Infrared temperature measurements in micro-channels and micro-fluid systems

International Journal of Thermal Sciences 50 (2011) 853e868

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Infrared temperature measurements in micro-channels and micro-fluid systems G. Hetsroni*, A. Mosyak, E. Pogrebnyak, R. Rozenblit Department of Mechanical Engineering, Technion e Israel Institute of Technology, 32000 Haifa, Israel

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 July 2010 Received in revised form 18 November 2010 Accepted 6 January 2011 Available online 12 February 2011

This is a critical analysis of the application of infrared technique on devices in the range of tens to hundreds of micro-meters. Such devices are typical in micro-scale systems. Investigations performed during the last decade were used to analyze the specific features of micro-scale IR measurements. The method is illustrated by various examples of heat transfer determination using image analysis of the heater temperature as well as direct measurement of the liquid temperature. Ó 2011 Elsevier Masson SAS. All rights reserved.

Keywords: Infrared technique Temperature measurement Micro-system Micro-channel Heat transfer Boiling

1. Introduction The problem of dissipating high heat fluxes has received much attention due to its importance in such applications as cooling of electronic equipment, micro-heat exchangers and many others. The most effective way of cooling is pumping liquid inside these devices through micro-channels or porous media. The investigation of heat transfer in micro-systems may be conducted using temperature measurements by devices like thermocouples or by thin-film resistance sensors. Typically, surface temperature measurements are performed either by using thermocouples located at some depth below the wallefluid interface of the micro-channel (Qu and Mudawar [1]; Peng and Peterson [2]; Tso and Mahulikar [3]), or by a few thin-film resistance thermometers deposited directly on the bottom side of a silicon (Si) heat sink (Koo et al. [4]; Zhang et al. [5]; Popescu et al. [6]). In these studies, the temperature measurements were restricted to a few local points in the heat sink. The drawback to these methods is that the information on the temperature fields is revealed only for a limited number of points. Moreover, the sensors (thermocouples and sensor wires for electrical current supply) in turn may be considered as some parasitic supplementary heat sinks adversely affecting the precision of the temperature measurements.

* Corresponding author. Tel.: þ972 48 292058; fax: þ972 48 238101. E-mail address: [email protected] (G. Hetsroni). 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.01.006

The IR is a well-established measurement technique in macroscale heat transfer research (Astarita et al. [7]; Carlomagno and de Luca [8]). Micro-scale IR offers the possibility to measure, nonintrusively, local temperatures in geometries in the range of tens to hundreds of micro-meters, dimensions that are typical of components in micro- and meso-scale systems. However, it has received little attention because of the need to account for several sources of measurement errors. Several studies of single- and two-phase flow and heat transfer in micro-channels have been reported in the past 10 years, and are summarized in review papers (Palm [9]; Ghiaasiaan and AbdelKhalik [10]; Sobhan and Garimella [11]; Kandlikar [12]; Hassan et al. [13]). In his review of single- and two-phase micro-channel flows, Palm [9] suggested that heat transfer results of various single-phase flow studies were contradictory, with both high and low Nusselt numbers, Nu, reported for laminar flows. Sikanen et al. [14] presented experimental IR and computational (finite element model) results of temperature distributions of an electrokinetic separation chip. Discrepancies between measurements were attributed to the difficulties in measuring fluid and surface temperatures in micro-channels. Hollingworth [15] measured the local channel wall temperature distribution in single- and two-phase mini-channel flows using thermochromic liquid crystal imaging of the heated side wall. The three other side walls were kept adiabatic. Most of the data presented were for flows in the turbulent or transitional regime, and agreed well with correlations in the literature. Hapke et al. [16] used

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Nomenclature Cp d D h _ m n q Re S T X z

thermal capacity, (J/kg K) inner tube diameter, (m) outer tube diameter, (m) heat transfer coefficient, (W/m2 K) flow rate, (kg/s) refractive index heat flux, (W/m2) Reynolds number area temperature, (K) coordinate along the test section, (m) coordinate across the micro-channels, (m)

Greek

b 3 k

distortion coefficient emissivity thermal conductivity, (W/m K)

IR to examine the outside wall temperature distribution for flow boiling in rectangular micro-channels and concluded that it is possible to detect the streamwise position of flow boiling regions using this technique. Muwanga and Hassan [17] demonstrated the use of un-encapsulated thermochromic liquid crystal thermography to measure the outer surface temperature of a micro-tube. Recently, Patil and Narayanan [18] described an IR technique for direct microchannel wall/near-wall fluid temperature measurement in liquid flows through Si micro-channels. Direct measurement of wall temperature is desirable because it provides for an accurate estimation of the local heat transfer variation along the channel. The study carried out by Hetsroni et al. [19] was among the first where IR was used to analyze the uniformity of the thermal field on the surface of micro-heat sinks. The test module was fabricated from a square-shape silicon substrate of 15  15 mm. The wafer of this device had a system of parallel triangular micro-channels with a base of 250 mm. Xu et al. [20] also measured the temperature field on the backside of a silicon chip surface by a high-resolution highaccuracy IR image system. IR image system was focused on the effective heating area of 15.0  4.2 mm. The authors suggested that the temperature distributions on the back surface of the silicon chip could follow the dynamic change of the transient flow patterns, in spite of the fact that recording rate of the IR image system used in this study was only 4 images per second. They explained a low rate of oscillations by the slow processes of the periodic wetting and dryout. Patil and Narayanan [21] presented an uncertainty analysis of a temperature measurement in convective micro-channel flows using IR. This technique was used to determine both the local temperatures of the visualized channel wall and the liquid temperature near this wall in IR partially transparent heat sinks. Experiments were performed on a 13 mm long, 50 mm wide and 135 mm deep silicon micro-channel with a constant heat flux. Uncertainty in the fluid temperature varies from a minimum of 0.60 K for the Reynolds number, Re ¼ 297 to a maximum of 1.33 K for a Re ¼ 251. This paper discussed sources of a noise in the temperature measurement and the limitations of such technique for this case. The temperature distribution of the wall was recorded by Diaz and Schmidt [22] at a frequency of 150 Hz using an IR camera with experimental accuracy of 0.3 K The test section was a rectangular channel of 0.3 mm height, 12.7 mm width and 200 mm length. Han et al. [23] first demonstrated an micro-infrared, IR mPIV technique by measuring the velocity field in a micro-nozzle with a 300 mm depth and 40 mm throat width. The solid motion of

l n z u

wavelength, (m) kinematic viscosity uncertainty coefficient frequency, Hz

Subscripts av average CR critical FC free convection G,IR IR temperature measurement of a background screen f fluid f,in fluid inlet f,out fluid outlet max maximal w wall W,IR IR temperature measurement of a micro-scale object wall W,TC temperature measurement of a micro-scale object wall by thermocouples

