Natural Convection Heat Transfer Effects with Micro Finned Structures

Transcription

1 Natual Convetion Heat Tansfe Effets with Mio Finned Stutues Saad MAHMOUD, Raya AL-DADAH*, David ASPINWALL, Leung SOO * Coesponding autho: Tel.: ++44(0) ; Fax: ++44(0) ; .k.aldadah@bham.a.uk Shool of Mehanial Engineeing, Univesity of Bimingham, Bimingham, B15 TT, UK Abstat Mio-sale natual onvetion plays an impotant ole in heat emoval fom mioeletoni omponents and Mio-Eleto-Mehanial Systems (MEMS) devies. Natual onvetion of maofin aays has been extensively studied by many eseahes ove the past seveal deades; howeve analysis of fee onvetion aound miofin aays is less well eseahed. The objetive of this wok was to expeimentally investigate the effets of mio fin height and spaing fo a hoizontally mounted heat sink on heat tansfe oeffiient when opeating unde steady state natual onvetion onditions. An aay of mio finned oppe heat sinks was fabiated using mio-eleto dishage wie mahining (µ-edwm) with fin height anging fom 0.5 to 1.0mm and fin spaing fom 0.5 to 1.0mm espetively. Results showed that values of the onvetive heat tansfe oeffiient ineased with ineased fin spaing and deeased as fin height ineased. Keywods: Mio Fins, Natual Convetion, Mio Heat Sinks, Miomahining Nomenlatue: A i : Radiation heat tansfe aea (m ) F i-k: View fato fo the fin vaious sufaes H: Fin height (mm) h : Convetive heat tansfe oeffiient (Wm - K -1 ) I: Eleti uent (Amps) k: Themal ondutivity (Wm -1 K -1 ) L: Heat sink length (mm) Nu: Nusselt numbe Q : Convetion heat tansfe ate (W) Q input : Input heat tansfe ate (W) Q losses : Heat tansfe ate loss (W) Q : Radiative heat tansfe ate (W) Ra: Rayleigh numbe : Chaateisti length fo vetially aligned finned heat sinks (m) S: Fin Spaing (mm) t: Fin thikness (mm) t b : Fin base thikness (mm) T w : Sufae tempeatue (ºC) T a : Ambient ai tempeatue (ºC) U : Unetainity V: Eleti voltage (Volts) W: Heat sink width (mm) Geek Symbols α: Themal diffusivity (m s -1 ) β: Themal expansion oeffiient (K -1 ) ε: Emmissivity of oppe ν: Kinemati visosity (m s -1 ) σ: Stefan-Boltzmann (Wm - K -4 ) 1. Intodution With the limitations of spae and powe, mio sale natual onvetion plays an impotant ole in heat emoval mehanisms in many engineeing appliations e.g. ooling of mioeletoni omponents, mio stutued devies and Mio-Eleto-Mehanial-System (MEMS) devies based on fee onvetion suh as mio mahined onvetive aeleometes [1-4]. Natual onvetion of maofin aays has been extensively studied by many eseahes ove eent deades [5-9], howeve analysis of fee onvetion aound miofin aays has not eeived the neessay attention in line with eent advanements in mio engineeing

