HEAT TRANSFER IN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS

ISTP-16, 005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA HEAT TRANSFER IN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS Valére Ménard*, Phlppe Reulet**, Davd Nörtershäuser*, Stéphane Le Masson*, Perre Mllan** *France Telecom R&D -, Avenue Perre Marzn - BP 40 307 - Lannon Cedex - France **ONERA - BP 405-31055 Toulouse Cedex 4 - France Correspondng author: valere.menard@onera.fr Keywords: Electronc coolng, smplfed numercal model Abstract The present paper descrbes the development of a smplfed numercal model (SIMFEP 1 ) able to smulate heat transfer n an electronc package bured n sol and submtted to clmatc condtons. To valdate ths model, numercal results are compared wth expermental results obtaned wth ESSIC (Expermental Set-up SImulatng Clmate), a room equpped to smulate clmatc condtons. Nomenclature A absorptvty - α thermal dffusvty m²/s β thermal expanson coeffcent 1/K Cp specfc heat J/kg.K d heght, depth or thckness m σ Boltzmann s Constant W/m K 4 G j conductance between and j nodes W/K g gravty m/s² h cv convectve heat transfer coeffcent W/K.m² Q heat flux W/m² λ thermal conductvty W/m K L wdth m l Length m Nu L Nusselt number based on the length - Tmn mnmal temperature C Tref temperature of reference C ν knematc vscosty m²/s Sj surface m² s heats source at node W V ar velocty m/s Z vertcal coordnate of SIMFEP m 1. Introducton In order to enhance the deployment of xdsl servces, France telecom nstalls outdoor cabnet all over the country. Some cabnets are placed on the sdewalks but another possblty s to use underground telecommuncaton manholes. These bured connectng rooms have been desgned to receve passve equpment. Nevertheless, t remans possble to put nsde a watertght box contanng electronc cards. The coolng method chosen s natural convecton because t s free mantenance. However, ths one s not very powerful and the strongly unfavorable thermal condtons (small ground conductvty and solar heat flux on the top) make dffcult the respect of ETIS² standard temperature. In order to optmze the coolng effect of natural convecton, a smplfed numercal model called SIMFEP s developed. Ths model must smulate the heat transfer n a bured connectng box submtted to clmatc condtons. Ths study presents the comparson of expermental results obtaned wth the clmatc L r radus coordnate of SIMFEP m ρ densty kg/m 3 t tme s t h tme hour t d tme day Ta ambent temperature C Tmax maxmal temperature C smulatng room ESSIC and the numercal 1 SImplfed Model For Electronc Package, ²European Telecommuncaton Standard Insttute 1

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan results obtaned wth the smplfed model SIMFEP. In a frst part, ths paper descrbes the prncple of a smplfed method and the real thermal problem. Next, ESSIC and SIMFEP prncples are explaned and appled to a specfc case. Fnally, expermental and numercal results are dscussed and compared.. Prncple of a smplfed method A smplfed method s a smulaton method stuated between correlatons and CFD codes. Its advantage s to allow the smulaton of a complex case wthout the tme cost of CFD codes. The most mportant dsadvantages are: the low precson n comparson wth a CFD code result; the need to estmate heat transfer coeffcent values. Ths method has been used to smulate some complex cases lke electronc packages coolng and the thermal response of buldngs to clmate varatons. Our case s stuated between these two thermal problems and s very complex for a resoluton wth a CFD code. 3. Descrpton of the real problem The real problem of a bured room contanng an electronc package nvolves several knds of heat transfer (fg.1): In the electronc package, the thermal problem s very complex and s a couplng between conducton, radaton and natural convecton. In the bured room, heat transfer s also due to conducton, radaton and natural convecton. In the earth, the thermal problem s a smple case of conducton. At the surface, the earth and the room ld are submtted to convecton and radaton. The solar radaton changes wth tme and s nl durng the nght. In ths case, several aspects make the resoluton dffcult: Two very dfferent heatng sources (solar or lghts radaton and electronc cards) are coupled. Ths problem s consttuted of several knds of heat transfer dependng on the consderate zone. Tme scales characterzng ths problem are very dfferent. Actually, the tme scale characterzng radaton effect s very fast whereas the clmate perodcty s 4 hours. The effect of the solar radaton s very fast whereas the earth temperature needs several days to converge to a perodc value. Fg. 1: Heat transfer modes n real condtons 4. Descrpton of the clmate mposed In a frst case, ths model must be appled to a well known problem n order to be valdated. To reach ths pont, we chose to compare the model to ESSIC measurements n an unfavorable case. Ths case s a hot clmate n the south of France (lattude of Bordeaux) n summer. The solar radaton and the ambent temperature have been measured and an average annual clmate wth these daly varatons has been defned. From these results, the most unfavorable case of a very hot day durng summer s chosen to be appled to ESSIC and SIMFEP.

