Dual-tracer fluorescence thermometry measurements in a heated channel

Exp Fluids (2010) 49:257–266 DOI 10.1007/s00348-010-0853-9 RESEARCH ARTICLE Dual-tracer fluorescence thermometry measurements in a heated channel Myeongsub Kim • Minami Yoda Received: 13 July 2009 / Revised: 19 February 2010 / Accepted: 22 February 2010 / Published online: 13 March 2010 Ó Springer-Verlag 2010 Abstract The exponential growth of component density in microelectronics has renewed interest in compact and high heat flux thermal management technologies that can handle local heat fluxes exceeding 1 kW/cm2. Accurate and spatially resolved thermometry techniques that can measure liquid-phase temperatures without disturbing the coolant flow are important in developing new heat exchangers employing forced-liquid and evaporative cooling. This paper describes water temperature measurements using dual-tracer fluorescence thermometry (DFT) with fluorescein and sulforhodamine B in laminar Poiseuille flow through polydimethyl siloxane-glass channels heated on one side. The major advantage of using the ratio of the signals from these two fluorophores is their temperature sensitivity of 4.0–12% per °C—a significant improvement over previous DFT studies at these spatial resolutions. For an in-plane spatial resolution of 30 lm, the average experimental uncertainties in the temperature data are estimated to be 0.3°C. 1 Introduction In 1965, Gordon Moore of Intel predicted that the density of transistors on a computer chip would double every two years. Since then, the microelectronics industry has managed to follow Moore’s Law, with a doubling in component density every 18–24 months. This exponential growth in component density has however created huge thermal M. Kim  M. Yoda (&) George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA e-mail: minami@gatech.edu M. Kim e-mail: mskim@gatech.edu management challenges as more and more transistors (the Intel dual-core Itanium 2, released in 2006, contains 1.7 billion transistors, for example) dissipate more and more heat. Chip average heat fluxes are projected to approach 100 W/cm2 within a decade (ITRS 2006), with local heat fluxes over hot spots with areas of O(103 lm2) up to an order of magnitude greater than this value. Even with the latest advances in heat sinks, forced-air cooling cannot dissipate heat fluxes of this magnitude and still meet size and space restrictions. Future microprocessor designs will therefore require new single-phase (liquid) and two-phase (evaporative) thermal management technologies with micron-scale addressability such as microchannel networks, jet and spray arrays, heat spreaders and thermosyphons (Asheghi and Yang 2005). A single chip cooled by a microchannel heat sink with a footprint of a few cm2 will need a network of up to several hundred microchannels connected by numerous manifolds for adequate cooling at such high heat flux values. Although thermal transport (due, presumably, to laminar flows) in such microchannel networks can be numerically simulated, these simulations require significant computation time because of the geometric complexity of these networks. These simulations are made even more complex by the spatial variations in heat flux due to chip ‘‘power maps,’’ i.e., the power dissipation profile. Such simulations are therefore too time-consuming at present for design optimization purposes. ‘‘Reduced order’’ models, which predict thermal performance using heat transfer correlations, are a more efficient way to design and optimize the cooling performance of such microchannel networks. It is unlikely, however, that classic convective heat transfer correlations apply to microchannel networks, because thermal coupling between the channels cannot be neglected due to heat spreading via the high thermal 123 258 Exp Fluids (2010) 49:257–266 conductivity of silicon, the leading material for microelectronic components and MEMS devices. By Newton’s Law of Cooling, the local heat flux normal to the surface q00s ¼ h ðTs  Tm Þ ð1Þ where h is the local heat transfer coefficient, and Ts and Tm are the local wall surface and mean (bulk) fluid temperatures, respectively. Developing local heat transfer correlations for various microchannel array geometries therefore requires accurately measuring the difference between the wall and bulk temperatures. Although a number of techniques such as infrared thermometry (IRT) can be used to measure Ts with good spatial resolution in many cases, there are far fewer techniques that can accurately and nonintrusively measure mean fluid temperatures, especially at micro(meter-)scale resolution. Although variations in the emission lifetime of phosphorescent and fluorescent compounds with temperature have been used for liquid thermometry (Hu et al. 