Microfluidics and Nanofluidics

, Volume 2, Issue 4, pp 291–300

Spatially resolved temperature measurement in microchannels

Authors

  • V.A. Patil
    • Department of Mechanical EngineeringOregon State University
    • Department of Mechanical EngineeringOregon State University
Research Paper

DOI: 10.1007/s10404-005-0074-3

Cite this article as:
Patil, V. & Narayanan, V. Microfluid Nanofluid (2006) 2: 291. doi:10.1007/s10404-005-0074-3

Abstract

Non-intrusive local temperature measurement in convective microchannel flows using infrared (IR) thermography is presented. This technique can be used to determine local temperatures of the visualized channel wall or liquid temperature near this wall in IR-transparent heat sinks. The technique is demonstrated on water flow through a silicon (Si) microchannel. A high value of a combined liquid emissivity and substrate overall transmittance coupled with a low uncertainty in estimating this factor is important for quantitative temperature measurement using IR thermography. The test section design, and experimental and data analysis procedures that provide increased sensitivity of the detected intensity to the desired temperature are discussed. Experiments are performed on a 13-mm long, 50 μm wide by 135 μm deep Si microchannel at a constant heat input to the heat sink surface for flow rates between 0.6 and 1.2 g min−1. 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.

Keywords

MicrochannelsMicroscale heat transferInfrared thermographySpatially resolvedTemperature measurementSingle-phase flows

List of symbols

a

absorption coefficient (cm−1)

Dh

channel hydraulic diameter (m)

e

radiant energy flux (W m−2)

G

radiant flux incident on the heat sink (W m−2)

H

height of the channel (m)

h

local heat transfer coefficient (W m−2 K−1)

i

location index in channel direction (x direction)

j

location index in a cross-direction to channel (y direction)

i

location index in detector array corresponding to i

j

location index in detector array corresponding to j

\( \ifmmode\expandafter\dot\else\expandafter\.\fi{m} \)

mass flow rate (kg s−1)

n

refractive index

Nu

Nusselt number \( ({\text{Nu}} = h\,D_{{\text{h}}}/k) \) (dimensionless)

q

heat flux to the heat sink (W m−2)

Re

Reynolds number \( ({\text{Re}} = V\,D_{{\text{h}}} /\nu ) \) (dimensionless)

\( \ifmmode\expandafter\bar\else\expandafter\=\fi{R} \)

total reflectance

S

radiation path length (m)

t

thickness of the medium (cm)

Tf

fluid temperature (°C)

V

channel mean velocity (m s−1)

W

width of the channel (m)

xi

distance of position i from the channel entrance (m)

Greek symbols

Δ

incremental value

ε

emissivity

λ

wavelength

μ

dynamic viscosity of fluid (Pa s)

ν

kinematic viscosity of fluid (m2 s−1)

ρ

surface reflectivity

τf

transmittance of water

Superscripts and subscripts

b

blackbody

cal

calibration

det

detector

e

emission

f

fluid

hsb

heat sink background

lens

camera lens

sens

sensed

Si

Silicon

1 Introduction

Proper thermal and fluidic design of microscale components and systems requires an in-depth understanding of fluid flow and heat transfer processes in microchannels. Detailed temperature measurements of convective flows through microchannels are scarce in literature. Obtaining such local data poses a significant challenge and, in many cases, the data obtained have considerable measurement uncertainties. The goal of this paper is to discuss the application of microscale infrared thermography (μ-IRT) to measure spatially local temperature in single-phase flows through microchannels.

IRT is a well-established measurement technique in macroscale heat transfer research (e.g., Astarita et al. 2000;Carlomagno and de Luca 1989). Microscale IRT offers the possibility to measure, non-intrusively local temperatures in geometries in the range of tens to hundreds of micrometers, 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 (Hestroni et al. 2003a).

Several studies of single and two-phase flow and heat transfer in microchannels have been reported in the past 15 years, and are summarized in review papers (Palm 2001; Ghiaasiaan and Abdel-Khalik 2001; Sobhan and Garimella 2000; Kandlikar 2002; Hassan et al. 2004). In his review of single- and two-phase microchannel flows, Palm (2001) summarized that heat transfer results of various single-phase flow studies were contradictory, with both high and low Nusselt numbers (Nu) reported for laminar flows. Discrepancies among the measurements were attributed to the difficulties in measurement of fluid and surface temperatures in microchannels.

