CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD

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1 CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD Svetozár Mlinrič Deprtment of Physics, Fculty of Nturl Sciences, Constntine the Philosopher University, Tr. A. Hlinku, SK Nitr, Slovki Emil: Abstrct The pper dels with mesurement of the thermophysicl properties (therml conductivity nd diffusivity) of PMMA (polymethylmtcrylte). The theory of the dynmic plne source method nd modified experimentl pprtus is described. Difference nlysis is used for serching the time intervl in which the mesured dt should be evluted. Besides the influence of the heter nd het losses from the lterl sides of the smple lso the influence of the noise is studied. Key words: thermophysicl properties, dynmic plne source method, difference nlysis Introduction Trnsient methods represent lrge group of techniques where mesuring probes, ie het source nd thermometer, re plced inside the specimen. This experimentl rrngement suppresses the smple surfce influence on the mesuring process. The temperture of the specimen is stbilised nd uniform. Then the dynmic het flow in the form of pulse or step-wise function is generted inside the specimen. From the temperture response to this smll disturbnce the thermophysicl prmeters of the specimen cn be clculted. Tble. Bsic chrcteristics of trnsient methods Het source Het genertion Het flow Het sourcethermometer Mesured prmeters Nme of method line step-wise rdil united λ Hot Wire plne pulse -dimensionl prt, λ Pulse Trnsient plne step-wise -dimensionl prt, λ Step-Wise Trnsient plne step-wise -dimensionl united effusivity Hot Plte Trnsient disc step-wise 3-dimensionl united, λ Hot Disc Trnsient circles step-wise 3-dimensionl united, λ Gustfsson Probe plne step-wise -dimensionl united, λ > W/mK DPS plne step-wise -dimensionl united, λ < W/mK Extended DPS The summry of trnsient methods is given in Tble [,].

2 The dynmic plne source (DPS) method is rrnged for one-dimensionl het flow into finite smple. On the rer side the smple is in contct with poor het conducting mteril so tht the temperture developed in the smple is close to dibtic. This method ppers to be useful for simultneous determintion of therml diffusivity nd therml conductivity λ of metls nd good thermlly conducting dielectrics. The extended dynmic plne source (EDPS) method is the modifiction of DPS method for low thermlly conducting mterils. The insulting mteril on the rer surfce of the smple hs been exchnged with very good het conducting mteril (het sink) which cuses tht the process fter short time pproches the stedy-stte condition. Experimentl The rrngement of the experiment is shown in Fig., where the plne source (PS) disc is plced between two identicl smples hving the sme cross section s the disc. The rer side of the smple is in contct with het sink, which is mde of lrge Al blocks. The PS disc, which simultneously serves s the het source nd thermometer, is mde of nickel film µm thick covered from both sides with kpton lyer. The dimeter of the disc is mm nd the thickness of both specimens is bout 3 mm. het sink Smples l PS disc Fig The setup of the experiment S R Power supply PS PCL 7 PC Fig Experimentl circuit design. R - constnt resistor, PS - disc, S - switch

3 The het flux, in the form of step-wise function, is generted by switching on the electricl current s shown in Fig.. Using the constnt resistor, the electricl current nd voltge cross the PS disc re mesured. Dt cquisition is relised by mens of multichnnel PC plug-in crd PCL 7 (Advntech). So tht the power s well s the instntneous vlues of the disc resistnce nd temperture cn esily be computed. Compring with previous works [, 3], in this experimentl rrngement chep power supply is used. The dvntge of this solution resides in the fct, tht the mesurement results re not influenced by smll instbility of the set current. 3 Theory Fig. 3 shows the theoreticl temperture function which is solution of the prtil differentil eqution with boundry nd initil conditions corresponding to the experimentl rrngement. The temperture function is given by [] F HG ql t F n Θ T( t)= + π β ierfc H Gn, () λ πθ t n= II KJ KJ where q is het current density nd λ therml conductivity. Θ is the chrcteristic time of the smple nd is given by Θ= l, () where l is thickness nd therml diffusivity of the specimen. Prmeter β describes the het sink imperfection nd ierfc is the error function integrl [4]. The principle of the method resides in fitting of the theoreticl temperture function given by () over the experimentl points. In cse of the best fit, both prmeters λ nd cn be determined. The method of fitting bsed on lest-squres procedure ws described in detil []. shift time strobe stedy-stte condition T T(t) T Θ t Fig 3 Temperture function - temperture increse s function of time