2006; Mendels et al. 2008), the most commonly used optical technique is fluorescence thermometry (FT), which exploits the changes in the emission intensity of various fluorophores (Nakajima et al. 1990). For a given fluorophore solution at a known molar concentration C, the emission intensity imaged at a given location If ðTÞ ¼ AIo gðTÞ ð2Þ where A is related to the collection efficiency of the imaging system, and Io is the intensity of the excitation (i.e., illumination). The temperature-dependent portion of If, g(T), depends on the quantum yield and the molar absorption coefficient of the fluorophore. The majority of FT studies use the temperature-sensitive species rhodamine B (RhB), usually excited at a wavelength of 532 nm, to measure water temperatures ranging from *20°C to *60°C (Coolen et al. 1999; Seuntiëns et al. 2001). The accuracy of FT is improved by using a ratiometric approach where the variations in emission intensity reflecting the temperature distribution are decoupled from those due to nonuniformities in the excitation intensity. Dual-tracer FT (DFT) takes the ratio of the emissions from two different fluorescent species, A and B, excited by the same illumination (so IoA ¼ IoB ): I 0 ðTÞ  IfA ðTÞ gA ðTÞ / : IfB ðTÞ gB ðTÞ ð3Þ Coppeta and Rogers (1998), who summarized the properties of a number of temperature-sensitive species, demonstrated in their ‘‘dual-emission’’ technique that the ratio of the signals from fluorescein (Fl) and RhB gave a 2D mean steady-state temperature fields in a thermal plume with an accuracy of 1.8°C. Sakakibara and Adrian (2004) 123 used the ratio of the emissions from RhB and Rhodamine 110 (Rh110) instead to measure water temperatures with an accuracy of 0.17°C. Two-color and three-color FT takes instead the ratio of the emissions from a single species over two and three distinct wavelength bands, respectively, from a single excited fluorophore. Lavieille et al. (2001, 2004) used RhB to measure temperatures in a combusting and evaporating ethanol spray and reported accuracies of 1°C for two-color FT and 0.5–1°C for three-color FT. More recently, fluorescence thermometry has also been used to measure temperature fields in micron-scale flows with a spatial resolution of O(10–100 lm). Ross et al. (2001) used RhB to measure bulk temperatures in electrokinetically driven flows in a 1-cm-long microchannel with a trapezoidal cross-section of 30 9 20–75 lm at an estimated precision of 2.4–3.5°C for fluid temperatures ranging from 15 to 90°C. Kim et al. (2003) used RhB and Rh110 in their ‘‘ratiometric’’ technique to measure steadystate temperature fields for the buoyancy-driven flow inside a 1 9 10 9 45 mm test cell and reported uncertainties (based on 95% confidence intervals) of 2–0.4°C for spatial resolutions of 150–1,200 lm, respectively. Natrajan and Christensen (2009) used RhB and sulforhodamine 101 (Sr101) to measure the steady-state temperature gradient maintained across an array of parallel microchannels by hot and cold thermal reservoirs and reported standard deviations as great as 0.6 and 0.5°C for ethanol and water temperatures, respectively, at a spatial resolution of about 22 lm. The majority of DFT studies use a temperature-sensitive species, such as RhB, and a temperature-insensitive species, such as Rh110, where the signal from the latter should be directly proportional to the excitation intensity. More recently, however, it has been shown that the accuracy of DFT can be further improved by using two temperaturesensitive species whose temperature sensitivities are ‘‘inverted,’’ where ogA =oT [ 0 and ogB =oT\0. Shafii et al. (2009) reported temperature sensitivities of 4% per °C in their macroscale studies of solidification using Fl and sulforhodamine B (SrB), while Sutton et al. (2008) found temperature sensitivities ranging from 4.5 to 6.5% per °C using fluorescein 27 and RhB. These sensitivities are a major improvement over the values of -1.7 and -2.7% per °C reported by Sakakibara and Adrian (2004) and Natrajan and Christensen (2009), respectively, in their DFT studies. In the experiments described here, water temperatures were measured using Fl and SrB in the laminar (Reynolds numbers of 3 and 8) Poiseuille flow over a *23-lm-thick ‘‘slice’’ of the flow near the wall of a square channel heated along one sidewall. Given that this flow is steady, the emissions from the two species were imaged by the same camera separated by a few seconds using different filters. Exp Fluids (2010) 49:257–266 The setup used here therefore cannot capture time-resolved (i.e., instantaneous) temperature field data, but, as demonstrated by Shafii et al. (2009) for Fl and SrB, as well as by other researchers for other fluorophore pairs (Sakakibara and Adrian 2004; Natrajan and Christensen 2009), the