Typically, surface temperature measurements are performed either using thermocouples located at some depth below the wall–fluid interface of the microchannel (e.g., Qu and Mudawar 2003; Peng and Peterson 1994; Tso and Mahulikar 2000), or by a few thin-film resistance temperature detectors deposited directly on the bottom side of a silicon (Si) heat sink (e.g., Koo et al. 2001; Zhang et al. 2002; Popescu et al. 2002). In these studies, the temperature measurements were restricted to a few local points in the heat sink.

Recently, a few studies on non-intrusive quantitative thermal imaging of mini- and microchannel heat sink surface temperatures have been reported. Hestroni et al. (2003a) presented a technique using IRT to determine the outer wall temperature of a 1.07-mm capillary tubing. To reduce the background radiation, a controlled temperature background surface at the same mean temperature as the heated capillary tubing was utilized. Hestroni et al. (2001, 2003b) performed visualization studies of flow boiling in triangular cross-section microchannel arrays for two different plenum designs using high-speed imaging for flow visualization and IR radiometry of the heater surface. Irregularities in spanwise heater surface temperatures due to flow instabilities under uniform and non-uniform heat flux conditions were observed. Hollingworth (2004) measured the local channel wall temperature distribution in single- and two-phase minichannel flows using thermochromic liquid crystal imaging of heated side wall. The three other side walls were held 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. (2002) used IRT to examine the outside wall temperature distribution for flow boiling in rectangular microchannels and concluded that it is possible to detect the streamwise position of flow boiling regions using this technique. Muwanga and Hassan (2005) demonstrated the use of un-encapsulated thermochromic liquid crystal thermography to measure the outer surface temperature of a microtube. Recently, Patil and Narayanan (2005) described an IRT technique for direct microchannel wall/near-wall fluid temperature measurement in liquid flows through Si microchannels. Direct measurement of wall temperature is desirable because it provides for an accurate estimation of the local heat transfer variation along the channel.

1.1 Objectives

Application of μ-IRT to microchannel convective flows, with an emphasis on the experimental and data analysis procedures required for quantitative measurement of the desired temperature, is presented in this paper. This technique can be applied for direct measurement in IR-transparent heat sinks of (a) the visualized wall temperature for convective flows through microchannels with IR-opaque walls, or (b) the liquid temperature of an opaque fluid near the visualized channel wall for transparent channel walls. This paper discusses the theory and procedure for the above measurements, and specifically reports measurement of the latter. Sources of noise in temperature, measurement uncertainties, and limitations of the technique are presented. Experiments are performed for deionized water flow through a Si microchannel at a fixed electrical power input to the heat sink. Water temperatures are determined for four different flow rates varying from 0.6 g min−1 (Re=200) to 1.2 g min−1 (Re=300).

2 Estimation of desired temperature

2.1 Estimation of fluxes from relevant radiation sources

For application of μ-IRT, it is important to enhance the contribution of energy radiated from the desired source compared to other (noise) sources of thermal radiation. In microscale geometries, this is a challenging task, and requires a combination of good test section design, and experimental and data analysis procedures. This section summarizes the various sources that constitute the net radiant energy flux from the heat sink based on classical radiation theory (Siegel and Howell 2002).

Consider, as shown in Fig. 1, that an IR detector is focused, by a system of optical components, on an IR-opaque fluid flowing inside a microchannel that is located within a transmitting heat sink substrate. For purposes of this discussion, consider that the fluid is water and the heat sink is made of Si. As mentioned previously, in this situation, μ-IRT provides a measure of the fluid temperature near the visualized channel wall. Depending on the degree of opacity of the fluid, the detected fluid temperature will represent a near-wall average liquid temperature. Note that the discussion provided in this section is equally applicable to a situation, where the channel wall is coated with an IR-opaque material. In this case, the channel wall surface temperatures can be directly measured, and the fluid can be either IR-transparent or IR-opaque.
https://static-content.springer.com/image/art%3A10.1007%2Fs10404-005-0074-3/MediaObjects/10404_2005_74_Fig1_HTML.gif
Fig. 1