a micro-rotor was also measured with this infrared diagnostic system. The IR mPIV technique was further discussed by Liu et al. [24], who obtained quantitative measurements in micro-tubes at various flow rates. The measurements were shown to agree well with laminar flow theory. Although the IR mPIV technique has shown great promise, implementation of IR mPIV can be difficult due to a low signal-to-noise ratio. IR thermography has recently been applied to micro-fluidic chips (Franssila et al. [25]; Patil and Narayanan [18]). It offers a compromise between spatial resolution, sensitivity and response time. In IR thermography, there are no external species added to the flow, and the flow is undisturbed by the measurement. In this work, IR thermography is applied to study thermal characteristics of a polymer electrophoresis chip under real operating conditions. Precise determination of the temperature distributions under real conditions is one of the most challenging tasks because the temperature changes are typically fast and relatively subtle, on the order of few degrees centigrade. Here, IR thermography was the method of choice because it offers high temporal resolution (w20 ms) with good spatial resolution in combination with a wide field of view and high thermal sensitivity (<20 m K). The method has been applied either with IR transparent materials (Patil and Narayanan [18]), or for mapping of surface temperatures of externally heated micromixers (Golonka et al. [26]), and micro-evaporators (Hardt et al. [27]). Jones et al. [28] carried out infrared micro-particle image velocity measurements in a micro-channel heat sink. Proper thermal design of heat sinks for micro-systems requires an in-depth understanding of the heat transfer processes. Such knowledge may be achieved on the basis of correct temperature measurements in micro-channels of various configurations and locations inside the micro-device. Obtaining such database for micro-systems poses a significant challenge for researchers and designers. The aim of the present paper is to analyze the possibility of the IR technique for the study of heat transfer in micro-systems. The main problem for micro-scale Infrared temperature measurement is deriving high-resolution signal from very small area in the presence of a high noise level from other sources of thermal radiation. Such problem requires high-quality Infrared video technique and imposes some restrictions on the design of the experimental setup. In parallel with requirements for experimental setup, the researchers should carefully develop the measurement procedure and elaborate the procedure of extraction of the data from measured signal through calibration and image processing.

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2. Methodology of infrared measurement in micro-systems 2.1. Basic radiation model

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some background radiation reflected by the object, but the one that falls directly within the field of view of the IR camera. In spite of an undesired radiation of the background is unfocussed spatially it may comprise a considerable part of the total radiation collected by the objective of Infrared camera, because the object is micro-sized. Consider using simplified model of micro-scale IR measurement on the examples.

The heat transfer results obtained in micro-channels show significant differences from those obtained in larger size channels (Palm [9]; Ghiaasiaan and Abdel-Khalik [10]; Sobhan and Garimella [11]; Kandlikar [12]; Hassan [13]). Use of IR technique in experimental studies of convective heat transfer problems have proved to be an effective tool in overcoming several limitations of the standard sensors originating both for temperature measurements and flow visualization. The use of quantitative IR thermography requires the solution of several problems. The problems include accurate characterization of IR system performance and its calibration; the use optics to increase the spatial resolution; the choice of the most appropriate heat flux sensor and its characterization especially with regard to the lateral thermal conduction effects etc. (Astarita et al. [7]; Carlomagno and de Luca [8]; Sikanen et al. [14]). Here, we consider effects of the radiation losses, the body surface emissivity and the correct geometrical identification of the measured points. The basic radiation model of the measurement of a temperature field in the micro-device is presented in Fig. 1. According to this model, in general, the micro-scale object is located between a face layer (nearest to the Infrared camera) and foreground layer. The micro-scale object may represent either any part of the wall surface of the micro-device or liquid in the micro-channel for cooling such devices. In the latter case we will measure the liquid temperature close to the surface. Both the face layer and the foreground layer may be present or omitted in this model according to the characteristics of the microobject studied. The transparency to an Infrared radiation of the face layer and the object may vary from transparent to completely opaque. Each layer and object itself in such model may have different emissivity and temperature. If the face layer is absent in this model or transparent to IR radiation, the detector of the Infrared camera may collect the sum of the emitted and reflected energy coming from the object. We should add to this sum the energy transmitted through the object from the foreground layer (e.g. the heater to model the heat flux) if the object itself is transparent to IR radiation. If the face layer is opaque we can judge the thermal regime of other parts only by indirect way. The detector of the IR camera may collect not only

2.2.1. Temperature measurements on a flat surface For non-intrusive temperature measurements by thermochromic liquid crystal technique the hue-temperature correspondence should be obtained (Hollingworth [15]; Muwanga and Hassan [17]). The main problem is the improvement of precision in the quantitative measurements of the hue. The good results obtained in the last decade by the widespread use of IR in experimental studies of convective heat transfer problems have proved this technique to be an effective tool in these studies. A very convenient method to measure the heat transfer coefficient is the so-called heated thin foil technique. This consists of coating the model surface with a very thin metallic foil and heating it by Joule effect. By measuring the surface temperature it is possible to compute the heat transfer coefficient from the foil to the flowing stream. In this case the basic model is simplified. This model of IR temperature measurement with an opaque face layer is shown in Fig. 2. Thin-film opaque heater (1) is deposited on the surface of the wafer (3) facing the IR radiometer (5). The liquid is circulated in micro-channels (2). The micro-channel system is sealed by a cover (4). In this case a temperature at any point inside the micro-object should be estimated by calculation. The face layer in this case must be thin and its material should have high enough thermal conductivity. According to this method the face layer should be heated by supplying electrical current to determine the heat transfer coefficient. The temperature measured by IR cameras on the surface of a face layer is slightly higher than the temperature of the microchannel wall. Hetsroni et al. [19] and Tiselj et al. [29] estimated numerically that this deviation is about 0.15e0.8 K in the range of heat fluxes, materials and dimensions typical to micro-systems. So the temperature measured by the IR camera must be corrected according to the calculated estimation for given topology and material of micro-device.

Fig. 1. Basic radiation model of the measurement of a temperature field in the microdevices.

2.2.2. Temperature measurements on the surface of capillary tubes The study of heat transfer in micro-systems such as metal capillary tubes requires also taking into consideration the effect of direct radiation from the background that falls within the field of view of the IR camera. An incoming radiation from extraneous elements to the infrared sensor cannot be neglected, when obtaining temperature measurements of small-size devices. New method described by Hetsroni et al. [30] was applied to decrease a systematic error caused by background radiation. The proposed method is based on compensating the background radiation by controlling its temperature to the level equal to the temperature of the capillary tube. This is achieved by recording the infrared data against a background, whose temperature was maintained at a given value by a thermostat. Schematically this method is depicted in Fig. 3. The surface temperature TW,IR of the small-sized object is determined from the infrared image, which is recorded by the IR camera against the background. The background temperature TG,IR was also measured by the infrared camera. Both the object and the background screen were made of the same stainless steel and were painted by the same matt black paint, so that the object and background had equal emissivity 3. A thermocouple

2.2. Methodology of steady-state wall temperature measurements

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2

A

4

A-A

Tfout

Tfin

3

A

1

5 Fig. 2. Simplified model of the IR measurement with an opaque face layer. 1. Face layer (thin-film heater), 2. Micro-channel, 3. Wafer, 4. Cover, 5. IR video.

array was used to obtain the value of background temperature (T-type thermocouples of dimension 0.3 mm were used). The thermocouples were spaced on the background screen surface and provided the temperature distribution on the surface. This temperature distribution showed that the screen’s temperature was uniform along the tube. The method could be considered as image compensating method. In other words the capillary tube becomes almost indistinguishable against the background, like a “disappearing filament” used in some methods of radiation pyrometry. A series of experiments was then conducted to evaluate the precision of the temperature measurements on the heated surface of the capillary tube, using the method described above.

