Heat Dstrbuton Analyss of a Thck Flm Transcutaneous Gas Sensor LIZA LAM, JAROMIR BILEK, JOHN ATKINSON School of Engneerng Scences Unversty of Southampton Hghfeld, Southampton UNITED KINGDOM Abstract: - The partal pressure of oxygen and carbon doxde n the arteral blood s an mportant factor for doctors to determne the respratory condtons of patents. Transcutaneous blood gas montorng s a popular non-nvasve measurement technque for obtanng fast and relatvely accurate responses. In ths nvestgaton, thck flm technology was employed to develop a blood gas system based on an amperometrc sensor whch conssts of a heatng module to elevate the temperature at the skn surface to transcutaneous levels. The heatng module ncluded a heatng element and ts temperature was regulated by a temperature control crcut. Usng an nfrared camera, the transent and steady-state temperature dstrbuton of the heatng element was analyzed. A three-dmensonal theoretcal model was also establshed to evaluate the temperature response of the sensor and subsequently compared wth the results of the practcal prototype. Based on the analyss and development, future heatng modules for transcutaneous sensors could be generated more easly, hence effectvely mprovng the desgn stages. Key-Words: - Thck flm, transcutaneous, blood gas, sensor, heatng element, temperature dstrbuton, transent, steady-state 1 Introducton Healthcare and medcal servces have always played mportant roles n part and parcel of daly lves. In order to understand and determne the medcal status of patents, dfferent parameters throughout the human body were measured and analyzed. On such mportant medcal parameter s the measurement of blood gas levels n the arteral blood. Ths s essental for doctors to montor the respratory condtons of patents, n partcular the preterm neonates who are undergong surgery or experencng respratory dffcultes. Transcutaneous blood gas measurement, ntroduced n the early 1970s [1] s a popular, nonnvasve technque that allows on-gong, contnuous montorng features. For ths measurement, the surface of the skn must be n the specfc temperature range wthn the sensng area [2]. Ths temperature must be hgh enough to obtan recordable results, but at the same tme t has to be suffcently low so as not to burn or damage the skn. Ths crtcal temperature, at whch the skn wll be damaged, vares for dfferent ndvduals and t also depends on the poston at whch the sensor s placed on the human body. In general, ths crtcal temperature s found to be approxmately 46 C [3]. Thck flm technology [4] s one technque that allows hgh volumes of producton wth hgh repeatablty and at low cost. The manufacture of sensors usng ths technology s found sutable and s adopted commonly n many ndustres. Hence, thck flm technology was employed to develop the transcutaneous blood gas sensor. In ths paper, the focus s concentrated on the temperature dstrbuton on the surface of the sensor n order to determne ts effects on the overall performance. The man objectve s to study the heat dstrbuton on the sensor substrate. A temperature control crcut was desgned n order to provde the requred controlled temperature for the transcutaneous measurement. A theoretcal smulaton of the heat dstrbuton was performed usng the ANSYS software based on fnte element method (FEM). The results were then compared to the expermental observatons for a more comprehensve nvestgaton. The results could be used n future prototypes to acheve low cost sensor desgn solutons. 2 Sensor Desgn The complete blood gas sensor conssted of two man parts, namely the heater and gas sensor modules [5, 6]. In ths paper, the heater module s the man topc of nvestgaton. To fabrcate the heater module, termnal pads for solderng connecton were made from slverpalladum (AgPd) nk whle the heatng element was made of platnum (Pt) nk. Pt exhbts nterestng characterstcs such as hgh temperature coeffcent of resstance (TCR). It s also a stable materal whch can be exposed to a varety of envronments
at hgh temperatures wthout degradaton. The temperature characterstc of Cermet Pt used s lnear wthn requred temperature range wth TCR of 3500 ± 200 ppm/k [7]. The thck flm process began by prntng each layer usng a unque screen that contaned the desred template layout. Ths was followed by the dryng and frng processes to bnd the nk onto the substrate whch n ths case was alumna (96% Al 2 O 3 ). The heatng element meander area s shown n Fg. 1. temperature range for both the front and back of the substrates were the same. It was also mportant to note that heat was transferred through the alumna substrate readly at the transent stage of operaton. (a) 3 Experment Contact pad Fg.1 Heatng Element Pattern 3.1 Equpment and Procedure Experments were carred out wth the nfrared (IR) camera DeltaTherm and supportng software DeltaVson. The DeltaTherm camera s manly used for thermal stress analyss but can be also appled n other applcatons [8]. It contans a 128 by 128 array of ndum-antmony (InSb) detectng elements. The temperature dstrbuton was measured on both sdes of the substrate, the front and the back. The front was defned as the sde where the heatng element was prnted and therefore t was supposed that the overall maxmum temperature should be found on ths sde. The temperature dstrbuton of each sde of the substrate was measured on separate occasons under the same operatng condtons n order to obtan comparable results. 