Schematic of the test section and μ-IRT system. The detail of the microchannel on the right indicates the different radiative flux components in Eq. 1

The detail of the heat sink in Fig. 1 shows the net energy flux radiated from a sub-area (Δx, Δy) of the near-wall fluid. It mainly consists of four components: (1) radiation emitted by water (desired energy flux), (2) radiation emitted by the bulk channel Si wafer by virtue of its elevated temperature, (3) net-reflected radiation that is incident on the Si substrate from the detector, and (4) net-unfocussed radiation from the heat sink background (hsb), which is the surface directly below the fluid channel,
$$ e_{{{\text{net}}(ij)}} = e_{{{\text{f}}(ij)}} + e_{{{\text{Si}}(ij)}} + e_{{{\text{r}},{\text{det}}(ij)}} + e_{{{\text{hsb}}(ij)}} . $$
(1)

In general, each location (i, j) will have varied contributions of the terms on the right side of Eq. 1. For example, for the experiment discussed in this paper, the last term in Eq. 1 contributed predominantly to enet in the sub-areas located outside the microchannel. In the physical sub-areas that are within the field of view of the microchannel, it is desirable to maximize the contribution of the first term (signal) and eliminate/mitigate contributions of all other terms (noise). For measurement of IR-opaque wall temperatures, note that the fourth term is identically zero for the sub-areas in the field of view of the microchannel.

The variations in radiation sensed by different pixels of the sensor array, edet,sens (see Fig. 1) is represented as
$$ e_{{{\text{det}},{\text{sens}}({i}\ifmmode{'}\else$'$\fi{j}\ifmmode{'}\else$'$\fi)}} = C_{{ij}} e_{{{\text{net}}(ij)}} . $$
(2)

The sensor used in this experiment (details are provided in a later section) detects photons in the bandwidths of [3.4–4.1] and [4.5–5.1] μm. Because radiation in these bandwidths is alone sensed by the detector, good experimental and data analysis procedures for IRT are needed. The sensed intensity will differ at each pixel from the net radiated intensity given by Eq. 1 by the factor Cij due to variations in (a) the configuration factor between the physical measurement area and the corresponding sensor pixel array, and (b) the type of irradiation from the sources in Eq. 1 at each (i, j) location of the object plane (e.g., diffuse, normal, or specular). In addition, Cij also accommodates for intensity variations due to noise from the camera optics. The voltage signal proportional to the detected intensity that is recorded by the data acquisition system will, in addition, include electronic noise of the system.

Another source of thermal noise, that from the camera surroundings, can creep into the detected intensity measurement in several ways, such as those by (1) unfocussed stray radiation incident on the detector array from the camera and lens walls due to variations in the surrounding temperature, (2) surrounding noise reflected from the heat sink (forms a part of enet), and (3) attenuation of intensity due to the participating medium between the camera and the heat sink. The first noise source can be estimated by the addition of an intensity term in Eq. 2 (Horny 2003). This noise was minimized by a careful camera design and separate calibration of each lens used with the camera by the manufacturer and has, therefore, been neglected in this analysis. Because the configuration factor from the surroundings to the imaged area is calculated to be very small (8.13×10−4), the second noise source can be neglected. The third noise source is negligible because the distance between the camera optics and the target test section is small (<30 mm) and the camera optics is equipped with narrow band stop filters located in front of the detector array that significantly attenuates atmospheric CO2 and H2O vapor emissions.

Radiative quantities and properties in Eq. 1 need to be estimated to obtain the water temperature from the net intensity. To highlight important concepts while retaining simplicity of the analysis, the following assumptions are introduced.
  • 1. The location (i, j) of the physical sub area (Δx, Δy) is ignored.

  • 2. The temperature variation through the depth of the heat sink substrate is assumed negligible. This is a reasonable assumption because of the high thermal conductivity of Si substrate.

  • 3. As a consequence of the first assumption, the path length for participating radiation analysis is assumed to be equal to the thickness of the medium. Ideally, this will hold exactly for normal radiation, and be larger for radiation incident from other angles.