DFT technique can measure transient temperature fields using two cameras with appropriate filters. The results presented here are, to our knowledge, the first time that DFT using two species with inverted temperature sensitivity has been used and validated at micronscale spatial resolutions. Section 2 describes the aqueous solution of the two temperature-sensitive fluorescent dyes, fluorescein (Fl) and sulforhodamine B (SrB) and then details the heated channel and optical system used in these studies. Results from in situ calibration studies of the temperature sensitivity of Fl and SrB illuminated volumetrically at 514 nm, as well as the temperature sensitivity of the ratio of the Fl and SrB signals, are also presented. Section 3 details numerical simulations performed with the computational fluid dynamics (CFD) software package FLUENT to validate these DFT data, which were obtained in the presence of a significant temperature gradient within the fluid. Section 4 presents and discusses the initial DFT temperature results and compares them with the numerical predictions, while Sect. 5 summarizes this work. 2 Experimental description 2.1 Fluorophore solution The majority of temperature-sensitive fluorophores have a quantum yield, and hence an emission intensity, that decreases with increasing temperature, because the nonradiative dissipation in most cases increases with increasing temperature. Fluorescein, however, has an emission intensity that, when excited at a wavelength k = 514 nm 259 (significantly off its absorption peak), increases with increasing temperature, because its absorption at 514 nm also increases with temperature (Coppeta and Rogers 1998). Although there are several fluorophores whose emission intensity decreases with increasing temperature, SrB was chosen among these as the second species because: (1) it can also be excited at 514 nm due to its relatively broad absorption spectrum; and (2) its emission band, with a peak at 591 nm, has little overlap with that of Fl, with a peak at 518 nm (Shafii et al. 2009). Figure 1 shows the normalized absorption spectrum measured by a spectrometer (HR4000CG-UV-NIR, Ocean Optics, Inc.) (left) and the normalized emission spectrum measured by a fluorescence spectrometer (QuantaMaster, PTI, Inc.) (right) as a function of wavelength k for 5 lmol/L Fl (solid line) and 5 lmol/L SrB (dashed line) both in the same aqueous solution, at pH 9.2. The absorption spectra verify that both Fl and SrB can be excited at a wavelength of 514 nm. The emission spectra show that the fluorescence from the Fl and the SrB can be isolated from each other using appropriate filters. Shafii et al. (2009) isolated the SrB emissions from those of the Fl using a longpass filter that only transmitted light at k C 600 nm and reported that the leakage of Fl emissions through this filter, or ‘‘cross-talk’’ with the Fl, was no more than 0.1% of the total signal. In microscale thermometry, it is especially important to ensure that the fluorophores have minimal surface adsorption on channel materials such as silicate glasses, silicon (oxide) and polydimethyl siloxane (PDMS) to minimize background noise in geometries where the surface area to volume ratio is significantly greater than that at the macroscale. Although RhB is often used in FT because of its marked temperature sensitivity, most of the rhodamine dyes are zwitterions with a positively charged portion that strongly adsorbs onto negatively charged surfaces such as glass, silicon and PDMS at moderate pH. Aqueous Fig. 1 Absorption (left) and emission (right) spectra for Fl (solid line) and SrB (dashed line). The arrows on both spectra indicate the excitation at 514 nm; the shaded and hatched regions on the emission spectrum denote the wavelengths transmitted by the filters that isolate the emissions from Fl and SrB, respectively 123 260 Exp Fluids (2010) 49:257–266 solutions of 10 lmol/L Fl, where the Fl is a divalent anion in solution, and 10 lmol/L SrB, both at pH 9.2, were found to have negligible adsorption on fused-silica surfaces at temperatures of 20–60°C (Suda-Cederquist 2007). Dual-tracer fluorescence thermometry was used to measure temperature fields in an aqueous solution of 5 lmol/L fluorescein, 5 lmol/L sulfohodamine B and 7 mmol/L sodium tetraborate (Na2B4O7), which was prepared by dissolving appropriate amounts of the disodium salt of Fl (FL116, Spectrum Chemical), the sodium salt of SrB (86183, Fluorescence grade, Fluka), and the decahydrate salt of Na2B4O7 (ACS reagent grade, Acros Organics) in deionized water. The addition of the tetraborate salt ensured that the solution pH was 9.2 at a solution temperature of 19°C, as measured by a pH meter (WD-3561420, Oakton), to maximize the quantum yield of Fl. The pH of the Fl-SrB solution varied