Fig. 3. Scheme of infrared measurement of surface temperature capillary tube and calibration method. 1. Calibration section, 2.Thermocouple, 3. Electrical contacts, 4. Screen (background), 5. IR video camera.

The heated part of the tube (outer diameter is D ¼ 1.5 mm, inner diameter is d ¼ 1.072 mm) was 150 mm long. The tube was fixed in a horizontal position and placed at the distance 0.05 m from the screen of the background. Electric current was supplied to the heated tube from a DC power supply. A calibrated, Teflon coated, T-type thermocouple of diameter 0.3 mm was inserted inside the heated tube. In this case (direct heating by electrical current) the thermocouple measured the temperature of the inner tube wall. The thermocouple could be adjusted exactly to any desired position along the axis of the heated tube. The temperature of the outer surface T W,TC was calculated from the power dissipation per unit volume of the tube. The measurements of the thermocouple showed that the temperature along the tube T W,TC was uniform, within 0.1 K. The temperature of the background TG,IR was varied and controlled within 0.1 K. Both, the thermal image data of the surface temperature T W,IR of the heated capillary tube and the temperature T W,TC, measured by thermocouple inserted inside tube, were recorded simultaneously under steady-state conditions. The series of runs was carried out to determine this temperature difference, where the value of T W,IR was measured for the given temperature T W,TC at various temperatures of the background temperature TG,IR. The IR used in this experiment had a spectral band of 3.4e5 mm and a temperature range of 10 to 450  C with a sensitivity of 0.07  C at 30  C. The radiometer has a 256  256 platinum silicide focal plane array detector, which provides a superior image without the use of mechanical scanning. Image update range is 50 Hz. Through calibration, the radiometer is very accurate in a narrow temperature range giving typical noise equivalent temperature difference (NETD) only, which is less than the sensitivity. A typical horizontal resolution is 1.2 mRad or 256 pixels/line. IR dynamic range is 16 bits and digitizing resolution is 12 bits (4096 levels). Focus range is from 20 cm to infinity. Fig. 4 shows the difference between infrared measurement of the tube surface and the inserted calibrated thermocouple (T W,IR  T W,TC) relative to the difference of (T W,IR  TG,IR). It can be seen that the magnitude of disagreement (T W,IR  T W,TC) depends on the difference (T W,IR  TG,IR). When the temperature of the background TG,IR is equal to the temperature T W,IR on the surface of a small-size object (measured by infrared radiometer) the object temperature becomes very close to the calibrated temperature of thermocouple inside of the tube. The same method was used to determine temperature distribution on the heated wall and heat transfer coefficient under

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1.5

inner diameter 1.072 mm, outer diameter 1.5 mm and 0.600 m in length was placed horizontally. It is divided into two sections. The development section 5 is 0.245 m in length. It was used for the flow and thermal field development. The test section 6 of 0.335 m in length was used for collecting the experimental data on heat transfer and pressure drop (Fig. 5a). The details of the experimental setup are shown in Fig. 5b. The test section was not insulated, because the outer temperature of the heated wall, TW,IR, was measured by the IR radiometer. On the other hand, the insulation of small-size diameter tube is reasonable, if the critical diameter of an insulation DCR ¼ 2k/hFC is less than the tube diameter. The estimation of the value of the critical diameter of an insulation gives the magnitude of DCR ¼ 13.3 mm, at the heat transfer coefficient of the free convection is hFC ¼ 15 W/m2 K and heat conductivity of this insulation is k ¼ 0.1 W/m K. So, in our case, the size of the tube diameter (D ¼ 1.5 mm) assures much less heat losses, without any insulation, than a thick layer of the high-quality insulation. The inlet and outlet of this test section were connected to junctions 11. The inlet and outlet temperatures of the working fluid along the tube were measured by 0.3 mm type T thermocouples 7,8 calibrated with an accuracy of 0.1 K. The DC current was supplied by a power supply through electrical contacts 4 to direct heating the stainless steel tube. The flow rate of the working fluid was controlled by adjusting the frequency of the peristaltic pump 3 and

TW,IR-TW,TC

1 0.5 0 -0.5 -1 -1.5 -15

-10

-5

0

5

10

15

TW,IR-TG,IR Fig. 4. Difference between temperatures of the capillary wall, measured by infrared camera, and the calibrated thermocouple depending on the difference between the object and screen temperatures.

condition of laminar water flow into circular capillary tube. The experimental apparatus is shown in Fig. 5a and b. Water was flowing from the entrance tank 2 and was supplied to the capillary tube by a peristaltic pump 3. The flow rate was measured by weighing method using the electronic scales 1. The tested tube of

a

-

+

3

857

4

5

6

7 Tf,in

8 Tf,out

2

9

10 1

4

Tfout

11

5

11

6

245

4

Ø 1 .5

Tfin

+

Ø 1.0 7

b

335

Pout

Pin

600 Fig. 5. Experimental apparatus. a) schematic diagram of the experimental facility: 1. Electronic scales, 2. Entrance tank, 3. Pump, 4. Contacts of power supply, 5. Development section, 6. Test section, 7. Thermocouple for measurement of inlet fluid temperature, 8. Thermocouple for measurement of outlet fluid temperature, 9. Exit tank, 10. Infrared camera, 11. Junction. b) test section.

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was measured by a weighing method. Then the water was collected at the exit tank 9. The temperature field on the test section surface was recorded by the Infrared radiometer 10. The temperature distributions of the heated water, Tf, and of the heated wall, Tw, in the flow direction, X, is shown in Fig. 6 (X is the distance from the inlet). According to theoretical predictions the temperature increases linearly. Average Nusselt numbers presented in Table 1 agree quite well with the theoretical one of Nu ¼ 4.36. 2.2.3. Numerical study of the heat transfer measurements on the surface by IR technique Numerical modeling in combination with a non-contact temperature monitoring method, IR thermography, was used by Sikanen et al. [14] to examine electrolyte heating as well as heat transfer properties of a polymer chip under real electrophoresis conditions. The IR thermography provided high sensitivity (<20 m K) as well as fast response time (w20 ms), which are both crucial when studying relatively small temperature changes caused by rapid evolution of Joule heating in electrokinetically actuated flows. For IR-opaque polymer chips used in this study, the micro-channel inner temperatures cannot be directly measured with IR thermography. However, the measured temperature distribution on the chip surface was shown to qualitatively reflect the same temperature profile that exists on the micro-channel inner wall. The accuracy of the model is within 1  C when the deviation in electrochemical processes is taken into account. The simulation results also suggest that the temperature on the chip surface qualitatively reflects the temperature inside the micro-channel with an average offset of 1e2  C. This work showed that the repeatability of the electrophoresis experiments on chip is not always ideal with respect to electrochemical processes. Standard deviations of about 20% were observed in the measured currents during injection and separation which resulted in 40e50% deviations in Joule heating between repeated experiments under identical conditions. Thereby, the results suggest that the contribution of these inaccuracies to analytical performance and repeatability should not be automatically neglected. If the heat capacity of the test surface is sufficiently low, the fluctuating temperature on the foil can be measured using highframe-rate infrared thermography. This method, however, has an inherent problem in that the temperature on the test surface attenuates both in time and space due to thermal inertia and conduction. In the study of Nakamura [31], the frequency response