HEAT TRANSFER IN AN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS The ambent temperature daly varaton and the power of the radatng flux at the surface are defned and mposed both to ESSIC and SIMFEP as a boundary condton durng 10 days. 4.1 Radatng flux The clmate perodcty s based on a characterzng tme of 4 hours. t, t h and t d represent the tme respectvely expressed n second, hour and day (Eqn. 1). 4. Ambent temperature Equatons 5 to 7 defne the ambent temperature mposed (Fg. ). The mnmal temperature s Tmn = 18.5 C and the maxmal temperature s Tmax = 31.5 C. The temperature of reference s the average of the two extremes temperatures (Eqn. 4). Tref = (Tmn + Tmax)/ (4) t = t d 3600 4 = t h 3600 wth: [ t ] = s ; [ t h ] = h and [ t d ] = day (1) For 0 t < 5 : h π Ta = Tref 1 + cos t 9 8 For 5 t < 15 : h ( + ) (5) Equatons and 3 defne the heat flux smulatng the solar effect, nl durng the nght and reachng a maxmal value at 13 hours. For 5 t 1: h 4 3 Q = A th B th + C th D th + E For 0 t < 5 or 1 t < 4 : Wth: h < h 3 () Q = 0 W. m (3) π Ta = Tref 1 sn t 15 8 For 15 t < 4 : h ( ) π Ta = Tref 1 + cos t 15 8 ( ) (6) (7) A 4 = 0.1141 W. m h B = 5.934 W. m C = 97.9 W. m D = 58.85 W. m 3 h h 1 h E = 847.95 W. m Fg. : Heat flux and ambent temperature varatons 3

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan 5. Presentaton of ESSIC ESSIC s an expermental set-up desgned to smulate a chosen clmate. In a closed room, a France Telecom connectng box s bured and submtted to the smulated clmatc condtons. To create a radaton representatve of the solar effect, 303 ncandescence lghts are dsposed on the celng. To obtan a homogeneous flux, the lghts are arranged n row wth a space of 33 mm. At the north wall, 4 fans are placed just among the lghts to reduce ther temperature and keep t nferor to 40 C. Behnd the fans, an aperture allows the exteror ar to come n and at the opposte wall another aperture allows the hot ar to come out. Each lght has a varable power wth a maxmal value of 300 W and the resultng power receved at the ground surface s close to the real condtons. The resultng power at the surface (Fg. ) has been calbrated and s checked durng experments. The ar temperature of the room s controlled and regulated. Four electrc heaters allow to ncrease the mean temperature whereas two fans can fall t. The bured room s a concrete box of L5T model (179 88 10 mm). Electronc cards power (100W) s smulated by three heatng resstances. The estmaton of natural convecton between the electronc cards and package walls s very complex. Thus, to smplfy the smulated problem, a fan s placed n the electronc package under the electronc cards. By ths way, the forced convecton nduced allows to homogenze the temperature and the electronc package can be ntroduced as a smple node n the smulaton. The electronc package used s small n comparson wth the bured room n order to permt the full development of the flud flow by natural convecton. There are 16 thermocouples dsposed on the room wall, n the ar, n the ground and n the bured box. The thermocouples placed outsde of the bured box are protected from the lght radaton wth an alumnum paper. Fgure 3 s a smplfed scheme of ESSIC confguraton whereas fgure 4 shows the box geometry and thermocouples postons. Table 1 descrbes the geometry dmensons. The frst and second column present respectvely the wdth and the length. The thrd column s the vertcal component and can be the heght, the depth or the thckness dependng of the element consdered. L (m) l(m) d(m) ESSIC Room 6 4 3 Bured room L5T model 1.79 0.88 1. Room ld 1.79 0.88 0.01 Electronc package 0.66 0.55 0.38 Tab. 1: Characterzng dmensons of ESSIC Fg. 3: Scheme of ESSIC prncple 6. Presentaton of SIMFEP In ths numercal model, the geometry s smplfed to be supposed cylndrcal n order to use a cylndrcal symmetry. 6.1 Boundary Condtons Ths problem has 4 dfferent boundary condtons: The box contanng electronc cards s supposed to be homogeneous n temperature. 4

