icrocasules in the telate. Accounting for a sall variation due to the foration of voids within the HP structure of the telate and a size distribution of the icrocasules, the volue fraction of etal and PM will be within a few ercent of.6 and.74, resectively. A scheatic of such a telate with sheres of equal diaeters and the resulting coosite structure can be seen in Figure 1. This structure is created in OMSOL by iicking the stes in the fabrication rocess, by creating a HP telate of sheres, overlaying a etal block on the telate, and finally, triing the edges. This structure is later used to deterine the theral conductivity of MMM-PM coosites in OMSOL. (a) Figure 1. Scheatic of the structure of MMM-PM coosites. (a) PM icrocasule telate with the sheres in HP arrangeent. (b) MMM-PM coosite obtained by overlaying etal over the icrocasule telate and triing the edges. In this study, we consider coer and aluinu for the etal foa and araffin wax P116, used in the literature by several other investigators, for the PM. Relevant theral roerties of these aterials are listed in Table 1. While the elting teerature and latent heat of fusion are obtained fro ref [4], the other roerties of P116 listed in the table are only reresentative values for araffin waxes. Table 1. Theral roerties of coer, aluinu and araffin wax ρ (kg/ 3 ) c (kj/kg.k) k (W/.K) T ( o ) ΔH (kj/kg) oer 8933.39 4 - - Aluinu 7.91 37 - - Paraffin (s) 9.5.1 Wax (l) 8.5.1 47 1 3 EFFETIVE THERMAL PROPERTIES 3.1 Theral conductivity (b) As can be seen fro the structure deicted in Figure 1, the MMM-PM coosite can be classified as one with internal orosity. The etal fors a continuous hase and the PM icrocasules are disersed inside the etal atrix. The Maxwell-Eucken equation (Eqn. 1) can be used to evaluate the effective theral conductivity of such coosites with one hase disersed inside a continuous second hase. k k e k k k k ( k ( k k ) f k ) f...(1)
arson et al., coared the redictions fro the Maxwell-Eucken equation with exeriental results for various coosites and showed that they are in good agreeent for a wide variety of coosites[11]. Figure shows the variation of theral conductivity of both the etal-pm coosites and the etal foa, with the volue fraction of the etal evaluated using the Maxwell-Eucken equation. It can be seen that the theral conductivity of the etal-pm coosite is the sae as the theral conductivity of the bare etal foa, which indicates that the contribution of the PM to the overall theral conductivity of the etal- PM coosite is negligible. This is due to the three orders of agnitude difference between the theral conductivity of the etal and the PM for both coer and aluinu. The sae conclusion can be drawn fro Figure 3, which shows the siulated teerature and heat flux fields in a reeating unit of the MM-PM coosite, obtained by alying a teerature gradient across the geoetry shown and erforing the siulation in OMSOL using the heat transfer odule. As indicated by the heat flux lines, the ath of the heat flow is riarily through the etal foa, and the PM is effectively byassed. This allows us to searate the heat transfer hysics in the MMM and the hase change hysics in the PM at tie scales that are higher than the diffusion tie scale for the icrocasules. For a icrocasule of radius 1 µ, the diffusion tie scale is on the order of.1 sec; this tie scale decreases quadratically with decreasing icrocasule length scale. The short diffusion tiescale of the icrocasules leads to short tie resonse of the heat sreader, which in turn results in sooth charge and discharge characteristics of the heat sreader and can therefore be effectively used for transient cooling of electronic coonents. Effective theral conducivity (W/ K) 5 4 3 1 oer foa oer-pm coosite Aluinu foa Aluinu-PM coosite OMSOL, MMM-PM OMSOL coosites..4.6.8 1 Volue fraction of etal Figure. Variation of theral conductivity of etal-pm coosites with volue fraction of the etal. Solid lines and circular and square arkers are generated by alying the Maxwell-Eucken odel to etal-pm and etal-air resectively. Diaond and triangular arkers enclosed within the dotted line are siulation results for MMM-PM coosites fro OMSOL for coer and aluinu resectively. Figure also shows the theral conductivity of MMM-PM coosites at a etal volue fraction of.6 (enclosed in the dotted ellise), evaluated using OMSOL by alying a heat flux boundary condition to one of the faces of the structure shown in Figure 1b and evaluating the resulting teerature gradient. The siulation redicts an effective theral conductivity of ~74 W/. K for MM-PM coosites and ~ 44 W/. K for MAM-PM coosites, and the results atch well with the theral conductivity evaluated using the Maxwell-Eucken equation. oer PM 3 K 31 K 3 K Figure 3. Teerature and heat flux fields in a reeating unit of the MM-PM coosite. 