Table 1 Average Nusselt number at laminar flow into the tube of d ¼ 1.072 mm. Reynolds number Re

Heat flux, q, kW/m2

Average Nusselt number Nu

80 80 80 160 160 160

8.75 11.71 17.15 14.70 19.70 27.04

4.30 4.12 4.40 4.31 4.50 4.18

and the spatial resolution of a thin foil were examined analytically considering heat losses. In order to derive general relationships, non-dimensional variables of fluctuating frequency and spatial wavenumber were introduced to formulate the temporal and spatial amplitudes of the temperature on the test surface. Based on these relationships, the upper limits on the detectable fluctuating frequency and spatial wavenumber were successfully formulated using governing parameters of the measurement system. This enables to evaluate quantitatively the reliability of the heat transfer measurement by infrared thermography. The values, were evaluated by Nakamura [31] for the practical conditions and indicated that IR measurement technique is promising for investigating the spatio-temporal behavior of heat transfer caused by flow instabilities. 2.3. IR measurements in liquid 2.3.1. Measurements through IR transparent cover Measurement of liquid flows temperature in micro-channel heat sinks requires diagnostic techniques with micro-scale spatial resolution. The local fluid temperature may be measured through the IR transmitted face layer. Fig. 7 shows the scheme of the IR measurement for this case, which resulted from the basic model. The liquid is circulated in micro-channels (2) etched in the wafer (3). The heater (4) is attached to the top surface of the wafer (3). The micro-channel system is sealed by IR transparent window (1). The liquid temperature is measured by the IR camera (5) through this window. Measurement of the temperature field by means of the IR radiation emitted from the liquid surface requires careful calibration of the emissivity. The reflection loss is usually defined as a percentage of the original intensity. The loss is a function of the refractive index (n) of the optical window material, the state of polarization and the angle of incidence of the light. In the simplest case, the reflection loss from one surface for un-polarized light, normally incident upon a surface, is given as

R ¼

ðn  1Þ2 ðn þ 1Þ2

(1)

Reflections from the second surface must be considered for infrared transparent layer. In this case internal transmittance may be estimated as

T ¼

Fig. 6. Local temperatures of water and the heated wall at q ¼ 14.7 kW/m2, Re ¼ 160. >-wall temperature, ,-water temperature.

2n
n2 þ 1

(2)

The information on the transmittance of IR windows of thickness, in the range of wavelengths is usually listed by the manufacturer, see for example Table 2. Sapphire and Silicon may be used as infrared window materials primarily for the 3e5 mm band, whereas ZnS and Germanium used as infrared windows in the thermal band (8e14 mm). The latter group of windows may be used in the devices subjected to harsh environments.

G. Hetsroni et al. / International Journal of Thermal Sciences 50 (2011) 853e868

2 A

3

4

A-A Tfout

A

859

Tfin

1

5 Fig. 7. Direct measurement of the liquid temperature through IR transmitted face layer. 1. IR transmitted face layer, 2. Micro-channel, 3. Wafer, 4. Heater, 5. IR camera.

An increase in the transmittance value can be attained by coating the side facing the IR camera, of the cover layer with an anti-reflection coating in the wavelength range of the detector. These data have to be kept in mind at the calibration setup of the IR camera. 2.3.2. Flow in micro-channels Measurement of liquid temperature in the micro-channels was carried out by Mishan et al. [32]. The experimental apparatus is shown in Fig. 8. Filtered water at room temperature was used as the working fluid. The water was pumped from the entrance tank by a miniature gear pump through the inlet calming chamber, inlet manifold to the micro-channels in the test module, and from the micro-channels through the outlet manifold, outlet calming chamber to the exit tank. The test section and arrangement of the thermocouples is shown in Fig. 9. The mass flow rate of the water was measured by a precision flow meter calibrated by a standard weighting method. The test module was fabricated of 14  20 mm and 1.25 mm thick aluminum plate. Sixteen micro-channels were machined on one side of this plate using a precision sawing technique. The micro-channels were of 320 mm wide and 750 mm deep with an accuracy of 10 mm. Electric resistor, which was used as a heat source, was located on the other side of the plate. The serpentine electrical heater of 10  10 mm had been attached to the surface of the aluminum by chemical vapor deposition technique and provided a uniform heat flux. The heat sink housing was made of Teflon in order to decrease the heat losses to the environment and keep the inlet/outlet manifolds temperature at constant value. A plate made of polycarbonate plastic was attached to the test section by several screws and served as transparent cover, which was used also for measurements of fluid temperature by thermocouples. During the measurements of the fluid temperature in the micro-channels, by IR technique, a cover made of sapphire glass was employed. The transparent window of sapphire had

a wavelength range of 0.15e7 mm, which makes possible to perform visual observations and also IR measurements through the cover. When radiant energy strikes surface, a part of the radiation is reflected, part is absorbed and part is transmitted. The transmission of sapphire window with 10 mm thickness is shown in Fig. 10. From this figure one can conclude that the transmission is constant for most of the wavelength range. The transmission value for the wavelength of l ¼ 5 mm and T ¼ 273 K is about 85%. This value of transmissivity makes possible measurements through sapphire by IR technique. Before these measurements a calibration procedure was conducted. For such calibration the water temperature moving into the manifolds was measured simultaneously by thermocouples and by IR camera in the range of 30 C e 90 C. For each steady-state experimental conditions an energy balance was performed. It should be noted that when the heat balance is based on temperature difference (T6  T2) the heated portion of the channels is shorter than the total length of the test section. Thermocouples T6 and T2 were placed into outlet and inlet calming chamber, respectively. When the measurements were conducted by thermocouples T5 and T3 the heated portion of the channels was the same as the channel length. These thermocouples were installed at the surface of the transparent cover adjoined to the top of the micro-channels. It was important to investigate the difference between temperature measured by thermocouples T5 and T3 and bulk temperature into the micro-channels. It should be also taken into account the heat transfer to the ambient, conducted through the thermo-electrodes and through the power wires connected to the power supply. This problem was especially serious in the case of comparison between the temperature measurements by thermocouples to those made by the IR. The following value of z was used as a measure STD of thermal uncertainty in the present experiment

z ¼ ½ðT6  T2Þ  ðT5  T3Þ=ðT6  T2Þ

(3)

Table 2 Properties of IR transmitted materials. Material

Transmission range, mm

Refractive index

Reflection loss, %

Thermal conductivity, W/(m K)

Density, kg/m3

Silicon (Si) Sapphire (Al2O3) Germanium (Ge) Zinc sulphide (ZnS), multispectral

1.2e15 0.17e5.5 1.8e23 0.37e13.5

3.42 at 5 mm 1.75 at 1.1 mm 4.0 at 11 mm 2.2 at 10 mm

46.2 at 5 mm 14 at 1.1 mm 53 at 11 mm 24.7 at 10 mm

163.3 at 273 K 27.2 at 300 K 58.6 at 298 K 27.2 at 298 K

2330 3970 5330 4090

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Entrance tank Gear pump Data Flow meter

Sensors Exit Outlet

Inlet manifold Micro-

Heate IR Camera

Fig. 8. Measurement of fluid temperature in the micro-channels. Experimental setup and apparatus.