2 appliations [1, 9]. The lage sufae to volume atios fo miostutues and miodevies has meant that paametes elating to sufae effets have a geate impat on miosale flow and heat tansfe mehanisms. Consequently, visous foes play a moe dominant ole than inetia foes in miosale natual onvetion heat tansfe [3]. Also, ompessed bounday layes at vey small sale play a ole in impoving onvetive heat tansfe oeffiient. Hee, expeimental esults have shown that the values of natual onvetion heat tansfe oeffiient fo miofabiated heated stutues ae geneally lage than those at maosale [1, 10]. The objetives of this wok wee to expeimentally investigate the effets of mio fin height and spaing on the natual onvetion heat tansfe oeffiient. minimise heat leakages fom all sides exept the top finned sufae, the test piee and the mat heate wee plaed in a 5mm deep squae poket milled on the top fae of 100x100x4mm fibeglass (GRP) blok with themal ondutivity of 0.04Wm -1 K -1. The test piee and the fibeglass blok wee housed in a 00x30x100mm styopo blok with themal ondutivity of 0.03Wm -1 K -1. Tempeatues wee measued using two T type themoouples plaed in two holes 1mm diamete mahined at opposite ones at the base of eah test piee. Figue shows a geneal shemati fo the expeimental set-up.. Expeimental Setup Mio-eleto dishage wie mahining (µ- EDWM) poess employing wies < 100µm diamete was used to fabiate an aay of 1 oppe test piees with diffeent fin geometies. Figue 1 shows a shemati fo a typial test piee (heat sink) aangement. Table 1 shows geomety vaiations fo the 1 mahined oppe test piees with fin height (H) anging fom 0.5mm to 1mm, and fin spaing (S) anging fom 0.5mm to 1mm espetively. Fin thikness (t) and base thikness ( t b ) wee kept onstant at 1.0mm and 5mm espetively and all test piees had a squae base aea with L =W =31.75mm. Dimensions of test piees wee measued using Wild M3Z miosope with X, Y digital miomete with 1µm esolution. The measued values deviate fom the nominal values listed in table 1 by maximum of ±4% in the fin spaing and ±3% in the fin height. Test piees wee heated fom the base using an eletial mat heate of simila sufae aea apable of supplying up to 10W. The powe input to the heate was ontolled using a vaiable output powe supply devie. In ode to Figue 1: Heat sink geomety Test piee No Fin height (H) Fin spaing (S) Test piee No Fin height (H) Fin spaing (S) Test piee No Fin height (H) Fin spaing (S) Table 1: Fin geomety vaiation, all dimensions ae in mm

3 In this set up, the heat input to the test piee was dissipated to the ambient suoundings though adiation and natual onvetion modes of heat tansfe in addition to heat losses fom the bak of the test piee and the sides though the GRP and the styopo. Theefoe, the natually onveted heat an be alulated fom: Q = Q Q Q (1) input losses Figue : Shemati of the expeimental set-up (outesy of Y. Li) 3. Data Analysis All test piees shown in Table 1 wee evaluated togethe with a 31.75x31.75x5mm flat oppe plate test piee used fo benhmaking. Powe input anged fom 0. to 1.6W and tempeatues wee measued at steady state onditions. Steady state onditions wee typially eahed at aound 60 minutes fom initiating a powe input. Figue 3 shows the two themoouple tansient and steady state tempeatue eadings fo test piee with H=0.5mm and S=0.75mm as powe input ineased, togethe with ambient tempeatue. The unetainty in the themoouples eadings is ±0.3ºC based on manufatue data. Figue 3: Themoouples tempeatues (test piee H=0.5mm and S=0.75mm) vesus powe input Q is the adiated heat tansfe alulated using: 4 4 Q = εσ Ai Fi k ( Tw Ta ) () whee ε is the emmissivity of ommeially available oppe taken fom Suyanaayana [11] as 0.15, σ is the Stefan-Boltzmann onstant fo adiation heat tansfe. A i is aea of the elevant fin sufae e.g. top, side, fae and base. F i-k ae the view fatos fo the vaious fin sufaes and wee alulated using methodology pesented by Kulkani and Das [1]. The adiation heat tansfe ate was found to ange fom 9 to 13% of the total heat input. T w is the sufae tempeatue as obtained by aveaging the two themoouples eadings. T a is the ambient ai tempeatue. The main unetainty in evaluating the adiation heat tansfe omes fom the value of the oppe emissivity and is estimated to be ±6% based on published data. The heat tansfe losses though the GRP and the styopo wee evaluated as a funtion of the sufae tempeatues suounding the test piee. These losses wee found to be less than ±6% of the heat input with unetainty value anging fom ±0.4% at high tempeatue diffeene to ±.1% at low values. The powe input Q input was measued using an eletoni wattmete model EW604. The eadings of the wattmete wee ompaed to powe alulated fom supplied uent and voltage measuements. The uent and voltage wee measued at immediate input onnetions to the heate to eliminate losses in the leads of powe supply. An aveage deviation of ±% was measued between wattmete eadings and the powe alulated by:

4 Q input = V * I (3) The unetainty of measuing the uent is ± (0.3 peent of the eading plus 0.05 peent of the full sale) as stated by the manufatue data sheet. The voltmete is a lamp mete with unetainty of ±% of the eading. This lead to an unetainty of ±.0% in measuing the powe input diet to the heate. The oveall unetainty in Q was evaluated fom the unetainties in Q input, Q and Q losses as disusses above. This was found to be a maximum of ±6.7%. The onvetive heat tansfe oeffiient was alulated by: Q h = (4) As ( Tw Ta ) whee A s is the total sufae aea of the finned stutue. The unetainty in the heat tansfe oeffiient was alulated using equation 5, taking into aount the unetainty in the vaious tems used in equation 4 with values listed in table. U h h = ± U Q Q U + A As s U Tw + Tw T Tem Unetainty Q ±6.7% A s ±5% T w 0.3K T a 0.3K Table : Measuements unetainty a U T a + Tw Ta (5) The unetainty of the onvetive heat tansfe oeffiient is alulated to be a maximum of ±8.6% at the minimum tempeatue diffeene used. 4. Results and Disussion In ode to validate the esults fom the expeimental poedue, a flat plate was tested and its esults wee ompaed to well established oelations. Figue 4 depits the Nusselt numbe vesus Rayleigh numbe fo the hoizontal flat plate. The esults ae ontasted with oelations eommended by Matoell et al. [13], Lewandowski et al. [14] and Fujii and Imua [15] as doumented in geneal heat tansfe text books e.g. [16]. It an be seen that the flat plate esults agee well with the oelation of Fujii and Imua [15]. The oelation eommended by Matoell et al. [13] unde-pedited the expeimental esults while the oelation eommended by Lewandowski et al. [14] ove-pedited the expeimental esults. Hee it is woth noting that both the Nusselt and Rayleigh numbes wee alulated using the width of the heat tansfe sufae as the haateisti length. It is lea fom the above that the expeimental tehnique employed was valid. Figue 5 shows the vaiation of onvetive heat tansfe oeffiient vesus sufae to ai tempeatue diffeenes fo the test piees with S=0.5mm and the flat plate. It an be seen that the flat plate has the highest heat tansfe oeffiient. This highe heat tansfe oeffiient of the flat plate ompaed to the finned sufaes is onsistent with the findings of Kim et al [9]. Figue 6 shows the vaiation of heat tansfe oeffiient with fin height fo fin spaing of 0.5mm, 0.75mm and 1mm. It an be seen that as the fin height deeases, the heat tansfe oeffiient ineases. This ould be explained as follows; as the fin height ineases the thikness of the bounday laye ineases to be highe than the spaing between the fins. Hene the tempeatue diffeene available fo diving onvetion heat tansfe will be edued. The figue also shows that the heat tansfe oeffiient ineases with ineasing the fin spaing.

5 Figue 4: Nusselt numbe vesus Rayleigh numbe fo the hoizontal flat plate. Figue 5: Compaison of flat plate heat tansfe oeffiient with finned sufaes. Figue 7 ompaes the diffeene in heat tansfe oeffiient fo fin heights of 0.5mm and 1.0mm with heat input at the diffeent fin spaings used. It an be seen that initially the diffeene in oeffiient ineases with ineasing heat input and then flattens out. Also the diffeene in heat tansfe oeffiient ineases with ineasing fin spaing. Kim et al. [9] poposed a oelation fo heat tansfe pefomane of mio finned sufaes in the fom: Nu = 1.18 Ra (6) H L Figue 6: Effet of fin height on the heat tansfe oeffiient. 3 h g ( - T ) whee β T a Nu, Ra w = = k να and =HS/(H+S) with H being the fin height and S being the fin spaing. Ai popeties used in the alulations of both Ra and Nu wee obtained at the film tempeatue defined as the aveage of T w and T a exept fo the themal expansion oeffiient β whih was obtained based on T a.