The total reflectance of Si for radiation incident from the air or water sides is given by (Siegel and Howell 2002)
$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{R}_{{{\text{Si}}}} = \frac{{\rho _{1} + \rho _{2} (1 - 2\rho _{1} )\tau ^{2}_{{{\text{Si}}}} }} {{1 - \rho _{1} \rho _{2} \tau ^{2}_{{{\text{Si}}}} }}, $$
(3)
where subscript 1 refers to the interface on which radiation is incident (in this case, the Si–water interface) and subscript 2 refers to the interface through which radiation leaves the substrate (in this case, the Si–air interface).
For a constant absorption coefficient throughout the substrate (assumption 2), the transmittance of radiation through the radiation path length of 215 μm of Si (assumption 3) from the channel top wall to the outer side facing the detector (see heat sink detail in Fig. 1) is given by
$$ \tau _{{{\text{Si}}}} = {\text{exp}}( - a_{{{\text{Si}}}} t_{{{\text{Si}}}} ). $$
(4)

Using the bulk absorption coefficient of Si (Hordvik and Skolnik 1977) of 4.2×10−4 cm−1 at 3.8 μm in Eq. 4 results in τSi=1. Note that although this value holds good only for λ=3.8 μm, due to the scarcity of absorption coefficient data for Si in open literature in the IR detector bandwidth, this value is assumed to be representative for the two detector bands of 3.4–4.1 and 4.5–5.1 μm.

With τSi=1, Eq. 3 can be simplified such that the resulting total reflectance of Si to radiation incident on either the air or water side will be identical and given by
$$\bar{R}_{\text{Si}} = \frac{{\rho _{{\text{Si}}{\text{--}}{\text{a}}} + \rho _{{\text{Si}}{\text{--}}{\text{f}}} - 2\rho _{{\text{Si}}{\text{--}}{\text{a}}} \rho _{{\text{Si}}{\text{--}}{\text{f}}}}} {{1 - \rho _{{\text{Si}}{\text{--}}{\text{a}}}} {\rho _{{\text{Si}}{\text{--}}{\text{f}}}}}. $$
(5)
Because the extinction coefficients for air, water, and Si are negligible in detector IR bandwidth, the surface reflectivity at their interfaces can be evaluated by
$$ \rho _{{1{\text{--}}2}} = {\left( {\frac{{n_{1} - n_{2} }} {{n_{1} + n_{2} }}} \right)}^{2} , $$
(6)
where n1 and n2 are the refractive indices of the mediums that form an interface.
The net transmittance of Si to radiation emitted by water at the water–Si interface can be evaluated by
$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} = 1 - (\ifmmode\expandafter\bar\else\expandafter\=\fi{R}_{{{\text{Si}}}} - \rho _{{\text{Si}}{\text{--}}{\text{f}}}). $$
(7)
Note that net transmittance as given by Eq. 7 differs from transmissivity of Si, τSi (see Eq. 4) because multiple reflections are taken into account in calculation of \( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \). It is also different from the “overall” transmittance defined in Siegel and Howell (2002) in that the reflection from the first interface is not considered. The radiation flux emitted by water within the Si substrate is given by (Siegel and Howell 2002)
$$ e_{{\text{f}}} = n^{2}_{{{\text{Si}}}} \varepsilon _{{\text{f}}} \sigma T^{4}_{{\text{f}}} $$
(8)
and that water radiation flux leaving the heat sink is given by
$$ e_{{\text{f}}} = \frac{1} {{n^{2}_{{{\text{Si}}}} }}\ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} e_{{\text{f}}} = (\ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \varepsilon _{{\text{f}}} )\sigma T^{4}_{{\text{f}}} . $$
(9)
The latter equality in Eq. 9 uses Eq. 8. Incorporating the preceding analysis, Eq. 1 can be written as
$$ e_{{{\text{net}}}} = \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \varepsilon _{{\text{f}}} e_{{{\text{b}},{\text{f}}}} + \varepsilon _{{{\text{Si}}}} e_{{{\text{b}},{\text{Si}}}} + \ifmmode\expandafter\bar\else\expandafter\=\fi{R}_{{{\text{Si}}}} G_{{{\text{det}}}} + e_{{{\text{hsb}}}} , $$
(10)
where eb refers to the radiative flux emitted by an ideal radiator. Because τSi≈1, the absorbance and, hence, the emittance of channel Si wafer is equal to zero. This in turn implies that the radiation emitted by Si is negligible and hence the second term on the right side in Eq. 10 can be neglected. Because the detector is cryogenically cooled to a temperature of 77 K, the detector radiation reflected from top Si wafer is negligible. The use of an anti-reflective coating also reduces the contribution of this flux. Thus, the third term in Eq. 10 is also negligible. The refractive indices of air, Si, and water in range 3.5–5.1 μm are 1 (Siegel and Howell 2002), 3.43 (Edwards and Ochoa 1980), and 1.4 (Bertie and Lan 1996), respectively. Using Eqs. 5, 6, and 7, the values of \( \ifmmode\expandafter\bar\else\expandafter\=\fi{R}_{{{\text{Si}}}} \) and \( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) are estimated to be 0.39 and 0.79, respectively.