3. Voluetric heat caacity and theral diffusivity Effective voluetric heat caacity and theral diffusivity are calculated using Eqns. and 3 resectively: Pe f k e e Pe P f...() where the voluetric secific heat, P c, is the P roduct of density and secific heat. The effective theral roerties evaluated in this section are used for all subsequent analyses. 4 STORAGE APAITY AND TIME RESPONSE P...(3) An order of agnitude analysis is erfored on the storage caacity utilization and the tie resonse of the heat sreaders ade fro the coer-pm and aluinu-pm coosites using the effective theral roerties evaluated in the revious section. A heat sreader of diensions 1 c x 5 c x 3 (d x b x h) that is aroriate for a tablet is considered for the urose of this analysis. The size of the icrocasules is assued to be sall enough such that the theral roerties of the heat sreader can be considered to be hoogeneous, and the diffusion tie scale of the icrocasules is sall coared to the tie scales of interest in the analysis. Microcasules of radius ~1 µ sufficiently satisfy these conditions. The axiu energy storage caacity during the PM elting rocess is the roduct of the voluetric latent heat of
fusion of the PM, the volue of the heat sreader, and the volue fraction of the PM; it does not deend on the theral roerties of the etal atrix. As deicted by the dotted red and blue lines in Figure 4, the axiu energy storage caacity and the theral conductivity of the heat sreader follow oosite trends. Therefore, the relative volue fraction of etal-pm in the coosites ust be chosen aroriately for otial tie resonse and theral storage caabilities. The storage caacity utilized at a given tie deends on the volue through which the heat radiating fro the center of the heat sreader diffuses and is calculated using Eqn. 4, where the thickness and width of the heat sreader reach the diffusion length scale liits first, after which the heat continues to sread lengthwise. Storage caacity utilized (kj) Storage caacity utilized (kj) 3 1 Peak at f =.36 3 in 1 in 3 s in 1 s oer..4.6.8 1 3 1 U H Peak at f =.354 ( bh e, t) f, l l Volue fraction of etal (a) 3 in 1 in 3 s in 1 s Aluinu..4.6.8 1 Volue fraction of etal (b)...(4) 4 3 1 1 Figure 4. Maxiu available storage caacity (red dotted line), storage caacity utilization with resect to tie (black solid lines), and effective theral conductivity (blue dotted line) of (a) coer-pm and (b) aluinu-pm coosites. Storage caacity utilization is calculated based on diffusion length scale analysis using Eqn. 4, and effective theral conductivity is calculated using the Maxwell-Eucken equation (Eqn. 1) Effective theral conducivity (W/ K) Effective theral conducivity (W/ K) Figure 4 shows the storage caacity utilized as a function of the etal volue fraction for both coer and aluinu as the elting rocess coences. The oints of intersection of the storage caacity utilization curves with the axiu available storage caacity line (red dotted line) indicate the ties required to fully utilize the storage caacity for a given etal volue fraction. Although there is a axiu for the caacity utilization for any given tie, at a etal volue fraction of.33 and.35, resectively, for coer and aluinu, the etal volue fraction range of ~.-.5 can be considered as the otial range for theral storage caacity utilization. However, within this range, lower etal volue fractions are referable to axiize total available storage caacity. Figure 4 indicates that the available storage caacity is reached within a few inutes in the otial etal volue fraction range. As exected, the tie resonse of the coer- PM heat sreader is faster than that of aluinu-pm heat sreader. Figure 5 shows the ass of the etal-coosite heat sreader and the axiu available storage caacity for the heat sreader diensions under consideration. Based on the data in Figures 4 and 5, we conclude that while coer-pm coosites have better tie resonse, aluinu-pm coosites are lighter for the sae total storage caacity. Thus, the etal for atrix in these coosite heat sreaders ust be chosen based on the tie resonse and weight requireents of the secific alication. Mass of heat sreader (g) 15 1 5 For heat sreader of diensions 1 c x 5 c x 3 Aluinu oer..4.6.8 1 Volue fraction of etal Figure 5. Variation of axiu available storage caacity (blue line) and ass (black lines) of the heat sreader with etal volue fraction. A lued caacitance assution is ade to evaluate the teerature resonses of a solid coer heat sreader and a MM-PM coosite heat sreader to a reresentative heat inut fro a tablet shown in Figure 6a, with the results lotted in Figure 6b. Predictions based on this assution are valid for ties greater than the diffusion tie scales of the resective heat sreaders (t > 5 sec for the coer heat sreader and t > in for the MM-PM heat sreader), and the condition is et adequately for the 5 in tie scale considered. Heat dissiation fro the heat sreader to its surroundings is neglected in this analysis. As seen in the Figure 6, use of the MMM-PM coosite heat 3 1 Maxiu storage caacity (kj)