3.2 Expermental Results Fg. 2 shows the temperature dstrbuton over the heated area after one mnute of operaton. It s noted that each change of shade n the contour plots represents a temperature change of 0.5 C wthn the regon. As shown n Fg. 2, the area of the heater s ndcated by the whte rectangular outlne (8.8mm by 8mm) and a grd s ncluded for better graphcal comparson of the mages. The hghest temperature occurred approxmately at the mddle part of the heatng element along the x-axs. The back of the substrate also ndcated a more unform concentrc dstrbuton of the heated regon. The overall Fg.2 Transent Heat Dstrbuton on Substrate Surface (after one mnute) (a) Front-Same Sde as Heatng Element; Back It was found from further experments of the measurements wth IR camera, the state after fve mnutes could be depcted as a stable response gven that the temperature control crcut was set to regulate at an unchanged temperature. Ths generalzaton was acceptable as the mages taken after ten or twenty mnutes later remaned relatvely unchanged as compared to the fve mnutes effect, seen n Fg. 3. Smlar observatons were found on both the transent and steady-state dstrbutons. A slght mbalance of non-symmetry n Fg. 3(a) could be caused by low-speed arflow from the left sde durng the measurement. Despte these naccuraces, t can be assumed that the temperature dstrbuton was smlar on both sdes of the substrate n the stable state. y x
(a) flud moton, a dstncton s made between a free or natural convecton and a forced convecton [9]. Newton's law of coolng expressed the heat flux from sold surface to a flud by q = h A ( Tw T ) (2) where q s heat transfer rate (W), h s the flm coeffcent (W/m 2.K), T w s wall temperature (K) and T s the free stream temperature (K). Radaton s the transfer of thermal energy by electromagnetc waves. The wavelengths of radated waves can range from the long nfrared to short ultravolet, dependng on the temperature of the body [10]. Stefan-Boltzmann law of radaton descrbes ths heat flow transfer as 4 4 q = σ ε A T T (3) ( ) where q s the heat transfer rate from surface (W), σ s the Stefan-Boltzmann constant (W/m 2.K 4 ), ε s the effectve emssvty, A s the area of surface (m 2 ) and T, T j are absolute temperatures at surface and surface j, respectvely (K). j Fg.3 Steady-state Heat Dstrbuton on Substrate Surface (after fve mnutes) (a) Front-Same Sde as Heatng Element; Back 4 Theoretcal Model 4.1 Defnton In general, there are three heat transfer mechansms that descrbe heat flow away from a heat source across a certan structure: conducton, convecton and radaton. Heat conducton s defned as the transfer of the heat through a sold when a temperature dfference exsts across the sold. Fourer's law of heat conducton states that the heat flux s proportonal to the temperature gradent n the specfed drecton n. The law s gven by q n " = k (1) n where q n s the magntude of the heat flux n the n drecton (W/m 2 ), k s thermal conductvty of materal (W/m.K) and T s the temperature (K). Heat convecton s the transfer of energy n the form of heat from a boundng surface to a flud and defnes the heat exchange condtons at the boundary of the sold body. Dependng upon the cause of the Usng Eqns 2 and 3 as well as sutable coeffcent values, the heat transfer rates were calculated for the nvestgated samples. It was found that heat transfer rate for convecton was approxmately ten tmes larger than that for radaton. In ths nvestgaton, heat radaton was neglected because the effect on the temperature wthn the heated area at 45 C was consderably small. Thus, t was acceptable to assume that the heat transfer was domnated by conducton and convecton. 4.2 Numercal Model Numercal soluton n ANSYS heat flow analyss s based on the frst law of thermodynamcs [11]. Ths law s used for descrbng the heat conducton and convecton wth dfferent boundary condtons appled durng the evaluaton. The formulaton of natural convecton equatons follows the same basc prncples that govern general flud moton. Further smplfcatons must be done to provde the soluton [12] whch results n the governng equaton for sotropc materal n terms of rectangular coordnates ρ C + v + v + v (4) p x y z t x y z 2 2 2 T T T = q + + + gen k 2 2 2 x y z where v s velocty of mass transport of the heat, ρ s the densty of the sold, C p s the specfc heat, q gen s