6 They stated that the above oelation pedited thei expeimental esults with an aveage deviation of 6.3%. They tested a numbe of mio and mini finned sufaes aligned vetially with fin heights of 100µm, 00µm and 1mm. The fin spaing used anged fom 30µm to 360µm fo the 100 and 00µm fin height and 0.7mm to 7.7mm fo the 1mm fin height. They also tested 00µm and 1mm miofinned piees aligned hoizontally and onluded that the effet of oientation is negligible. Theefoe, thei oelation was used to pedit the uent expeimental esults shown in Figue 8. Figue 7: Change of heat tansfe oeffiient (h 0.5 -h 1.0 ) vesus the heat input fo diffeent fin spaing. Nusselt numbe (Nu) Expeimental esults Kim et al [9] Rayleigh numbe (Ra ) Figue 8: Expeimental esults ompaed to Kim et al. [9] oelation. 5. Conlusions With the emeging potential of mio fined stutues in heat emoval mehanisms fo mio sale appliations, the oeffiient of heat tansfe by natual onvetion plays an impotant ole. Results fom the pesent wok have shown that the values of onvetive heat tansfe oeffiient ineased with ineased fin spaing. In ontast, the onvetive heat tansfe oeffiient was shown to deease as fin height ineased. This tend is simila to that epoted by Kim et al. [9]. The highest value fo onvetive heat tansfe oeffiient of 8.158Wm - K -1 was eoded at the lowest fin height of 0.5mm and spaing of 1.0mm. A maximum edution in onvetive heat tansfe oeffiient of 34.8% due to fin height inease fom 0.5mm to 1.0mm was eoded at the maximum tempeatue diffeene of 100K with a fin spaing of 1.0mm. It is lea fom this eseah that moe wok is needed to investigate wide anges of fin heights, spaing and heating loads, in ode to detemine the optimum geometies fo miofinned heat sinks unde the equied opeating onditions. 6. Aknowledgments The authos aknowledge the help povided by Ms. Y. Li in aying out some of the expeimental wok and data pepaation. Additional thanks go to Advantage West Midlands (AWM) fo funding the West Midlands Mio Mahining Cente at Bimingham, ontaining the µ-edwm equipment. 7. Refeenes [1] X. Jak Hu, Anku Jain, Kenneth E. Goodson, Investigation of the natual onvetion bounday ondition in miofabiated stutues Intenational Jounal of Themal Sienes, Volume 47, Issue 7, July 008, pp

7 [] S. Banejee, A. Mukhopadhyay, S. Sen, and R. Ganguly, Natual onvetion in a bi-heate onfiguation of passive eletoni ooling, Intenational Jounal of Themal Sienes, Volume 47, Issue 11, Novembe 008, pp [3] Z. Guo and Z. Li, Size effet on miosale single-phase flow and heat tansfe, Intenational Jounal of Heat and Mass Tansfe, 46, 003, pp [4] A. Chaehoi, F. Mailly, L. Latoe, P. Nouet, Expeimental and finite-element study of onvetive aeleomete on CMOS, Sensos and Atuatos A, 13, 006, pp [5] B. Yaziioghu and H. Yunu, Optimum fin spaing of etangula fins on a vetial base in fee onvetion heat tansfe, Heat Mass Tansfe Jounal, 44, 007, pp [6] M. Fujii, Enhanement of natual onvetion heat tansfe fom a vetial heated plate using inlined fins, Heat Tansfe Asian Reseah, 36 (6), 007, pp [7] Y. M. Ko, C. W. Leung, S. D. Pobet, Steady-state fee-onvetive ooling of heat exhanges with vetial etangula fins: Effet of fin mateial, Applied Enegy, Volume 34, Issue 3, 1989, pp [8] L. Dialameh, M. Yaghoubi, O. Abouali, Natual onvetion fom an aay of hoizontal etangula thik fins with shot length, Applied Themal Engineeing, Volume 8, Issues 17-18, Deembe 008, pp [9] J. S. Kim, B. K. Pak, and J. S. Lee, Natual onvetion heat tansfe aound miofin aays, Expeimental Heat Tansfe, 1:1, 008, pp [10] C. Chen and H. Weng, Natual onvetion in a vetial miohannel, Jounal of Heat Tansfe-ASME, 17, 005, pp [11] N. V. Suyyanaayana, Engineeing heat tansfe, West Publishing Company, 1995, ISBN , Table A9, p. A0. [1] D. P. Kulkani and D. K. Das, Analytial and numeial studies on miosale heat sinks fo eletoni appliations, [13] I. Matoell, J. Heeo and F. X. Gau, Natual onvetion fom naow hoizontal plates at modeate Rayleigh numbes, Intenational Jounal of Heat and Mass Tansfe, Vol. 46, 003, pp [14] W. M. Lewandowski, E. Radziemandska, M. Buzuk and H. Bieszk, Fee onvetion heat tansfe fluid flow above hoizontal etangula plates, Applied Enegy, Volume, 66, 000, pp [15] T. Fujii and H. Imua, Natual onvetion heat tansfe fom a plate with abitay inlination, Intenational Jounal of Heat and Mass Tansfe, Vol. 15, 197, p [16] J.P. Holman, Heat Tansfe, Seventh edition, MGaw Hill, ISBN , 1990, Chapte 7, p. 341.