In the range 100 < Re < 580 the value of STD was z ¼ 8.4%. It depends on Reynolds number and decreased with an increase in the Re. The results agree with heat balance data reported by Lelea et al. [33] for annular micro-channel of d ¼ 300 mm. From both investigations it is clear that, as Re decreases, the outlet temperature of water increases. This results in an increase of the temperature of the thermo-electrodes and an increase of heat conduction through electrodes to the ambient. For a given values of flow rate and heat flux, the IR images at the surface of the transparent cover adjacent to the top of the microchannels were clearly observed. Fig. 11a shows the IR image (top view) of the central part of the test module obtained at the Reynolds number Re ¼ 100 and heat flux q ¼ 25.0  104 W/m2. Fig. 11b shows the temperature distribution in the spanwise direction. The flow is from the right to the left, the field of view is 3.6  3.6 mm in both streamwise and spanwise directions. The gray level scale on the left of the thermal pattern shows that the temperature on the channel walls is about 31.2  C whereas the temperature of the water was about 29.9  C. The sequences of such images were used to determine the fluid temperature along the micro-channels and the magnitude of the local Nusselt number. In Fig. 12 the experimental results of the local value of Nu are plotted vs. the non-dimensional axial distance, X* ¼ X/DhRePr for the respective experimental conditions together with those reported by Warrier et al. [34]. The measured values agree quite well with our data and numerical results, especially near the fully developed region. The experimental data in Fig. 12 indicate that the local Nu number decreases and approaches a constant value with increasing X*. As seen from Fig. 12 the present experimental data

Fig. 9. Measurement of fluid temperature in the micro-channels. Arrangement of thermocouples.

are in reasonable agreement with theoretical results. It can be concluded that for rectangular micro-channels the local value of Nu is in good agreement with conventional theory including the entrance region. The same results were reported by Lelea et al. [33] on heat transfer and fluid flow of distilled water in micro-tubes of 0.1, 0.3, and 0.5 mm with Re number range up to 800. Although the single-phase fluid flow in micro-channels was now well understood, less attention has been devoted in the literature to flow distribution within a heat sink. The technique that has grown in popularity is micro-particle image velocimetry (mPIV). The use of mPIV has been limited to applications in which optical access to the fluid flow is available at visible wavelength. In some applications such as stacked micro-channel heat sinks, optical access to the liquid in the visible spectrum is unavailable. In this case the IR range would be advantageous for measuring the flow fields in micro-devices (Han et al. [23]; Liu et al. [24]; Franssila et al. [25]; Patil and Narayanan [18]; Golonka [26]; Hardt [27]; Jones [28]). The flow distribution in a 76-channel heat sink with average channel dimensions of 110 mm  371 mm was studied by Jones et al. [28] using IR mPIV. An image-processing algorithm was developed that significantly improves the quality of IR mPIV recordings, allowing IR mPIV to be used in lower signal-to-noise ratio environments. The IR mPIV system layout is shown in Fig. 13. IR light from a laser system was delivered to the micro-device through a fiber optic cable. A microscope objective, corrected for light in the 480e180 nm range, collects the light scattered by the seed particles. The pixel size of the IR camera was 30 mm  30 mm. A particle diameter of 2.0 mm was found to be adequate for this study. The visibility of the particles was greatly affected by the incident angle of the fiber optic delivery system. The optimum angle was 30 . The measurement uncertainty of the velocity was approximately 3%. The test piece consists of 76 deep reactive ion etched (DRIE) channels in a silicon substrate with inlet and outlet manifold sections. Although the glass is transparent to visible light, the particles are illuminated through the silicon substrate (see Fig. 13) in a configuration that would not be possible using standard mPIV. The flow distribution is shown in Fig. 14. Velocity profiles in various channels across the heat sink are shown in Fig. 14a for Re ¼ 10.2 and Fig. 14b for Re ¼ 102. Also plotted in Fig. 14a and b are the mean theoretical velocity profiles evaluated from the known total flow rate through the heat sink and channel dimensions. Very little flow maldistribution is observed at the lower flow rate (Re ¼ 10.2), at which all of the measured velocity profiles fall very close to the mean velocity profile. Non-intrusive local temperature measurement in convective micro-channel flows using IR thermography is presented by Patil and Narayanan [21]. The heat sink was inverted for IR visualization such that the water flow was visualized through the channel wafer. For calibration, water at Tf ¼ 23.5  C was pumped through the micro-channel and intensity maps were recorded at specific locations along the channel. These multiple images were later used to determine precision errors in detected intensity as a part of the calibration errors. The test section design, and experimental and data analysis procedures that provide increased sensitivity of the detected intensity to the desired temperature were discussed. Experiments were performed on a 13 mm long, 50 mm wide by 135 mm deep Si micro-channel at a constant heat input to the heat sink surface for flow rates between 0.6 and 1.2 g min1. Uncertainty in fluid temperature varies from a minimum of 0.60  C for a Reynolds number (Re) of 297 to a maximum of 1.33  C for a Re of 251.

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Fig. 10. Transmission vs. wavelength at 10 mm thickness of Sapphire glass.

Fig. 15 shows the fluid temperature plotted vs. axial distance made non-dimensional with hydraulic diameter. Note that temperature decreases with increase in Re since the heat flux supplied by the heater is a constant. The temperature profile as expected shows first a steep non-linear followed by a linear rise along the micro-channel. Although the technique described here provides the opaque fluid temperature, it is unclear whether the measurement refers to fluid temperature exactly at the fluidewall interface or is representative of an average over a certain depth of fluid near the wall. 2.3.3. Temperature monitoring of small amounts of liquid Temperature monitoring can be a way of detecting chemical and biochemical reactions inducing heat and for controlling thermal conditions in chemical analyses such as the micro-polymerase

chain reaction (PSR), nebulizer chips (Franssila et al. [25]), and electrophoretic separation chips (Sikanen et al. [14]). Temperature monitoring of small amounts of liquid in micro-chemical chips or micro-fluidic chips is being needed in expanding applications of micro-total analysis systems (m-TAS) (Dittrich et al. [35]). Conventional IR imaging might be a good choice for non-contact measurement and imaging of temperature. Fudym et al. [36] obtained IR images of microchip with 25 mm deep micro-channels filled with water that were locally heated by a neighboring resistive film and managed to quantify temperature differences in the water by using the Laplacian of the field. However, detecting changes in the temperature of a liquid in a microchip is considerably more difficult than on a solid surface because IR radiation from the liquid is small compared to by radiation from the microchip’s materials. Most of these materials are transparent to visible light but absorb mid- and far-IR radiation (Sahba and Rockett [37]; Merschman et al. [38]), which means they emit radiation with the same wavelength. Hsieh et al. [39] obtained IR images of mineral oil in a micro-fabricated PCR chamber without a cover, i.e., an open chamber, and used them to evaluate the temperature uniformity in the chamber.

8

7

N

6

5

4

3

2 0

0.005

0.01

0.015

0.02

25

X* Fig. 11. The temperature field, Re ¼ 100, q ¼ 25  104 W/m2. a) IR image, b) Temperature variation in the spanwise direction.