heat generaton rate per unt volume, k s thermal conductvty, T s temperature and t s tme. The ANSYS model was meshed before applyng any load. Ths s an mportant step n analyss as fner meshng results n more accurate solutons, but t demands more computatonal tme for the soluton. The meshed model of the heated area s shown n Fg. 4. Fg.4 Meshed Model A heat generaton load was appled to the heatng element model. The ntal load was obtaned from usng the resultant values evaluated from the power measured n pror experments as shown n Fg, 5. It was mportant to assume that the effectve volume of the heatng element was the same as that of the model. Power [W] 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 Tme [s] Fg.5 Measured Power to Heatng Element for Frst Mnute The second stage of applyng loads on the model was the heat convecton from the substrate to the surroundng ar. Heat convecton was characterzed by the flm coeffcent and the bulk temperature of ambent ar. The flm coeffcent depends on the physcal geometry and the flud thermo-physcal propertes. Typcal values for ar natural flow are n the range of 2 to 30 W/m 2.K [12]. Due to numerous random varables whch nfluenced convecton, t was essental to smplfy the consderatons. Wth that, several flm coeffcent values were used n the model. It was found that the most sutable value for the flm coeffcent was 15 W/m 2.K. The bulk temperature of ambent ar n the model was set at the average room temperature of 22 C. 4.3 Theoretcal Results The transent analyss showed the heat transfer over the sensor wth respect to tme. It was necessary to perform ths analyss to verfy that the crtcal temperature of the model was not exceeded on the substrate upon the stablzaton of the heat dstrbuton. The maxmum temperature was stablzed approxmately after the frst mnute and therefore t was adequate to carry out the modelng for ths perod. (a) 45 C 43 C 41 C Fg.4 Meshed Model Fg.6 Transent Analyss after (a) 5 s, 30 s Applyng the ntal heat generaton load as determned from Fg. 5, the transent responses after 5 s and 30 s of operaton are llustrated n Fg. 6. It can be seen that the maxmum temperature of 44.955 C begns at the mddle regon of the heatng element (n the x-axs drecton). The change n shade generally depcts 1 C change n temperature. After 30 s, the area around the heatng element reached requred transcutaneous levels. Fg.7 Steady-state Analyss
The steady-state analyss was also carred out. A constant supply of power load was appled to the heatng element. The value of 0.272 W was determned from averagng the expermental results. Hence, the correspondng heat generaton of 1.045x109 W/m 3 was appled. The graphcal result of the steady-state analyss s presented n Fg. 7. followed smlar trends. Therefore, the ANSYS analyss can be employed effectvely for the modelng of the temperature dstrbuton and analyss of the temperature unformty on the substrate. 5 Dscusson 5.1 Compare Expermental and Theoretcal Results Several heaters were fabrcated and measured wth the IR camera. The expermental results were compared wth the theoretcal mathematcal model of the sensor. The am was to valdate the model of temperature dstrbuton and to establsh the knd of ANSYS analyss that would be deal for comparson between theoretcal desgn and practcal applcaton. The transent analyss s shown n Fg. 8 wth each shade representng a varaton of 0.5 C and 1 C for the expermental and theoretcal results respectvely. It was noted that the temperature dstrbuton n the desgnated sensng area was uneven although the heatng element pattern was relatvely unform. The rate of the temperature change was lowest n the area on the upper edge of the heatng element. Further away from the heated area near the contact pads, the rate of temperature change ncreased and ths suggested that the area would not be sutable for blood gas measurements whch requred a stable transcutaneous temperature. 45-45.5 C 46 C Fg.9 Comparson of Steady-state Response for (a) Expermental, Theoretcal 5.2 Analyss of the Results The modeled substrate was desgned wth the same dmensons as that of the real substrate. The propertes of the materal used were practcal values from the manufacturer s specfcatons. However, due to estmatons and smplfcatons, dfferences between the mathematcal model and the real sensor, such as the flm coeffcent values, were present. Several assumptons had to be also made durng the desgn process of the model. Frstly, as llustrated n Fg. 10, the cross-secton of the thck flm heatng element s not a basc geometrcal shape, apparently to some extend t s hemsphercal. 45-45.5 C 46 C Fg.8 Comparson of Transent Response for (a) Expermental, Theoretcal As seen from the mages n Fg. 9, the steadystate temperature dstrbuton obtaned from the modelng and experments are smlar. The temperature dstrbutons were also comparable to that of the transent analyss (n Fg. 8). Although there were dstnct dfferences n the magntude of temperatures denoted by the dfferent shades, the characterstc of the temperature dstrbutons Fg.10 Cross-secton of the Actual Thck Flm Heatng Element The thckness of the element was not constant and t was dffcult to acheve the actual model of ts shape. Hence, a smple rectangle was used nstead as shown n Fg. 11. Ths smplfcaton could have caused the dfferences between the theoretcal and theoretcal results. The naccuraces n the heat generaton would subsequently emerge.