by no more than 0.2 pH units as the solution temperatures varied from 20 to 60°C. The solution was filtered through 1.5 lm pore size filter paper (09-804-70A, Grade G6, Fisher Scientific) with a Büchner funnel and degassed by a vacuum pump for [2 h before use. 2.2 Heated channel and optical setup The temperature of the Fl-SrB solution was measured in Poiseuille flow through a channel with a square crosssection 1 mm on a side and a length of 28 mm heated on one side. The channel (Fig. 2) was molded in a block of polydimethyl siloxane (PDMS) of nominal dimensions 35 9 25 9 5 mm, which was cured using standard procedures (Duffy et al. 1998) at 60°C for 12 h and plasma oxidized to make the PDMS surface hydrophilic. A 50-W cartridge heater (FIREROD, Watlow), 3 mm in diameter and 31 mm in length, was embedded in the PDMS at a minimum edge-to-edge distance of 0.5 mm from the channel sidewall to create a temperature gradient across the channel. The 1-mm square trench in the PDMS block was sealed by a fused-silica ‘‘lid’’ (44.5 9 44.5 9 1 mm) on the bottom. The PDMS sides of the channel were exposed to the atmosphere under ambient conditions, while the fused-silica bottom of the channel sat upon a steel microscope stage. A syringe pump (NE-500, New Era Pump System, Inc.) drove the Fl-SrB solution through the PDMS-glass channel at volume flow rates of Q = 1 and 8 lL/s. The Reynolds numbers Re for these two Poiseuille flow cases based on the channel cross-sectional dimension and average speed were 1 and 8, respectively. The pump was connected to the channel inlet port by 0.8-mm ID silicone tubing (51134K14, McMaster-Carr), and the solution was discarded after exiting the channel through more 0.8-mm ID silicone tubing attached to the outlet port. The temperature of the fluid inside the channel T was monitored by two T-type miniature thermocouples (TC) (HYP1-30-1/2-T-G-60-SMPW-M, Omega Engineering, Inc.) with a bead diameter of 0.3 mm, which were inserted through the PDMS block and placed symmetrically upstream and downstream of the imaged region roughly in the center of the channel with a streamwise spacing of about 1.2 cm (cf. Fig. 2). The TC were calibrated to an accuracy of 0.2°C, and the TC readings were recorded by an A/D data acquisition board (HP34970A, Agilent Technologies) onto a PC HD. For all experiments, the PDMS-glass channel was placed on the steel stage of an inverted microscope (DM IL, Leica), and the entire channel cross-section of the channel was volumetrically illuminated by a light sheet formed from the 60 mW beam at k = 514 nm of an argonion laser (543-MA-A03, Melles Griot) passing through an excitation filter (z514/109, Chroma Tech). The power of the illumination beam varied by no more than 1% over 5 h, 35 mm Heater Flow 25 mm Channel Heater 1 mm TC 1 0.5 Lid Stage TCs Filters Objective Top View Fig. 2 Top (left) and side (right) views of the channel with singlesided heating. The checkered rectangle and line (in the channel) indicate the region imaged by the microscope objective in the top and 123 Side View side views, respectively. Flow goes from left to right in the top view and out of the page in the side view Exp Fluids (2010) 49:257–266 as measured by a laser power meter (Lasermate Q, Coherent). As shown in Fig. 2, the fluorescent emissions from a ‘‘slice’’ of the flow just above the fused-silica wall were imaged through the bottom of the channel by a 109 magnification, 0.25 numerical aperture microscope objective (506084, N Plan, Leica) and appropriate filters and recorded by a CCD camera (Pixelfly vga, Cooke Corporation) with an intensifier (VS4-1845, OPELCO, Inc.) as 640 9 480 pixels 8-bit images on a PC HD. The Fl emissions from a ‘‘slice’’ of the flow just above the fusedsilica wall were imaged through a bandpass filter (NT48083, Edmund Optics) that only transmitted light at k = 529–555 nm (shaded region, Fig. 1). The SrB emissions were isolated from those of the Fl by a longpass filter (NT47-618), Edmund Optics) that only transmitted light at k C 600 nm (hatched region, Fig. 1), similar to that used by Shafii et al. (2009). A sequence of 140 images spanning 3.4 s of the emissions from Fl and SrB was recorded at a framing rate of 41.7 Hz and an exposure of 20 ms. Both sequences were recorded within a few seconds of each other by switching between the appropriate filters that were next to each other in a translating filter holder. The thickness, or dimension along the optical axis, of the imaged region was estimated to be about 23 lm, based on the depth of field of the objective. The magnification of the imaging system, determined from a scale with 20 lm divisions, was measured to be 2.67, corresponding to 3.7 lm/pixel for the 9.9 lm CCD pixels. The physical dimensions of the 640 9 480 images are therefore 