International Journal of Heat and Mass Transfer

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1 International Journal of Heat and Ma Tranfer 5 (9) Content lit available at ScienceDirect International Journal of Heat and Ma Tranfer journal homepage: Technical Note Study of the enitivity of a thermal flow enor Tae Hoon Kim, Dong-Kwon Kim, Sung Jin Kim * School of Mechanical, Aeropace & Sytem Engineering, Korea Advanced Intitute of Science and Technology, Daejeon 35-71, South Korea article info abtract Article hitory: Received 3 April 8 Received in revied form 8 October 8 Available online 1 November 8 The enitivity of a thermal flow enor i invetigated in thi tudy. A imple numerical model for analyzing heat tranfer phenomena in the thermal flow enor i preented. In order to validate the propoed model, experimental invetigation are performed. Baed on the reult from the validated model, a correlation that predict the enitivity of the thermal flow enor i preented. From the correlation, the manner in which the heat lo, the poition of the temperature enor, the input power, and the heater length affect the enitivity of the thermal flow enor i invetigated. Ó 8 Elevier td. All right reerved. 1. Introduction The meaurement and control of flow i critical in many engineering application, including emiconductor manufacturing procee, chemical procee, and MEMS device. The mot widely ued flow enor i a thermal flow enor, which ha the advantage of a mall ize, a hort repone time, and low power conumption [1]. The thermal flow enor typically conit of uptream and downtream temperature enor and a heater located between the two temperature enor a hown in Fig. 1(a). The ma flow rate i ened via the temperature difference caued by the heat tranfer interaction between a heated enor and a fluid tream, a hown in Fig. 1(a) [,3]. A hown in Fig. 1(b), the enitivity of a thermal flow enor i defined a the derivative of the temperature difference with repect to the ma flow rate at a zero flow rate. In other word, the enitivity i given a the following equation: S tðx ¼ Þ T t ðx ¼ ÞÞ _m _m¼ A the enitivity decreae, the ratio of the temperature difference to the ma flow rate decreae. If thi temperature difference become maller than the reolution of the temperature enor, the thermal flow enor cannot be ued to meaure the ma flow rate. Therefore, enitivity i a critical parameter in the deign of a thermal flow enor. A number of reearcher have tudied the enitivity of thermal flow enor. ammerink et al. [4] preented parameter that affect the enitivity of a thermal flow enor uing imple 1-D modeling. Sabate et al. [5], Roh et al. [6], and Kim and Kim [7] experimentally howed the effect of the poition of temperature enor and/or the heater power on the enitivity of the thermal flow enor. However, their reult were * Correponding author. Tel.: ; fax: addre: (S.J. Kim). limited to a qualitative evaluation. There i no reliable data or correlation by which it i poible to predict the enitivity in the deign of thermal flow enor quantitatively. The preent tudy contend with the enitivity of a thermal flow enor. In it, a imple numerical model of a thermal flow enor i preented. In order to validate the propoed model, experimental invetigation are performed. Baed on the reult from the validated model, a correlation that predict the enitivity of a thermal flow enor i preented. From the correlation, the manner in which the heat lo, the poition of temperature enor, the input power, and the heater length affect the enitivity of the thermal flow enor i invetigated.. Simple numerical model To analyze heat tranfer phenomena in a thermal flow enor, the phyical domain of the thermal flow enor i divided into two region: a enor tube region and an inner fluid region. The energy balance for each region i repreented by k t A t d T t dx þ h ipðt f T t Þ 1 R r ðt t T amb Þþq ¼ ðþ d T f k f A f dx _mc dt f f dx þ h ipðt t T f Þ¼ ð3þ where T, T f, A, h i,p,r r, and q are the tube temperature, inner fluid temperature, cro-ectional area, intertitial heat tranfer coefficient, wetted perimeter of the tube, thermal reitance per unit length for radial heat lo, and heat flux per unit length upplied from the heater, repectively [8]. The firt term on the left ide of Eq. () i the axial conduction term, and the econd term repreent the thermal interaction between the enor tube and the fluid. The third term denote the radial heat lo from the outer wall of the tube to the urrounding area. Similarly, Eq. (3) conit of a conduction term in the axial direction, the enthalpy change term of the /$ - ee front matter Ó 8 Elevier td. All right reerved. doi:1.116/j.ijheatmatranfer.8.1.6