4 4 Experimentl dt processing In this section we will discuss some effects which cn cuse the devition of the experimentl conditions from the idel one. We will show how some of these distortions cn be eliminted by the proper evlution technique. The first problem resides in the influence of the PS disc. The theory ssumes n idel PS disc - the homogeneous hot plne of negligible thickness nd mss tht is in perfect therml contct with the smple. The imperfection of the disc will cuse, tht the beginning of the mesured temperture function will be distorted. This time intervl, described by the chrcteristic time of the disc Θ D, is not suitble for computing of thermophysicl prmeters. Het losses from the lterl sides of the smple present the second problem. This cn be eliminted by optimising of the specimen thickness described in []. But pproching the stedy-stte condition the het losses re becoming more nd more importnt. This time intervl of the mesured temperture function lso cn not be used. So we expect, tht there exists time intervl in which the determintion of thermophysicl prmeters will not be erroneous. This importnt time intervl cn be find using the procedure which ws nmed difference nlysis []. The procedure is bsed on fitting within the time intervl (strobe) which is successively shifted in steps corresponding to the smple period. As in ech fitting new vlues of prmeters λ nd re computed, the shift time dependencies re obtined. Fig. 4 shows the results of the difference nlysis which ws performed with theoreticl points computed using eqution (). Quntiztion noise ws dded by rounding the points to 4 vlid numbers. Fig. 4 nd 5 shows the therml conductivity λ, therml diffusivity nd correltion coefficient r s the function of the shift time. The strobe ws 5 s..4 λ W/mK m /s lg(-r) Fig 4 Results of the difference nlysis - experiment modelling 3

5 .4 λ W/mK.3.4 λ W/mK m /s 3 m /s lg(-r) - lg(-r) ) I = 33 ma b) I = 663 ma Fig 5 Results of the difference nlysis - rel mesurements on PMMA Therml conductivity λ, therml diffusivity nd correltion coefficient r s the function of the shift time 4

6 Fig. 5 shows the difference nlysis of the rel mesurements on PMMA t vlues of the heting current ) I = 33 ma nd b) I = 663 ma corresponding to the totl temperture rise t the stedy-stte condition T =.9 C nd T = 8. C (Fig. 3), respectively. Fig. 4 nd 5 show the dependencies of the correltion coefficient r which expresses fitting process perfection. In order to get n illustrtive curve, the quntity lg(-r) ws plotted. The higher the scttering of experimentl points, the lrger vlue of this quntity. 5 Conclusions Fig. 4 shows tht for shift times less then 5 s the computed vlues of λ nd re nerly identicl to the vlues put originlly into the model nd mrked by horizontl lines. From the dependence of the correltion coefficient one cn conclude, tht the most ccurte results will be ttined t the shift time =, becuse the model does not contin the influence of the PS disc. Fig. 5 ) shows tht the sensitivity of the mesuring device ws not sufficient t the heting current I = 33 ma. The results re widely scttered nd resonble vlues cn be obtined only for shift time = - 5 s. The results in Fig. 5 b) re fr more stbilised. The influence of the PS disc is clerly seen nd chrcteristic time of the disc cn be determined Θ D = 5 - s. It is remrkble tht the dependencies of the correltion coefficient in model (Fig. 4) nd experiment (Fig. 5 b) re very similr for shift times > Θ D. In spite of this the dependencies of λ nd in Fig. 5 b) show the influence of het losses from the lterl sides of the smple for the shift times > 6 s. Therefore, the time window within which the fitting procedure cn be pplied is from to 8 s. The men vlues of λ nd for PMMA mteril, mesured t temperture of C with heting current 663 ma, re.94 W/mK nd. -7 m /s, respectively, which re in good greement with published vlues []. Dt uncertinty is for therml conductivity within 3% nd for therml diffusivity within %. Acknowledgements The uthor is grteful to the Institute of Physics t the Slovk Acdemy of Sciences for very helpful discussions. This work ws supported by grnt CGA V// UKF Nitr. References [] Kubičár, Ľ., Boháč, V. Trnsient methods for the mesurement of thermophysicl properties. in Thermophysics. Nitr: FPV UKF,, p [] Krwcki E., Suleimn B. M., ul-hg I., Nhi, B. An extension to the dynmic plte source technique for mesuring therml conductivity, therml diffusivity nd specific het of dielectric solids. in Rev. Sci. Instrum., October 99, vol. 63, p [3] Lbudová, G., Vozár, L., Mlinrič, S. Aprtúr n mernie termofyzikálnych vlstností mteriálov metódou dynmického plošného zdroj. in XII. DIDMATTECH 99. Nitr: PgF UKF,, p [4] Crslw, H. S., Jeger, J. C. Conduction of Het in Solids,. vyd. Oxford: Oxford University Press, 959, p

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