Fig. 12. Dependence of the local Nu on the dimensionless thermal entrance length. IR measurements: B-Re ¼ 100; C-Re ¼ 200; ,-measurements by thermocouples; - data by Warrier et al. [34].

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Fig. 13. IR mPIV system configuration (Jones et al. [28]).

Kakuta et al. [40e42] have been studying a convenient noncontact way of using near-infrared spectroscopy (NIRS) for measuring the temperature of aqueous solutions. This method is based on the temperature dependence of the near-infrared (NIR) absorption of water. For example, the peak of the absorption band of water near the wavelength of 1440 nm (n1 þ n3 band), corresponding to the combination of symmetric and antisymmetric vibrational modes of water molecules, shifts to a shorter wavelength when the temperature increases (Eisenberg and Kauzmann [43]; Lin and Brown [44]; Libnau et al. [45]; Segtnan et al. [46]). The temperature dependence has been known in NIR spectrometry in biomedical, agricultural, and polymer sciences, but it has usually been regarded as a disturbance. While some experimenters have made use of it to measure the temperature of various samples that contain water (Kakuta et al. [42]; Lin and Brown [44]; Hollis et al. [47]; Otal et al. [48]; Thomson et al. [49]), others have tried to cancel out the temperature effect in noninvasive measurements of glucose concentration (Arimoto et al. [50]; Jensen et al. [51]; Ye et al. [52]; Cui et al. [53]). An important advantage of an NIRS-based method is that it can obtain a temperature averaged over the light path within the medium, i.e., an average including internal temperatures. This is different from conventional IR thermometry, which essentially detects only surface temperatures. Another advantage is that the power of the irradiation light can be adjusted according to sample conditions such as thickness, area, and absorbance. A temperature imaging method based on the temperature dependence of the NIR absorption of water has been presented by Kakuta et al. [54]. The apparatus consists of a microscope, NIR camera, and narrow-band pass filter for measuring the absorbance at 1412 nm. The halogen lamp of the microscope emitted light from visible to NIR. The detector of the camera was an indium gallium arsenide array covering a wavelength range from 900 nm to 1700 nm. The observation area on the sample was 430 mm  345 mm. To detect the light intensity a narrow-band pass filter was inserted between the light source and the sample in the microscope. Pure water was put in a 0.5 mm thick quartz cuvette. The sample temperature was controlled by putting a thermo plate on the microscope stage. To form a temperature distribution through

Fig. 14. Flow distribution in the heat sink: (a) velocity profiles at Re ¼ 10.2, (b) velocity profiles at Re ¼ 102 (Jones et al. [28]).

electric current heating, a nichrome wire with a length of 50 mm and diameter of 50 mm was inserted through the cuvette branches into the water. The method is convenient because neither excitation light nor marker particle mixed in a sample is needed for the measurement. Calibration results for 0.5-mm thick water from 26.0  C to 40.0  C demonstrated a linear relationship between absorbance and temperature (Fig. 16). In Fig. 16, DB is the common logarithmic ratio of the intensity of light transmitted through the sample at a given temperature to of the intensity of light transmitted through the sample at temperature 26.0  C. Accuracy of the temperature determination was approximately 1 K. The obtained images were verified with the temperatures as calculated with a two-dimensional model for thermal conduction. The present imaging method would have chemical, biomedical, and

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863

Fig. 15. Axial profile of local fluid temperature Tf with Re (Patil and Narayanan [21]).

industrial applications for measuring the temperature distributions of aqueous solutions, aqueous gels, and biological samples with thermogenic reactions in m-TAS or biochip analyses. Although there are somewhat differences between the measured and calculated temperature profiles (maximum is approximately 1 K), they are a good match.

Fig. 17. Joint temperature measurements. Experimental facility: (1) entrance tank; (2) pump; (3) housing, (4) sample of porous medium; (5) temperature measurements ports; (6) differential pressure sensor; (7) IR camera; (8) IR transmitted glass; (9) top of test section; (10) two copper rods; (11) exit tank and (12) electronic scales.

2.4. Joint temperature measurement of the wall and the liquid Forced convection in porous media has been studied extensively. However, most studies were restricted to packed beds and granular materials, since they have direct application to naturally occurring porous media. There are relatively few investigations of transport phenomena in very high porosity media. The temperature field on the surface of metal foam used in the cooling system of high power device was studied by Hetsroni et al.

Fig. 16. Relationship between absorbance difference for imaging, DB, and temperature from 26.0  C to 40.0  C (the absorbance at 26.0  C is the reference). Average (diamond) and standard deviation (bars) were calculated over all pixels of 100 frames for each temperature. R represents the correlation coefficient (Kakuta et al. [54]).

[55]. Experimental facility is shown in Fig. 17. The porous insert of width 10 mm, length 54 mm and of 2 mm thickness, was placed in a channel, occupying the entire cross-section. The inlet and outlet temperatures of the working fluid on both sides of the tested part of a porous layer, of 34 mm length, were measured with 0.3 mm type T electrical isolated thermocouples. The face side of the insert was coated by black mat paint to equalize the emissivity of the aluminum alloy and the surface of the water. The inner heat generation was simulated by supplying D.C. power up to 400 A to the foam sample through copper rods. The heater could supply power up to 1.0 kW. The thermal field of the upper side of the porous strip was measured by high speed IR camera through IR transmitted glass of 3 mm thickness made of Zinc Sulphide (Multispectral). Microscopic lenses of the camera made it possible to reach the spatial resolution of 15 mm. Aluminum foam of 40 pores per inch (ppi) was studied. The experiments were carried out in the range of average liquid velocity 0.1  U  1.2 m/s in the channel with the porous insert. The range of heat flux was 0.02  q  0.25 kW/cm2. Under these experimental conditions the Reynolds number Re ¼ UD/n (D is the hydraulic diameter of the channel; n is the kinematic viscosity) varied in the range 200  Re  3800. The IR camera was calibrated by measuring the temperatures of water preheated the test section inlet in the range of 20e70  C. The uncertainties of the values of heat transfer coefficient and the Nusselt number are within 12.5% and 12.7%, respectively. The data from the IR radiometer were stored in a digital mode. For every set of flow and heat flux conditions the thermal fields of the surface were recorded. The thermal maps were then analyzed using the image-processing software. The software makes it possible to establish a temperature profile along any line, determine the mean temperature and the standard deviation (STD). An

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Fig. 18. Typical IR image of the foam surface and temperature profile along of flow direction (Re ¼ 3750, q ¼ 230 W/cm2).

example of temperature distribution of the surface of the porous material is presented in Fig. 18. IR image of the porous surface shows an increase in the temperature of the window along the flow direction (from left to right). Non-uniformity of the thermal field of the porous layer is determined also by the profile of the flow velocity. The disturbances of the temperature field on the porous sample surface introduced by the influx of the cold fluid from the main stream toward the wall were also studied. The size and configuration of these domains depend (at fixed parameters of channel flow) on the velocity and heat flux. Dependence of the Nusselt number on the Reynolds number is shown in Fig. 19. 3. Temperature measurements in low frequency processes The frequency response of temperature measurements by infrared technique was analyzed by Hetsroni et al. [56]. The authors estimated that the maximal frequency umax of the thermal process recorded by this method should not be over the value



umax ¼

b

0:5

1b

h

rcd

(4)