HEAT TRANSFER IN AN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS At the earth and ld surfaces, the heat transfer s due to convecton and radaton. The boundary condton n depth (z = -m) s a constant temperature measured wth ESSIC (T = 17.5 C). The vertcal boundary condton s supposed to be remote enough to be ndependent of the bured heated source. In ths case, the heat transfer drecton s only vertcal and t s possble to ntroduce an adabatc boundary condton. 6. Equatons resolved The problem consders several knds of heat transfer: radaton and convecton at the surface, convecton n the box, conducton n the walls and n the earth. The model s based on the fnte volume concept. For each node, the thermal balance equaton s solved: s + k j = 1 dt (8) Gj( T Tj ) = ρ VCp dt G j s the admttance of the heat transfer mode and s s a heat flux source at the node. In ths case there s one heat flux source: The electronc package: s = 100W Conducton: Convecton: Radaton: j G λ S j j = (9) Dj Gj = h Sj (10) ( T + T ) ( T T ) σ Sj j j (11) G = ε + The equaton 11 s solved usng an mplct scheme: s n+ 1 k n+ 1 n+ 1 Gj( T Tj ) + Gj( T n s j= 1 j= 1 + ρ V Cp T n+1 T t k n n n T ) j (1) The grd used for the resoluton s a 7 55 grd nodes horzontally refned close to the bured room (Fg. 5). 6.3 Thermophyscal propertes The thermal conductvty, the densty and the heat capacty of each materal used are presented n the table. Thermal conductv ty λ (W/ m.k) Densty ρ (kg/m 3 ) Specfc heat Cp (J/kg.K) Earth 0.4 100 975 Concrete (bured room walls) Cast ron (bured room ld) Electronc package 1.4 300 90 50 7000 500 15 300 500 Tab. : Physcal propertes of each materal Emssvty ε and absorptvty a of the ld and the earth are presented n the table 3. Emssvty ε Absorptvty a Earth 1 0.6 Ld 0.9 1 Tab. 3: Emssvty and absorptvty used n SIMFEP 5

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan 6.4 Estmaton of convectve heat transfer coeffcents Ths problem nvolves the defnton of several unknowns: the convecton coeffcents at the earth and ld surfaces and at box walls. 6.4.1 Convectve heat transfer at the surface At the surface, the convectve heat transfer coeffcent s ssued from correlatons. Accordng to the expermental results, there are 3 dfferent cases: Durng the nght, the ground temperature s close to the ambent temperature and the convectve heat transfer tends to zero. In contrary, durng the day the bured room ld s heated by the source. Thus, the convectve heat transfer coeffcent can be estmated usng the correlaton of natural convecton due to a horzontal hot plate. Durng the day, a coolng ar flow due to fans nduce a forced convectve heat transfer at ld and earth surfaces. Thus, the convectve coeffcent s estmated usng a correlaton of forced convecton. Natural convecton case (ld durng nght): The characterzng Raylegh number value 8 ( Ra > 10 ) based on the ld wdth L s large enough to obtan a turbulent state. Thus, the Nusselt number can be expressed as a functon of the Raylegh number followng the correlaton of Fshenden and Saunders [1]: 1/ 3 Nu L = 0.14Ra (13) L 3 gβ T λ c = 0.14 (14) υα h v 1/3 The hc value obtaned and ntroduce n the v code s: h v c = 3W / m. K Forced convecton case (Day): Durng the day, the h cv coeffcent s estmated usng the correlatons of Cole and Sturrock []. These correlatons are based on expermental results obtaned outsde and durng the nght n order to avod the solar radaton. Two cases are defned, dependng of the ar drecton. Ar drecton parallel to the wall: 1/ 3 = F v V (15) h cv = Ar drecton perpendcular to the wall: 1/3 = FV (16) h cv G + Wth F=5.7 W.s 1/3 /m 7/3.K and G=11.4W/m².K and V s the ar velocty. In our case, the ar velocty due to fans has not a constant drecton. Thus, the correlaton chosen s an average of the two correlatons: G 1/ 3 (17) = FV h cv + Ths relaton s appled usng a velocty v equal to the average of the velocty measured durng the day. The h cv value obtaned s: h 9W / m. K cv In the present study, the convectve heat transfer coeffcent at the ld surface used s the average between the coeffcents estmated durng the nght and durng the day ( hcv 6W / m. K ). 6.4. Convectve heat transfer n the bured room In the bured room, convectve heat transfer coeffcents are obtaned by CFD smulatons. Actually, the CFD commercal flud mechancs code FLUENT s used to smulate a 6