2.37 9 1.78 mm. The relationship between the emission intensity incident upon the intensified CCD camera and the resultant grayscale recorded on the digital image was found to be somewhat nonlinear. Camera calibrations were therefore performed to determine this relationship. Since Fl and SrB have different emission spectra and different quantum yields when excited at 514 nm, separate calibrations were performed for the emissions from these two species for a range of fluorophore concentrations, illumination intensities and imaging parameters. The fluorescence intensity for both species was found to be well approximated by secondorder polynomials, with an adjusted coefficient of determination R2 ¼ 99:7% and a root mean squared error (RMSE) below 1%. 261 passing the fluid through a copper-coil heat exchanger consisting of 15 m of 1.5 mm ID copper tubing immersed in a constant-temperature circulating water bath (GH-D8, Haake) before entering the PDMS-glass channel. The Reynolds number for the laminar Poiseuille flow Re based on the channel cross-sectional dimension of 1 mm, and average speed was 67, corresponding to a volume flow rate Q = 0.067 mL/s, to minimize thermal losses. Since no power was supplied to the cartridge heater during these calibrations, the fluid temperature T was determined by the set point temperature of the water bath. Data were acquired at least 20 min. after flow startup when the TC readings were within 0.2°C (i.e., the measurement accuracy of the TC) of the set point temperature of the water bath. As described previously, two sequences, each 140 images long, were acquired of the Fl and SrB emissions. After compensating for camera nonlinearities, the grayscale values were spatially averaged over a 150 9 250 pixels (0.56 9 0.93 mm) region in the center of the channel (Fig. 3) and then temporally averaged over all 140 (sub-)images in the sequence. Figure 4 shows this average  normalized by that at 20°C, I20 , as a function of intensity, I, solution temperature T measured by the TC at T = 20– 60°C for Fl (red triangles) and SrB (blue circles). The error bars denote the standard deviation of the data. The fluorescence from Fl increases by about 2.44% per °C, based on a linear curve-fit, whereas the signal from SrB decreases by about 1.54% per °C. Both values are in good agreement with the 2.43% per °C and the 1.55% per °C reported by Coppeta and Rogers (1998) for Fl and SrB, respectively. The calibration results for Fl and SrB were consistent over multiple independent experiments. The ratio of these two normalized signals, I 0 (gray squares), clearly has much greater variation with temperature than either the normalized Fl or SrB emissions, increasing from 1 at T = 20°C to about 4.0 at T = 60°C. A fifth-order polynomial curve-fit (R2 = 99.7%, RMSE = 0.06%) to I 0 (solid line, Fig. 4) gave: 2.3 Fluorescence thermometry calibrations Calibrations of the temperature response of the Fl-SrB solution at temperatures T = 20–60°C were performed in the same channel with the same optical system as those used in the DFT experiments. The temperature of the working fluid in the channel was kept at a constant value by Fig. 3 A typical 640 (columns) 9 480 pixels (rows) calibration image of SrB at T = 20°C showing the 150 9 250 pixels (0.56 9 0.93 mm) region in the center of the channel used for the temperature calibrations. The edge of the cartridge heater is just visible on the right side 123 262 Exp Fluids (2010) 49:257–266  I20 as a function Fig. 4 Average normalized fluorescence intensity I= of solution temperature T for Fl (triangles) and SrB (circles). The ratio of these two normalized intensities I0 (squares) is also given as a function of T, along with a fifth-order polynomial curve-fit to these data (solid line), given by Eq. 4 I 0 ¼ 1:64  107 T 5  3:21  105 T 4 þ 2:41  103 T 2  8:49  102 T þ 1:44 T  8:52 ð4Þ where the temperature T is measured in °C. The slope of Eq. 4 gives temperature sensitivities dI 0 =dT ranging from 4.0% per °C at T = 20°C to 12% per °C at T = 60°C, suggesting that this technique has greater sensitivity at higher temperatures. Nevertheless, these sensitivities are significantly higher than the -2.7% per °C reported by Natrajan and Christensen (2009) in their microscale DFT studies. A fifth-order polynomial curve-fit to the temperature as a function of I 0 (R2 ¼ 99:6%; RMSE = 0.6°C) gave: T ½ C ¼ 47:83 ðI 0 Þ5 þ 250:8 ðI 0 Þ4  476 ðI 0 Þ3 þ 384:7 ðI 0 Þ2  85:41 I 0 þ 14:64 ð5Þ Equation 5 was used to determine liquid-phase temperatures for the results presented in Sect. 4. The absorption and emission spectra shown in Fig. 1 suggest that there may be some ‘‘cross-talk’’ between the Fl and SrB emissions and that a small amount of the Fl emissions may be imaged through the longpass (k C 600 nm) filter. Moreover, the emission band of Fl and the absorption band of the SrB have some overlap, suggesting that some of the emissions from Fl may excite the SrB, resulting in ‘‘spectral conflict.’’ Both of these phenomena are issues for DFT with a single illumination source. To evaluate the effects of cross-talk and spectral conflict, three 140-image sequences were acquired of the flow 123 of three different solutions: the Fl-SrB-tetraborate solution, 5 lmol/L Fl and 7 mmol/L Na2B4O7, and 5 lmol/L SrB and 7 mmol/L Na2B4O7 at T = 55°C. This temperature, near the upper end of the temperature range studied here, was chosen to maximize cross-talk and spectral conflict, since the Fl emissions will be stronger, and the SrB emissions weaker, at higher T. All three sequences were acquired in the same setup used for the FT calibrations under identical experimental conditions within a single experimental run over *90 min by switching between syringes in the syringe pump. In all cases, the emission intensities recorded for all three solutions were identical within the standard deviations of the images, suggesting that these effects are negligible. These results are in agreement with those reported by Shafii et al. (2009) who reported that cross-talk and spectral conflict were negligible for 0.5 lmol/L Fl and 0.5 lmol/L SrB over optical pathlengths of at least 1 cm. 3 Numerical simulations The DFT results were validated by 3D finite-volume simulations of steady laminar flow through the channel using the commercial CFD software package FLUENT v6.2 run on a 2.4 GHz PC. Most of the channel, namely the entire cartridge heater, the PDMS block, the fused-silica lid and the steel microscope stage (cf. Fig. 3 (right)), was simulated in the numerical model, which consisted of 3 9 106 cells meshed using a hybrid tetrahedral scheme with a spatial resolution of 50 lm inside the channel. Computational limitations (specifically, the RAM on the PC was limited to 3.5 GB) precluded using a finer mesh to improve the spatial resolution of these simulations. Given that the average difference between the temperatures obtained at spatial resolutions of 50 and 100 lm was 0.09°C, however, linear interpolations of these numerical predictions should be a good estimate of the temperatures in the flow at finer spatial resolution. The temperatures were assumed to achieve steady state after 3 9 103 iterations, based on convergence tests for temperatures obtained over up to 104 iterations. In all cases, the numerical simulation results, averaged over the 0.3 mm diameter of the TC bead, were consistent with the TC readings at the corresponding locations. The inlet temperature boundary condition was the temperature measured in the FT experiments. Standard free-convection boundary conditions from empirical correlations for external flows (Incropera and DeWitt 2002) were imposed on the surfaces exposed to ambient conditions. The Churchill–Chu correlation for the average Nusselt number NuL for free convection from a vertical wall based on the average surface temperature was Exp Fluids (2010) 49:257–266 263 used for the sides of the PDMS block at typical Rayleigh numbers RaL ¼ Oð102 Þ: 1=4 0:67RaL NuL ¼ 0:68 þ h  9=16 i4=9 1 þ 0:492 Pr ð6Þ where Pr is the Prandtl number. An adiabatic boundary condition was imposed on the (vertical) side surfaces of the fused-silica lid since the heat transfer through the 1-mmthick lid was, as verified by FLUENT simulations, negligible compared to that through the top and bottom surfaces of the lid. For the upper surfaces of the glass lid and the PDMS block with RaL ¼ Oð105 Þ and RaL ¼ Oð106 Þ, respectively, the standard power-law correlation for free convection from the upper surface of a heated horizontal plate was used: 1=4 NuL ¼ 0:54RaL : ð7Þ Finally, for the bottom surface of the glass lid (i.e., that contacting the microscope stage) with RaL ¼ Oð106 Þ, the correlation for a lower surface of a heated plate was used: 1=4 NuL ¼ 0:27RaL : ð8Þ Because heat was only generated over the central 19.3 mm (axial extent) of the cartridge heater, a constant heat-generation rate boundary condition was imposed at the cartridge heater over this central section. Freeconvection boundary conditions were imposed over the Inconel surface of the rest of the heater, where the average Nusselt number for this heated vertical cylindrical surface at typical RaL ¼ Oð105 Þ was that given by Eq. 6 scaled by the transverse curvature parameter n, which was 1.383 for this geometry (Cebici 1974). The heat-generation rate was taken to be 90% of the electrical power input to the heater divided by the volume of the 19.3 mm long, 3 mm diameter central section. In this experimental setup, some of the power input to the heater will be dissipated in the solid portions of the channel (vs. transferred to the fluid) and the surroundings, since the upper portion of the cartridge heater is exposed to the atmosphere at ambient conditions. Given the difficulties in accurately estimating this thermal dissipation, the percentage of the input power transferred to the fluid was adjusted to a value that gave numerical predictions that were consistent with the DFT results in terms of the temperature change across the channel. It was assumed that only 90% of the input power was transferred to the flow for all the cases presented here. The major source of error in the numerical predictions is therefore due to error in estimating the fraction of the input power transferred to the fluid. 