2.2 Influence of heat sink background radiation

To determine the influence of the fourth radiant flux term in Eq. 1 on enet in the sub-area of the microchannel, the intensity attenuation of the radiant flux from the heat sink bottom surface through water in the microchannel must be determined. If this energy flux is completely attenuated by the 135-μm depth of water in the microchannel, it can be neglected from Eq. 1. The fraction of radiation transmitted through an absorbing and scattering medium depends on the spectral variation of the extinction coefficient of the medium and the radiation path length. As a first approximation, neglecting scattering, and emission, Bouger’s law (Siegel and Howell 2002) gives the net attenuation of radiation through an absorbing medium to be
$$ \frac{{e_{{\text{e}}} (S)}} {{e_{{\text{e}}} (0)}} = {\text{exp}}{\left[ { - {\int\limits_0^S {a_{\lambda } (y){\text{d}}y} }} \right]}. $$
(11)
Calculations were performed with aλ independent of path length (assumption 2) to estimate the optical thickness of water in the detector bandwidths. On an average, using a mean absorption coefficient of 319 cm−1 at 40°C over the detector wavelength bandwidth, a 135-μm deep water column attenuates in excess of 99% of the radiation incident upon it. Thus, the water opacity assumption is appropriate over the mean bandwidth of the detector. The Planck mean absorption coefficient,
$$ a_{{\text{P}}} = \frac{{{\int_0^\infty {a_{\lambda } e_{{\lambda {\text{b}}}} (\lambda ,T){\text{d}}\lambda } }}} {{\sigma T^{4} }} $$
(12)
was used to determine the mean absorption coefficient for water (Siegel and Howell 2002). Figure 2 shows the spectral variation of absorption coefficient based on values reported in Siegel and Howell (2002), along with the optical path depth for 99% attenuation of incident intensity at the discrete wavelengths. Also indicated in the figure are the detector bandwidths. The absorption coefficient for water in the wavelength range of the detector varies widely, from a high of 721 cm−1 at 3.4 μm to a low of 112 cm−1 at 3.8 μm. Of particular concern is the low absorption coefficient in the 3.6–4.4 μm range, which result in optical depths between 157 and 418 μm. A direct implication is that the temperature of the bottom surface is partially transmitted to the detector in these discrete wavelengths. This seriously hinders the accuracy of temperature measurement.
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Fig. 2

Bar graph indicating the spectral absorption coefficients for water in the detector bandwidth (data from Siegel and Howell 2002) and the variation of path length for 99% intensity attenuation

Modifications to the experimental test section or/and instrumentation can be made to mitigate the effect of selective transmission of radiation from the hsb surface. The bottom surface could be fabricated of a material that has a uniform and low emissivity. In addition (or alternately), a selective notch filter can be placed in the optical path of the detector to attenuate radiation in the wavelengths with low absorption coefficient. In this particular experiment, a notch filter in the 3.4–4.0 μm could be placed prior to the microscope objective, as indicated in Fig. 2. A distinct advantage of the selective notch filtering technique is that there is no additional complication to the microchannel fabrication. However, care has to be taken to maintain the filter at a constant temperature during both calibration and experiments. The method also suffers from disadvantages of higher cost and the necessity to change filters with the fluid in the microchannel.