2 T.H. Kim et al. / International Journal of Heat and Ma Tranfer 5 (9) Nomenclature A cro-ectional area, m C heat capacity, J/kg K h i intertitial heat tranfer coefficient, W/m K k thermal conductivity, W/m K ditance from the center of the thermal flow enor to the end of the channel, m h ditance from the center of the thermal flow enor to the end of the heater, m ditance from the center of the thermal flow enor to the temperature enor, m _m ma flow rate of the fluid, kg/ P wetted perimeter of the tube, m heat flux per unit length upplied from the heater, W/m q R r thermal reitance per unit length for radial heat lo, m K/W S enitivity of the thermal flow enor, C/(kg/) T temperature, C x axial coordinate Subcript amb ambient f fluid t tube fluid, and the thermal interaction term. Boundary condition are given a follow: T t ðx ¼ Þ ¼T f ðx ¼ Þ ¼T amb T t ðx!1þ¼t f ðx!1þ¼ ð5þ Governing equation are olved uing the control-volume-baed finite difference method. A power law cheme i ued for dicretization of the conduction and convection term. Dicretization equation are calculated uing the ADI method. All numerical data. m Senor Heater m = Senor Tube ð4þ in thi paper were obtained uing the numerical model preented in thi ection. 3. Experimental validation An experimental invetigation wa performed to validate the propoed numerical model. A thermal flow enor wa manufactured through imple microfabrication procee. Thin-film thermocouple and a heater were fabricated on a quartz wafer in puttering procee. The heater conited of nichrome and the thin-film thermocouple have compoition that are identical to thoe of tandard K-type thermocouple. A channel conited of PDMS (polydimethyliloxane). The quartz wafer and the PDMS channel were bonded by uing air plama. Fig. how the thermal flow enor. Detailed fabrication procee are explained in Ref. [7]. A flow enor are generally calibrated with nitrogen ga, nitrogen ga wa ued a the operating fluid in thi experiment. The purity Temperature Ambient temperature T = Δ T = f (m) x =. m > x Channel x = 4. mm Temperature Senor Heater h = 4.4 mm Temperaute difference (T t ( )-T t ( - )) (K) S : Senitivity 3 S Flow rate (SCCM) Port Channel Flow Direction Port Fig. 1. Operating principle of the thermal flow enor. (a) Schematic layout of the thermal flow enor. (b) Typical output of the thermal flow enor (not in cale). Fig.. Thermal flow enor [7]. (a) Thin-film thermocouple and a heater depoited onto a quartz wafer. (b) The thermal flow enor integrated with a PDMS channel.

3 14 T.H. Kim et al. / International Journal of Heat and Ma Tranfer 5 (9) of the nitrogen ga wa %. A hown, nitrogen ga pae through the PDMS channel. A calibrated tandard ma flow meter wa ued to control the ma flow rate of the nitrogen ga in the experiment. The range of the ma flow meter wa from to 1 SCCM (tandard cubic centimeter per minute). The heater wa powered by a DC power upply with power of.8 W. The length of the heater wa 4.4 mm a hown in Fig.. There were nine temperature enor in a thermal flow enor that meaure the temperature ditribution on the bottom urface of the channel. The ditance between two adjacent temperature enor wa 4 mm, a hown in Fig.. The temperature ignal from the thermal flow enor can be meaured directly uing a data acquiition unit. When obtaining the experimental reult, experiment were conducted five time. a Flow Rate = SCCM Numerical Reult Experimental Reult 4. Reult and dicuion Fig. 3 how the temperature ditribution along the PDMS channel. A can be een in the figure, the reult from the imple numerical model are in fair agreement with the experimental reult within a relative error of 1%. Therefore, the preented model i uitable for predicting the enitivity of a thermal flow enor. From Fig. 3, the heat tranfer phenomena in the thermal flow enor can be explained. A hown in Fig. 3(a), the temperature ditribution i ymmetric under a zero flow rate. When nitrogen ga flow through the PDMS channel, the urface temperature of the thermal flow enor in the uptream ection decreae while that in the downtream ection increae due to convection []. The temperature of the thermal flow enor reache it equilibrium ditribution when a balance exit among heat generation, flow convection, axial conduction, and heat lo. Thi ditribution become aymmetric, a hown in Fig. 3(b) and (c). Moreover, a higher ma flow rate implie a lower the urface temperature at the uptream ection of the channel and a higher urface temperature at the downtream ection of the channel. Thee phenomena are identical to the heat tranfer phenomena occurring in the circular enor tube of the MFC (ma flow controller) tudied by Kim and Jang []. Fig. 4 how that the poition of temperature enor affect the enitivity of the thermal flow enor. A hown in Fig. 4, the temperature difference meaured uing the enor located near the heater i larger compared to that obtained uing enor located further away from the heater for a fixed ma flow rate. Thi implie that the enitivity decreae a the ditance between the temperature enor increae. Finally, baed on the numerical reult, a correlation that predict the enitivity i obtained according to Eq. (1). The correlation i given a # Sðk t A t Þ D3 3 ¼ exp 4 D q 3 1 þ D 5 ð6þ C f k t A t R r where D 1 ¼ 4:6 þ :4 þ 15:8 h 1: # D ¼ :66 þ 7:54 15:8 þ 9:59 # 3 D 3 ¼ :14 þ :7 :5 # In Eq. (6), Sðk t A t Þ =q 3 C f i the dimenionle enitivity and =k t A t R r i the dimenionle radial heat lo. The correlation baed on the numerical reult can be applicable for b c Flow Rate = 3 SCCM Numerical Reult Experimental Reult Flow Rate = 5 SCCM Numerical Reult Experimental Reult Fig. 3. Temperature ditribution (input power =.8 W). (a) SCCM. (b) 3 SCCM. (c) 5 SCCM. :1 < < 1; : < k t A t R r < :6; :1 < h < :6 ð7þ Fig. 5 how the enitivity obtained both from the numerical reult and from the correlation. The correlation predict the numerical reult within a relative error of 1%. By uing the propoed correlation, the effect of the poition of the temperature enor on the enitivity can be invetigated. A hown in Fig. 5,