4 Results and discussion Experiments were then carried out for laminar steady Poiseuille flow subject to a temperature gradient across the channel at Reynolds numbers Re = 1 and 8 (corresponding to Q = 1 and 8 lL/s, respectively). The channel was now heated by the cartridge heater at an edge-to-edge distance of 0.5 mm from the sidewall supplied with 1.4 W (20 V at 69 mA) from a DC power supply (E3612A, Agilent Technologies). The temperature field in this laminar and steady flow was assumed to have reached steady state once the temperature reading from the TC downstream of the imaged region (cf. Fig. 2 (left)) varied by no more than 0.2°C over 2 min. Two sequences of 140 images, spanning 3.4 s of the emissions from Fl and SrB, were recorded within a few seconds of each other. The 640 9 480 pixel images of the emissions over a 23-lm-thick slice of the flow were truncated to 384 9 480 pixel images, corresponding to a physical field of view of 1.4 9 1.8 mm, centered about the channel, which was 277 pixels across. Figure 5 shows representative images of the Fl (left) and the SrB (right) emissions. Both images are mapped to the same set of grayscales, and, as expected, the Fl emissions are for the most part weaker than those of the SrB when excited at 514 nm. The truncated images were then corrected for camera nonlinearities, and the average grayscale value and the standard deviation in the grayscale value were calculated over all 140 images. The ratio of the Fl and SrB images was used to determine I 0 ; and a standard uncertainty propagation analysis was used to determine the uncertainty in the resultant temperature from the standard deviations of the Fl and SrB images. At Re = 1, the uncertainties were ±1 and 0.3°C at spatial resolutions of 3.7 lm (1 pixel) and 30 lm (8 pixels), respectively. At Re = 8, the uncertainties in the temperatures obtained using DFT were ±1.1 and 0.3°C at the same spatial resolutions. Given that the spatial resolution of these data normal to the image plane (i.e., along the optical axis) was *23 lm based on the depth of field of the microscope objective, the DFT data were averaged over a region 8 pixels, or 30 lm, square. Figure 6 compares pseudocolor temperature maps over a 1.1 9 1 mm region of the flow adjacent to the heater based on numerical predictions from FLUENT at a spatial resolution of 50 lm (left column) with those obtained from the DFT results for I 0 using Eq. 5 at a spatial resolution of 30 lm (right column) with at Re = 1 (top row) and 8 (bottom row). The DFT results for this 2D temperature field are in reasonable qualitative agreement with the numerical predictions. To quantitatively compare the numerical and experimental results, the temperature profile across the channel, 123 264 Exp Fluids (2010) 49:257–266 Fig. 5 Typical 640 9 480 pixels (2.37 9 1.78 mm) grayscale images at an exposure of 20 ms of Fl (left) and SrB (right) heated on one side at Re = 1. The white rectangle denotes the 384 9 480 DFT FLUENT T [°C] 50 0.5 1.1 mm Re = 1 Flow Heater Fig. 6 Pseudocolor map of water temperatures over a 1.1 9 1 9 23 lm region near the bottom of the channel at Re = 1 (top row) and Re = 8 (bottom row) predicted using FLUENT at a spatial resolution of 50 lm (left column) measured using DFT at an inplane spatial resolution of 30 lm and (right column). The dashed line represents the streamwise location where temperature profiles were extracted across the channel, or along the y-direction pixels (1.4 9 1.8 mm) region processed in these images. The edge of the heater is again just visible on the right side of both images 40 1 mm T [°C] 33 Re = 8 Flow 25 or along y, was extracted from both the DFT and FLUENT temperature maps shown in Fig. 6 at the streamwise location where the edge of the heater is at its minimum distance of 0.5 mm from the side wall of the channel (dashed line in Fig. 6). Figure 7 compares these temperature profiles across the channel (where the coordinate across the channel, y, is normalized by channel y-dimension L = 1 mm) measured by DFT using Eq. 5 (triangles) with those predicted by the