Fg.11 Cross-secton of the Rectangular Representaton of the Heatng Element The effect of overlappng contacts desgn between two thck flm lnes was another mportant assumpton, as descrbed n Fg. 12. For the thermal representaton, t was possble to estmate that the area wth two overlyng layers has almost the same propertes for heat transfer as that of a sngle layer at the same poston. All assumptons have been used n order to smplfy the desgn of the model. Subsequently, a faster and smpler mathematcal soluton was reached. (a) Fg.12 (a) Overlapped Thck Flm Materal, Smplfed Representaton 6 Concluson The transent and steady-state temperature dstrbutons of the heater module of the transcutaneous gas sensor were evaluated expermentally and theoretcally. From the experments, t was found that the dstrbuton was not unform n the mddle of the heatng element. The optmum poston for transcutaneous measurement was at the top edge of the heatng element. The maxmum temperature on the substrate was measured and evaluated to be approxmately 46 C. The theoretcal temperature dstrbuton obtaned from the model gave relatvely good representaton of the actual physcal heatng element. Although dfferent maxmum temperatures were observed, the dstrbuton trends were comparable for both the expermental result and model. Smplfcatons had been carred out durng the development of the model. Supported wth the measurements made from the IR camera, the errors due to assumptons were mnmzed for the ANSYS model. Therefore n concluson, the model proved to be useful for creatng new heater desgns. References: [1]M. L. Topfer, Thck-Flm Mcroelectroncs- Fabrcaton, Desgn and Applcaton, Ltton Educatonal Publshng Inc., 1971. [2]L. J. Grazan, A. R. Sptzer, D. G. Mtchell, D. A. Merton, C. Stanley, N. Robnson, L. McKee, Mechancal Ventlaton n Preterm Infants: Neurosonographc and Developmental Studes, Pedatrcs, 90, 1992, pp. 515-522. [3]S. Keston, Kenneth R. Chapman, Anthony S. Rebuck, Response Characterstcs of a Dual Transcutaneous Oxygen/Carbon Doxde Montorng System, Chest, 99, 1991, pp. 1211-1215. [4]F. Manaco, B. G. Nckerson, J. C. McQutty, Contnuous Transcutaneous Oxygen and Carbon Doxde Montorng n the Pedatrc ICU, Crtcal Care Medcne, 10 (11), 1982, pp. 765-766. [5]J. Bílek, Thck Flm Heatng Element and Desgn of Temperature Control Crcut, Dploma Thess, FEEC, Brno Unversty of Technology, Brno, 2001. [6]Y. Z. Lam, J. K. Atknson, A screen-prnted transcutaneous oxygen sensor employng polymer electrolytes, IEE-Medcal, Bologcal and Computng Engneerng Journal, Volume 41, No.4, pp. 456-463, July 2003. [7]Electro-Scence Laboratores, Inc., Data sheet for ESL-5545, Cermet Platnum Paste. [8]B. Boyce, J. Lesnak, Unque Applcatons of Thermoelastc Stress Analyss, Socety for Expermental Mechancs, 1999. [9]M. Santo-Zarnk, Some Applcatons of Thckflm Stran Gauge: Thermal Modellng and Optmsaton of Hybrd Thck-Flm Structures, IMAPS Poland Conference, 2000. [10]O. Lofgren, L. Jacobson, The Influence of Dfferent Electrode Temperatures on the Recorded Transcutaneous PO2 Level, Pedatrcs, 64 (6), 1979, pp. 892-897. [11]Taftan Data, The Frst Law of Thermodynamcs,1998, http://www.taftan.com/thermodynamcs/first. HTM [12]S. Kakaç, R. K. Shah, W. Aung, Handbook of Sngle-phase Convectve Heat Transfer, Wley, 1987, pp.1-7.