’ =T ’ where b ¼ 1  TW W0 is the distortion coefficient, which ’ from accounts for the deviation of the temperature fluctuations TW ’ corresponding to zero frequency; r, c, d are the their values TW0 density, thermal capacity and thickness of the heated layer, h is the

Fig. 19. Forces convection in porous media. Dependence of Nusselt number on the Reynolds number. Solid line - experiments [55], dashed line - turbulent heat transfer in smooth channels.

heat transfer coefficient. Estimation at 10% of uncertainty according to Eq. (4) for silicon substrate of 200 mm thickness in the range of the heat transfer coefficient of 1000e50,000 W/(m2 K), which spans the region from laminar flow to flow boiling, shows that maximal frequency is in the range 1e100 Hz. It is clear that using traditional method of heated foil has significant limitation in taking spatial resolution needed for the study of the temperature distribution within the scale of single micro-channel. The resolution in time of this method is sufficient only in the region of an intensive heat transfer and low frequency processes. Such method however was successfully used by Hetsroni et al. [19,57] and Xu et al. [20,58] for visualization of thermal patterns on a wafer wall and quantitative determination of average heat transfer coefficients and its slow fluctuations in time. The typical experimental facility according to our method is shown in Fig. 20. The loop consists of a liquid pump, piping, test module, and entrance and exit tanks. Working liquid was pumped from the entrance tank through the inlet plenum to the microchannels in the test module, and from the micro-channels through the outlet plenum to the exit tank. The test module, Fig. 21, was fabricated from a square-shape silicon substrate 15  15 mm, 530 mm thick. Pyrex cover, 500 mm thick, served as both an insulator and a transparent cover through which flow patterns and boiling phenomena could be observed. 21 parallel micro-channels were etched in the silicon substrate. The cross-section of each channel is an isosceles triangle with a base of a ¼ 0.25 mm. The angles at the base are 55 . An electrical heater of 10  10 mm, made of a thin-film resistor, had been deposited on the surface of the silicon, and served to simulate the heat source. The input voltage and current were controlled by a power supply and measured with an accuracy of 0.5%. Imaging Radiometer with frequency response of 180 Hz was used to study the temperature field on the electrical heater. We studied instabilities caused fluctuations in the pressure drop in flow boiling of water. It was found that the temporal behavior of temperature fluctuations corresponds to that of pressure fluctuations. The maximum values of the pressure fluctuations did not differ significantly from the pressure drop across the channels. The time variation of the mean and maximum heater temperature in the case of water cooling is presented in Fig. 22. The mean heater temperature (i.e., the average temperature of the whole heater) changed in the range of DTav ¼ 10 K. The maximum heater temperature fluctuated in the range of DTmax ¼ 6 K. In these studies the effect of background conditions on the measurements was determined according to the algorithm implemented in the IR camera software, because the conventional sizes (10  10 mm) of the heater (face layer). It was suggested that a level of thermal

G. Hetsroni et al. / International Journal of Thermal Sciences 50 (2011) 853e868

865

Fig. 22. Time variation of average and maximum heater temperature at q ¼ 200 kW/m2.

Fig. 20. Parallel micro-channels. Measurement of temperature fluctuations on the heated bottom.

noises arising due to unfocussed radiation incident on the detector from the camera objective and lens wall was negligible. The appropriate precision was reached by a careful calibration against the readings of the temperature of the thermocouples. Low frequency oscillations were also observed by Diaz and Schmidt [22]. Diaz and Schmidt [22] present an experimental investigation of flow boiling heat transfer in a single 0.3  12.7 mm2 rectangular micro-channel. Water and ethanol were employed as test fluids. The examined parameter ranges are: mass fluxes between 50 and 500 kg/m2 s and heat fluxes up to 400 kW/m2 at an outlet pressure of 0.1 MPa. IR thermography is employed to register the outer wall temperatures of the channel. This measurement method is especially appropriate for the analysis of the transient behavior of boiling in micro-channels, which has been often reported in the literature. Infrared images of the test section are recorded at a frequency of 150 Hz using the half image mode. Data are collected over 25 s and the behavior of the obtained wall temperatures is analyzed. The test section was a rectangular channel made of nickel alloy (Inconel 600) and has the dimensions: 0.3 mm height, 12.7 mm width and 200 mm length. The methodology of the data acquisition is presented by the authors. An analysis area is positioned on each thermographic picture of the channel, so that the spatio-temporal temperature distribution on the channel surface is available for the data

reduction. In this study, only the axial dependence of the temperature is considered. Thus, the temperature for each axial position is set to be the average of the temperatures corresponding to each pixel in a central region of the surface of the channel, approximately 3 mm wide, where the influence of the radial heat conduction can be neglected. The entire channel can be registered instantaneously with a spatial resolution in the axial direction of 0.7 mm/pixel. Oscillations of the temperature can be clearly recognized. The amplitude and frequency of the oscillations vary depending on the operating parameters and also on the vapor quality. The oscillations are found to increase with increasing heat flux and with decreasing mass flux. Therefore, low mass fluxes and the corresponding maximum heat flux are selected for both water and ethanol. Low frequency oscillations can be observed for low qualities. The maximum amplitude is found in the region of subcooled boiling, just before nucleate boiling begins. The maximum temperature difference in this region is found to be 30 K. The amplitude decreases strongly thereafter with increasing vapor quality. After the initial region, where nucleate boiling dominates, nearly constant wall temperatures are registered. A characteristic oscillation frequency of the wall temperature is not observed. The oscillations of the temperature presented in this work are measured at the outer surface of the channel and an influence of the wall thickness, in this case 0.3 mm, on both attenuation of the amplitude and phase shift is expected. The effect of the heat conduction through the wall is analyzed by using the computer software FLUENTÒ. One-dimensional heat conduction with heat generation is considered and periodic boundary conditions are set in the axial direction. Both inner and outer wall temperatures are shown in Fig. 23. It can be observed that, in this case, the wall thickness has a negligible influence on the phase shift. On the other hand, an attenuation of the amplitude of approximately 6% is found. From Figs. 22 and 23 one can conclude that period of the temperature fluctuations is about 0.2e0.3 s. 4. Uncertainty

Fig. 21. Measurement of temperature fluctuations on the heated bottom. Test section.

In general, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty. The uncertainty of the result of a measurement generally consists of several components, which may be grouped into two categories according to the method used to estimate their numerical values: those which

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where T W;IR is the average surface temperature of the tube wall on the test section, T f is the average value of the fluid. The value of the wall heat flux q is obtained as

q ¼

Fig. 23. Simulation results: outer and inner wall temperatures, ethanol, m ¼ 200 kg/m2 s, q ¼ 90 kW/m2, x ¼ 0.328, Fo (t ¼ 1 s) ¼ 44 (Diaz and Schmidt [22]).

are evaluated by statistical methods, and those which are evaluated by other means. The summary of the standard uncertainty components for the value of the heat transfer coefficient under condition of single-phase flow in a micro-channel measured by IR technique may be calculated according to the Standard (1995) [59] as it was presented in the study carried out by Hetsroni et al. [30]. The average values of the convective heat transfer coefficient is defined as

h ¼ 

q T W;IR  T f

;

(5)

  _ p Tf ;out  Tf ;in mC

pdl

;

(6)

_ is the flow rate, Cp is specific heat, d is the inner microwhere m channel diameter and l is the length of the test section. The temperature distribution along the tube was measured by an Infrared camera and then the average temperature of the heated surface,T W;IR , was calculated. The average value of the fluid temperature,T f , was calculated as T f ¼ ðTf;out þ Tf ;in Þ=2. Substitution of the heat flux value q calculated according to Eq. (6) into Eq. (5) gives a relation for the calculation of the heat transfer coefficient and estimation of its uncertainty.