HEAT TRANSFER IN AN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS bdmensonal square box contanng a hot square source wth a small aspect rato. Based on the expermental nformaton several temperature dfferences between the hot source and the box walls are tested. Actually, durng the day, temperatures measurements at the ld and near the electronc package are close whereas durng the day the temperature dfference s about 0 C (Fg 6). Flow structures obtaned descrbe two large recrculaton cells. Actually the flud s heated gong up along each vertcal wall of the hot source before beng cooled down by the box walls. Cells development depends of the temperature dfference between the top wall and the hot source compared to the temperature dfference between the top wall and the vertcal walls. Actually, when the hot source and the top wall are at the same temperature, the ascendng flow does not reach the top wall and the heated flow s cooled along the vertcal walls. These results prove that durng the nght the flux due to the electronc package s essentally dsspated by the top wall whereas durng the day, the heat transfer at the vertcal wall s more mportant. Moreover the case wth a cold top wall s much more effectve because t allows the full development of the flow. In all the cases the heat transfer at the bottom s very low. Fgure 7 s an example of the flow streamlnes structure obtaned wth a cold top wall. Thanks to these results some average values of the convectve heat transfer coeffcent can be estmated for each wall and ntroduced n SIMFEP: Electronc package: h cv = 8 W / m. K Top wall: h cv = 8 W / m. K Vertcal walls: h cv = 5 W / m. K Bottom wall: h cv = 1 W / m. K Fg. 7: Streamlnes obtaned for a case wth a cold top wall 7. Results 7.1 Expermental results The results present two knds of behavors. Actually, durng the nght, the box s essentally cooled by the ld that s very conductve. But, durng the day, the box ld s strongly heated by the lghts radaton and most of the heated flux comng from electronc cards s dsspated by the vertcal and the bottom walls. Fgure 8 shows the tme varatons of temperature measurements at the ld room and at the earth surface compared to the ambent temperature mposed. The earth surface temperature measurement nose s more mportant than at the other place because of the lghts radaton. At the earth surface, the temperatures measured n the dstance of the bured room ncrease at 5h to reach a maxmal value of about 45 C at 14h and decrease to 0 C. For a deeper pont ths varaton ampltude decreases and becomes nl for depth of m. Fgure 9 shows the temperature daly varaton n the bured room: 7