sreader liits the heat sreader teerature, and as a result, also liits the device skin teerature under the ergonoic liit for longer durations when coared to a heat sreader without hase change aterial. Additionally, the teerature of the MMM-PM coosite heat sreader after 5 in is 3 o below the teerature of the coer heat sreader, which is substantial. Power dissiated (W) Teerature ( o ) 5 5 1 15 Tie (in) (a) 1 9 8 7 6 5 4 3 5 1 15 Tie (in) (b) Figure 6. Teerature resonse of MM-PM heat sreader to a heat inut. (a) Reresentative ower rofile of an electronic device while erforing various actions and resulting heat generated during the rolonged usage. (b) Teerature resonse of a coer heat sreader and MM-PM heat sreader of diensions 1 c x 5 c x 3 to the heat inut in Figure 6a, calculated based on the lued caacitance odel. 5 ONLUSIONS oer heat sreader (f = 1) MMM-PM heat sreader (f =.6) A icroorous etal atrix (MMM)-PM coosite heat sreader fabricated through electrodeosition of etal over a telate of PM icrocasules is roosed for transient cooling alications. An order of agnitude analysis is erfored to understand the variation of tie resonse and storage caacity utilization of etal-pm coosite heat sreaders with resect to etal volue fraction, and it is found that the MMM-PM coosition (f =.6) falls in 4 Total heat generated (kj) the otial etal volue fraction range of.-.5. The MMM-PM coosite heat sreader teerature resonse to a heat inut, redicted based on a lued caacitance odel, showed that it is very effective at aintaining the device skin teerature under the ergonoic liit during rolonged device usage. The theral erforance of MMM-PM coosite heat sreaders can be further iroved through otiization of design araeters, including aterial choice and heat sreader geoetry. AKNOWLEDGEMENTS The authors gratefully acknowledge the financial suort of Seiconductor Research ororation (SR) through task 5.1. REFERENES [1] S. Linganeni, A. M. Marconnet, and K. E. Goodson, 3D Packaging Materials based on Grahite Nanolatelet and Aluinu Nitride Nanocoosites, Int. Mech. Eng. ongr. Exo., Noveber, San Diego, alifornia, USA, 13. [] M. K. Berhe, Ergonoic Teerature Liits for Handheld Electronic Devices, in ASME 7 InterPAK onference, Volue, 7,. 141 147. [3] I. Sauciuc, G. hrysler, R. Paydar, M. Walker, M. Luke, M. Mochizuki, and T. Eiji, Key challenges for the iezo technology with alications to low for factor theral solutions, Ther. Theroechanical Proc. 1th Intersoc. onf. Pheno. Electron. Syst. 6. ITHERM 6.,. 781 785, 6. [4] R. Mahalinga, Modeling of Synthetic Jet Ejectors for Electronics ooling, Twenty-Third Annu. IEEE Seicond. Ther. Meas. Manag. Sy.,. 196 199, 7. [5] M. M. Farid, A. M. Khudhair, S. A. K. Razack, and S. Al-Hallaj, A review on hase change energy storage: aterials and alications, Energy onvers. Manag., vol. 45, no. 9,. 1597 1615, 4. [6] X.-Q. Wang, A. S. Mujudar, and. Ya, Effect of orientation for hase change aterial (PM)-based heat sinks for transient theral anageent of electric coonents, Int. oun. Heat Mass Transf., vol. 34, no. 7,. 81 88, 7. [7] P. H. Vadwala, Theral Energy Storage in oer Foas filled with Paraffin Wax, Thesis, University of Toronto, anada, 11. [8] T. S. Eagleton and P.. Searson, Electrocheical Synthesis of 3D Ordered Ferroagnetic Nickel
Relicas Using Self-Assebled olloidal rystal Telates, AS heistry of Materials, vol. 16,. 57-53, 4. [9] G. Fang, Z. hen, and H. Li, Synthesis and roerties of icroencasulated araffin coosites with SiO shell as theral energy storage aterials, he. Eng. J., vol. 163, no. 1,. 154 159, 1. [1] L. Bayés-García, L. Ventolà, R. ordobilla, R. Benages, T. alvet, and M. a. uevas-diarte, Phase hange Materials (PM) icrocasules with different shell coositions: Prearation, characterization and theral stability, Sol. Energy Mater. Sol. ells, vol. 94, no. 7,. 135 14, 1. [11] J. K. arson, S. J. Lovatt, D. J. Tanner, and A.. leland, Theral conductivity bounds for isotroic, orous aterials, Int. J. Heat Mass Transf., vol. 48, no. 11,. 15 158, 5.