  _ Tf ;out  Tf ;in m ; h ¼ C  ld T W;IR  T f

(7)

where C ¼ Cp =p is the coefficient based on physical properties of the liquid. The summary of standard uncertainty components for the value of the heat transfer coefficient is summarized according to the Standard [59] in Table 3. Measurements of local heat transfer, Patil and Narayanan [18] indicate that the fully developed Nu estimated using IR technique are higher by 10e22% over the solution for laminar macro-scale flows (Shah and London [60]). The paper by Patil and Narayanan [21] discusses the theory and procedure of the measurement of the liquid temperature of an

Table 3 Summary of standard uncertainty components of heat transfer coefficient. Standard uncertainty component u(xi)

Source of uncertainty

Value of standard uncertainty u(xi)

vf j ci hjvx i

ui ðhÞ jci juxi h h h

_ uðmÞ

Flow rate Measured difference between inlet and outlet liquid temperatures Measured difference between the wall and the liquid temperatures Uncertainty in the estimation of the capillary diameter Uncertainty in the estimation of the test section length

1.7  106 kg/s 0.14 K

Tf;out Tf;in dlðT W;IR T f Þ _ m C dlðT W;IR T f Þ

1.02  102 7.04  103

uðTf;out  Tf;in Þ uðTW;IR  Tf Þ u(d) u(l)

C

0.17 K

C

_ f ;out Tf ;in Þ mðT dlðT W;IR T f Þ2

3.2  102

5  106 m

C

_ f ;out Tf ;in Þ mðT d2 lðT W;IR T f Þ

5.02  103

5  105 m

C

_ f ;out Tf ;in Þ mðT dl2 ðT W;IR T f Þ

3.58  104

C ¼ 1.33  103; degrees of freedom  8; neff(h) ¼ 15; k ¼ 2.13; uðhÞ=h ¼ 0:0347. U95 ¼ ku(h) W/m2 K; U95hðhÞ  100% ¼ 7:38%.

Table 4 Uncertainties in measured and estimated variables (Patil and Narayanan [21]). Measured variable

Total error

Comments

Wetted perimeter Channel cross-section Dh (mm)

0.0148 mm (0.004%) 2.0% 135 mm2 (2.0%)

Based on deviation from a 50  135 lm rectangular geometry Based on deviation from a 50  135 lm rectangular geometry Based on wetted perimeter and channel cross-section

Camera spatial resolution (mm) _ (g s1) Mass flow rate-m Water radiation flux leaving the heat sink-C 3f T Si Surface temperature-Tsur ( C)

10 2.3% (Re ¼ 297) to 4.0% (Re ¼ 204) 0.26% 0.15

Calibrated using a set flow rate from a syringe pump; data averaged over 20 min Includes bias and precision errors in intensity and calibration error in thermocouple used for fluid temperature measurement Calibration error of thermocouple

0.91 (Re ¼ 204) 1.33 (Re ¼ 251) 1.04 (Re ¼ 285) 0.60 (Re ¼ 297) 3.3% (Re ¼ 297) to 4.7% (Re ¼ 204)

Based on measurements

Estimated variable Tf ( C)

Re

Includes uncertainty in geometry and flow rate

G. Hetsroni et al. / International Journal of Thermal Sciences 50 (2011) 853e868

opaque fluid near the channel wall for transparent channel walls. Uncertainties in measured and estimated variables are presented in Table 4. 5. Conclusion The good results obtained in the last decade by widespread use of infrared technique in experimental studies of convective problems have proved the IR technique to be an effective tool in overcoming several limitations of the standard sensors originating both from measurement and visualization techniques. Better use of quantitative infrared thermography is subject to solution of several problems. These are mainly concerned with accurate characterization of the IR system performance and its calibration, the use of external additional optics to increase the spatial resolution, the choice of the most appropriate heat flux sensor and its characterization, especially with regard to lateral thermal condition effects and the radiation losses; the determination of the body surface emissivity, the correct geometrical identification of the measured points, the design of the optical access window including the choice of the most appropriate IR material. Resolution of these issues make measurement of the wall and the fluid temperature in micro-scale devices by IR technique possible, as is demonstrated in the present review. This study comprises critical analysis of the application of infrared technique in devices in the range of tens to hundreds micro-meters. Such devices are typical in micro-scale systems. Investigations performed within the last decade were used to analyze the specific features of micro-scale IR measurements. The method is illustrated by various examples of heat transfer determination using image analysis of the heater temperature as well as direct measurement of the liquid temperature. Acknowledgments This research was supported by the Technion VPR fund. R. Rozenblit was supported by a joint grant from the Center for Absorption in Science of the Ministry of Immigrant Absorption and the Committee for Planning and Budgeting of the Council for Higher Education under the framework of the KAMEA PROGRAM. References [1] W. Qu, I. Mudawar, Flow boiling heat transfer in two-phase micro-channel heat sinks - I. Experimental investigation and assessment of correlation methods, Int. J. Heat Mass Transf. 46 (2003) 2755e2771. [2] X.F. Peng, G.P. Peterson, Heat transfer characteristics of water flowing through microchannels, Exp. Heat Transfer 7 (1994) 265e283. [3] C.P. Tso, S.P. Mahulikar, Experimental verification of the role of brinkman number in microchannels using local parameters, Int. J. Heat Mass Transf. 43 (2000) 1837e1849. [4] J.M. Koo, L. Jiang, L. Zhang, P. Zhou, S.S. Banerjee, T.W. Kenny, J.G. Santiago, K.E. Goodson, Modeling of two-phase microchannel heat sinks for VLSI chips, in: Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (2001), pp. 422e426. [5] L. Zhang, J.M. Koo, L. Jiang, M. Asheghi, K.E. Goodson, J. Santiago, T.W. Kenny, Measurements and modeling of two-phase flow in microchannels with nearly constant heat flux boundary conditions, J. Microelectromech. Syst. 11 (1) (2002) 12e19. [6] A. Popescu, J.R. Welty, D. Pfund, D. Rector, Thermal measurements in rectangular microchannels, in: Proceedings of the IMEC&E2002, New Orleans (2002) LA, IMECE2002e32442. [7] T. Astarita, G. Cardone, G.M. Carlomagno, C. Meola, A survey of infrared thermography for convective heat transfer measurements, Opt. Laser Technol. 32 (2000) 593e610. [8] G.M. Carlomagno, L. de Luca, Infrared thermography in heat transfer. in: W.I. Yang (Ed.), Handbook of Flow Visualization. Hemisphere Publishing Corporation, Washington, DC, 1989, pp. 531e553. [9] B. Palm, Heat transfer in microchannels, Microscale Therm. Eng. 5 (2001) 155e175.

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