2.3 Role of anti-reflective coating and calibration

In Eq. 10, if the first term is the only significant radiation flux, the desired fluid temperature can be written in terms of the net intensity that is sensed by the detector using Eq. 2,
$$ T_{{\text{f}}} = {\left( {\frac{{e_{{{\text{det}},{\text{sens}}}} }} {{C_{{ij}} \sigma \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }}} \right)}^{{1/4}} . $$
(13)
The uncertainty in Tf arises from uncertainties in the estimation of the intensity sensed by the detector and uncertainties in fluid emissivity, the net transmittance of the heat sink substrate, and Cij, and can be evaluated using a propagation of errors method (Figliola and Beasley 2000),
$$ \begin{aligned}{} \frac{{u_{{T_{{\text{f}}} }} }} {{T_{{\text{f}}} }} = & \frac{1} {4}{\sqrt {{\left( {\frac{{u_{{e_{{{\text{det}},{\text{sens}}}} }} }} {{e_{{{\text{det}},{\text{sens}}}} }}} \right)}^{2} + {\left( {\frac{{u_{{\varepsilon _{{\text{f}}} }} }} {{\varepsilon _{{\text{f}}} }}} \right)}^{2} + {\left( {\frac{{u_{{\ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }} }} {{\ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }}} \right)}^{2} + {\left( {\frac{{u_{{C_{{ij}} }} }} {{C_{{ij}} }}} \right)}^{2} } } \\ = & \frac{1} {4}{\sqrt {{\left( {\frac{{u_{{e_{{{\text{det}},{\text{sens}}}} }} }} {{e_{{{\text{det}},{\text{sens}}}} }}} \right)}^{2} + {\left( {\frac{{u_{{C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }} }} {{C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }}} \right)}^{2} } }. \\ \end{aligned} $$
(14)
Note that Tf in the above equation is in absolute units and that the individual uncertainties of Cij, εf, and \( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) can be combined as \( (C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} ) \). Equation 14 shows that the uncertainty in temperature measurement can be reduced for the present technique by reducing \( u_{{e_{{{\text{det}},{\text{sens}}}} }} \), \( u_{{C_{{ij}} }} \), \( u_{{\varepsilon _{{\text{f}}} }} \), and \( u_{{\ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }} \) and by increasing enet,sens, Cij, \( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \), and εf. Uncertainties in sensed detector intensity arises due to bias and random errors within the camera optical path and the detector and camera electronics and are largely dependent on the camera and experimental procedure. Reduction in \( u_{{C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} }} \) can be achieved by a detailed in situ calibration. Increase in net transmittance of Si can be attained by coating the top side of the channel wafer with an anti-reflection coating in the range of the detector, thereby increasing the ρSi–a and hence \( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) to about 0.98. Note that Eq. 13 was used to determine the uncertainty estimate in Eq. 14, implying that the experimental and data analysis procedures eliminate the contributions of other noise radiation represented by Eq. 10. If this is not the case, Eq. 10 needs to be used for uncertainty calculations.

2.4 A note on the detected fluid temperature

Although the technique described here provides the opaque fluid temperature, it is unclear whether the measurement refers to fluid temperature exactly at the fluid–wall interface or is representative of an average over a certain depth of fluid near the wall. Because of the steep temperature profile and exponential intensity attenuation, a significant portion of radiated energy from water is expected to be restricted to a region of a few microns thick near the channel upper wall. In this sense, the temperature would represent an average fluid temperature in the near-wall region. Measurements of local heat transfer (Patil and Narayanan 2005) indicate that the fully developed Nu estimated using this technique are higher by 10–22% over the solution for laminar macroscale flows (Shah and London 1978). Because the detected fluid temperature was used as an estimate of the wall temperature, an overestimation of Nu indicates that the fluid temperature refers to an average near-wall temperature. An exact evaluation of the actual depth requires a complete solution of the radiation transfer equations in the fluid with consideration to absorption, emission, transmission of the fluid and convection. This aspect needs to be studied further.