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan n the electronc package (thermocouple 6), n the ar between the ld and the top of the electronc package (thermocouple 84), between the electronc package and the north vertcal wall (thermocouple 94), at the bottom of the bured room (thermocouple 5). The temperature measurements above the electronc package s larger than n the other ar zones of the bured room. All the zones of the bured room have a temperature varyng wth the daly perodcty, but the zone under the electronc package have a temperature varaton ampltude very low. 7. Numercal results The numercal results provde the evoluton of the temperature feld wth tme. Fg. 10 shows the temperature felds obtaned at 0h, 10h and 16h. On the left these felds show two hot zones: the ld and the electronc package. In the mddle zone, the earth s heated by the bured room and by ts surface. On the rght sde the temperature feld of the earth s ndependent of the bured room temperature and the temperature varatons are only due to clmatc condtons. 7.3 Comparson of the numercal and expermental results To compare the numercal and expermental results, we choose several ponts of reference correspondng to measurement ponts n ESSIC: ld temperature: thermocouple 95, electronc package: thermocouple 6, earth surface: thermocouple 14, earth at deep of 50 cm: thermocouple 3. numercal results. Ths fgure shows that the comparson between expermental and numercal results s n relatve agreement. The temperature levels have the same between ESSC and SIMFEP, except for the earth surface temperature. Ths pont could be mproved takng a dfferent heat transfer coeffcent for nght and day. 8. Concluson Ths paper has presented the development of SIMFEP, a smplfed model smulatng the heat transfer n an electronc package submtted to clmate varaton. To be valdated, SIMFEP was appled to a specfc unfavorable case and ts results were compared wth expermental results. The expermental part was realzed wth ESSIC, a room able to smulate a chosen clmate. The frst results show a good agreement between the smplfed model and expermental results. The further development of ESSIC must allow the varaton of the admttances wth tme to take nto account the convectve heat transfer varatons. References [1] Fshenden, M and Saunders, OA. An Introducton to Heat Transfer, Oxford Unversty Press, London, pp.95-99, 1950. [] Cole R J and Sturrock N S. The convectve heat exchange at the external surface of buldngs. Buldng and Envronment, Vol. 1, No. 1, pp 07-14, 1977. Acknowledgement The authors thank J. Gauter for hs techncal assstance durng the expermental nvestgaton wth ESSIC. Fgure 11 allows to compare the numercal results to the expermental measurements averaged on 3 days. All the ponts of reference present a same level for expermental and 8

HEAT TRANSFER IN AN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS Velocty measurement ponts 4 3 00 cm 150 cm South Earth Temperature measurement ponts -7 cm -4 cm -48 cm -7 cm 43 4 6 cm 40 98 41 97 Room L5T 54cm 89 5cm 10 1 18 cm 7 10 8 81 6 100 W 5 80 95 V 84 39 cm 66 cm 1 5 5 V1 11 Electronc package 8 10 5cm 38 cm 60 cm 94 45 46 47 48 1 Earth 100 cm 50 cm 14 15 3 33 North 0-5 cm -50 cm -75 cm -96 cm 39 39 cm 49 16-100 cm -10 cm 44 53 5 51 50 17-15 cm 31 30-140 cm 0 9 18 19-150 cm -00 cm Fg. 4: Bured room and thermocouple poston Fg. 5: Grd used for the smulaton wth SIMFEP 9

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan 65 60 55 Electronc package (thermocouple 6) Temperature ( C) 50 45 40 35 30 Ld (thermocouple 95) 0 4 6 8 10 1 14 16 18 0 4 Tme (hour) Fg. 6: Ld and Electronc package temperatures measured wth ESSIC durng a day 65 Ld room surface temperature Temperature ( C) 60 55 50 45 40 35 30 5 Earth surface temperature 0 Ambent temperature 15 1:00 0:00 1:00 0:00 1:00 0:00 1:00 0:00 1:00 0:00 1:00 0:00 Tme (hour) Fg. 8: Ld and earth surfaces temperature measurements wth ESSIC and ambent temperature mposed 10

HEAT TRANSFER IN AN ELECTRONIC PACKAGE SUBMITTED TO TIME-DEPENDANT CLIMATIC CONDITIONS 65 60 temperature ( C) 55 50 45 40 35 30 5 84 94 5 5 0:00 4:00 8:00 1:00 16:00 0:00 0:00 4:00 8:00 1:00 16:00 0:00 0:00 4:00 8:00 1:00 16:00 0:00 tme (hour) Fg. 9: Temperature measurements of thermocouples 5, 55, 84 and 94 wth ESSIC Fg. 10: Temperature feld obtaned wth SIMFEP at 10h, 16h and 0h 11

Valére Ménard, Phlppe Reulet, Davd Nörtershäuser, Stéphane Le Masson, Perre Mllan Fg. 11: Comparson of ESSIC and SIMFEP results 1