4 T.H. Kim et al. / International Journal of Heat and Ma Tranfer 5 (9) Temperature Difference [ C] q =.8 W Numerical Reult / =. / =.4 / =.6 Experimental Reult / =. / =.4 / = Flow Rate [SCCM] Fig. 4. Relationhip between the temperature difference and the flow rate. S(k t A t ) /q' 3 C f.1 1E -5 1E -8 h / =.11 Numerical Reult / =. / =.4 / =.6 Correlation / =. / =.4 / =.6 Experimental Reult / =. / =.4 / =.6 1E /k t A t R r Fig. 5. Comparion between the enitivity value from the correlation, the numerical reult, and the experimental reult. heat lo i cloely related to enitivity. The enitivity increae a the heat lo decreae. In addition, when =k t A t R r < 1, the enitivity increae a = increae. In contrat, when =k t A t R r > 1, the enitivity decreae a = increae. A the experimental condition in thi paper i under =k t A t R r > 1, the experimental reult how that the enitivity decreae a = increae. Fig. 6 how the enitivity for variou h = and = value. A hown in Fig. 6(a), when =k t A t R r < 1 the enitivity increae a h = increae regardle of the value of =. However, a hown in Fig. 6(b), when =k t A t R r > 1 the tendency of the enitivity i different from that of the enitivity under the condition of =k t A t R r < 1: Although the enitivity increae a h = increae, when h = < :35, the enitivity decreae a = increae. On the other hand, when h = > :35, the enitivity increae a = increae. 5. Concluion In thi tudy, the enitivity of a thermal flow enor i tudied. A imple numerical model for analyzing heat tranfer phenomena in a thermal flow enor i preented. Additionally, the propoed model i validated by experimental data. Baed on the verified numerical model, a correlation that predict the enitivity of a thermal flow enor i obtained. From the correlation, it i hown that the heat lo, the poition of temperature enor, the input power, and the heater length affect the enitivity of a thermal flow enor.

5 144 T.H. Kim et al. / International Journal of Heat and Ma Tranfer 5 (9) Acknowledgement Thi work wa upported by the Korea Science and Engineering Foundation (KOSEF) through the National Reearch aboratory Program funded by the Minitry of Science and Technology (No. M1646J41). Reference [1] N.T. Nguyen, Micromachined flow enor review, Flow Mea. Intrum. 8 (1997) [] S.J. Kim, S.P. Jang, Experimental and numerical analyi of heat tranfer phenomena in a enor tube of a ma flow controller, Int. J. Heat Ma Tranfer 44 (1) [3] I.Y. Han, D.-K. Kim, S.J. Kim, Study on the tranient characteritic of the enor tube of a thermal ma flow meter, Int. J. Heat Ma Tranfer 48 (5) [4] T.S.J. ammerink, N.R. Ta, M. Elwenpoek, J.H.J. Fluitman, Micro-liquid flow enor, Sen. Actuator A (1993) [5] N. Sabate, J. Santander,. Foneca, I. Gracia, C. Cane, Multi-range ilicon micromachined flow enor, Sen. Actuator A 11 (4) [6] S.-C. Roh, Y.-M. Choi, S.-Y. Kim, Senitivity enhancement of a ilicon micromachined thermal flow enor, Sen. Actuator A 18 (6) 1 6. [7] T.H. Kim, S.J. Kim, Development of a micro-thermal flow enor with thin-film thermocouple, J. Micromech. Microeng. 16 (6) [8] D.-K. Kim, I.Y. Han, S.J. Kim, Study on the teady-tate characteritic of the enor tube of a thermal ma flow meter, Int. J. Heat Ma Tranfer 5 (7) h i Fig. 6. The enitivity log 1 Sðk ta tþ =q 3 C f =k ta tr r < 1. (b) =k ta tr r > 1. for variou h = and =. (a)

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