FLUENT simulations (circles) at Re = 1 (a) and 8 (b). The error bar denotes the uncertainty in the temperature measured by DFT. To estimate the discrepancy between the DFT results and the numerical predictions, which are obtained at different spatial resolutions, fifth-order polynomials were 123 y curve-fit to both sets of temperature data (with R2 [ 0:995 in all cases), and the average discrepancy was determined between these data sampled at a spatial resolution of 30 lm. These discrepancies were 0.1 and 0.3°C at Re = 1 and Re = 8, respectively. At the higher Re, the DFT results are mostly higher than the numerical predictions, which may be due to errors in the FLUENT simulations. As discussed in Sect. 3, it is assumed that 90% of the input power is transferred to the fluid, and enhanced convection at the higher flow rate should increase heat transfer to the fluid. For the Re = 8 case, the discrepancy is greatest, 0.4– 0.5°C, for y=L\0:4, or the region of lowest water temperature of *27°C. This increase in the discrepancy at Exp Fluids (2010) 49:257–266 265 Channel y L y Heater L Heater T [°C] Channel Re = 8 Re = 1 y /L y/L Fig. 7 Comparison of fluid temperatures T as a function of normalized channel coordinate y/L measured by DFT at a spatial resolution of 30 lm (triangles) and predicted by FLUENT at a resolution of 50 lm (circles) at Re = 1 (left) and 8 (right). These temperature profiles are obtained at the streamwise location where the heater is nearest the side wall of the channel lower T is likely due to the lower sensitivity of the DFT technique and the relatively low level of Fl emissions at such temperatures. A temperature discrepancy of 0.5°C corresponds to a variation of less than 0.02 in I 0 (dI 0 =dT ¼ 0:035 at T = 27°C) or less than half the stan I20 for Fl (cf. Fig. 4) at the same temdard deviation in I= perature even in the ‘‘ideal’’ case where the temperature is constant over the entire image. These experimental results suggest that dual-tracer fluorescence thermometry using Fl and SrB, fluorophores with inverted temperature sensitivity, can be used to obtain accurate estimates of liquid-phase temperature fields at a spatial resolution of 30 lm, even in the presence of temperature gradients of about 4°C/mm. In both cases studied here, the average discrepancy between the experimental data and the numerical predictions is within the experimental uncertainty of the DFT measurements of 0.3°C. channel with a temperature gradient across the channel of about 4°C/mm are in agreement, on average, with numerical predictions. The largest issue in validating these experimental data is the uncertainty in estimating how much power is actually transferred to the fluid. New channels with thin-film heaters sandwiched between the PDMS block and the glass lid—a configuration where virtually all the input power remains within the channel—will therefore be used in subsequent studies. In terms of future work, combining fluorescence thermometry with evanescent-wave illumination will give liquid-phase temperatures averaged over the first *400 nm next to the wall, which in most cases is effectively the wall surface temperature. Fluorescence thermometry could then be used, with further development, to obtain nonintrusive measurements at the microscale of wall surface and bulk liquid temperatures in the same flow. 5 Summary Acknowledgments This work was supported by the National Science Foundation and Sandia National Laboratories through NSF grant CBET-0625825 from the Thermal Transport Processes Program (Dr. T. L. Bergman, program officer) and the Office of Naval Research through grant N00014-09-1-0298 from the Thermal Management Program (Dr. M. Spector, program manager). The authors thank K. D. Suda-Cederquist and Dr. T. G. Hwang for their help on the Fl and SrB absorption studies. This paper presents dual-tracer fluorescence thermometry results obtained with fluorescein and sulforhodamine B for liquid-phase temperatures. Although this pair of dyes is not novel, this is, to our knowledge, the first application of the Fl/SrB pair to obtain water temperature fields at micronscale spatial resolution for water temperatures ranging from 20 to 60°C. The experimental uncertainties for this method are ±1.1°C at a spatial resolution of 3.7 lm and ±0.3°C at a spatial resolution of 30 lm. These values are an improvement over those reported previously for microscale applications of fluorescence thermometry at similar spatial resolution. The experimental results obtained in steady Poiseuille flow at Re = 1 and 8 through a 1-mm square References Asheghi M, Yang Y (2005) Micro- and nano-scale diagnostic techniques for thermometry and thermal imaging of microelectronic and data storage devices. 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