3 Experimental facility and test section design

3.1 Microscale IRT system

The μ-IRT imaging system (CMC Electronics, TVS 8500) is a mid-wavelength (3.5–4.1, 4.5–5.1) μm range imager which consists of a front-illuminated 256×56 InSb focal plane array of photovoltaic type detectors, cryogenically cooled to ensure high-sensitivity and low-noise measurement. With a 30-mm fixed focal distance microscope lens, the camera can record intensity (and temperature) distributions at 60,416 locations in an area of 2.56×2.36 mm2, at a maximum rate of 120 frames/s. The camera and microscope lens were calibrated as a system by the manufacturer. For a known emissivity of the test article, the resolution of temperatures recorded with the microscope lens is better than 50 mK.

3.2 Experimental facility and test section

The experimental facility is shown schematically in Fig. 3a. A constant flow rate of water through the system was generated using pressurized air. The water flow rate was controlled by a micrometer needle valve and measured by a Coriolis flow meter (Micro Motion, Inc., Sensor Model CMF010, Transmitter Model 2700) and verified by a calibrated rotameter (Gilmont; Barnant Co.). Differential pressure between the microchannel inlet and atmosphere, and water temperature prior to the plenum were measured using a capacitance-type pressure transducer (Validyne, Inc., Transducer Model DP45 with Model CD15 modulator/demodulator) and a calibrated thermocouple (Type K), respectively.
https://static-content.springer.com/image/art%3A10.1007%2Fs10404-005-0074-3/MediaObjects/10404_2005_74_Fig3_HTML.gif
Fig. 3

Schematic of the experimental setup: a experimental facility; b test section

The test section schematic is shown in Fig. 3b. Primarily, it consists of a Si heat sink that contains a single 50 μm wide by 135 μm deep rectangular microchannel of length 13 mm, and a fluidic interconnect. The side and bottom channel walls were fabricated in a 350 μm channel wafer using a deep reactive ion etching technique. The fourth channel wall was formed by a second 350 μm cover wafer that was fusion bonded to the channel Si wafer. Fluid entered the channel through a nanoport fitting (Upchurch Scientific®) into a 2-mm-diameter inlet plenum that was laser drilled into the cover wafer. The heat sink was inverted for IR visualization such that the water flow was visualized through the channel wafer. As discussed in the previous section, to maximize sensitivity to the desired temperature measurement, a broadband anti-reflective coating in the wavelength range of 3–5 μm was deposited on the imaged side of the wafer. The company claims a total transmittance for Si in air of 0.97 with this coating.

The heat sink was heated from the cover wafer side by a 5-mm long, 12-mm wide, 250-μm thick Kapton™ heater (Minco). The heater was located approximately 2 mm away from the channel exit. A 25-μm thick copper foil, covering the area of heat sink past the inlet plenum fitting, was placed between the heater and the Si heat sink. The heater was attached to the copper foil by means of thermally conductive double-sided tape. The heat sink was firmly located above the copper foil and heater using adhesive tape around the periphery of the heat sink onto a Teflon® base and by a U-shaped plexiglass clamp (not shown in Fig. 3b for clarity). The Teflon base minimized the heat losses from the backside of the heater. Water exited the channel into a chamber cut into the test section Teflon® base. Because a jet was formed for most of the flow conditions tested, a foil deflector was located in the chamber to direct the jet into the exit chamber.

The placement of a uniform and low emissivity material (such as the copper foil in this case) below the microchannel in between the heat sink and heater was critical to avoid degradation of the detector intensity response to water temperature that is caused due to varying, large emission from the bottom and surrounding high-emissivity surfaces, such as the double-sided tape or the thick-film heater. As mentioned in the introduction, to eliminate background noise, Hestroni et al. (2003a) proposed a technique where the temperature of the background was closely matched with that of the object whose temperature was to be determined. This would require that the background temperature be independently controlled. The lack of such control over the hsb in the present experiments precludes the use of this technique. Note, however, that the background intensity (see Figs. 5 and 7) is fairly uniform or steadily varying along with the channel fluid intensity, such that their difference is almost constant.

4 Experimental procedure and data analysis

4.1 Calibration procedure

In Section 2.3, the importance of a high value of \( C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \), along with a low-uncertainty were identified as essential for a high-sensitivity and low-uncertainty fluid temperature measurement. Estimation of local variations in \( C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) can be made by an in situ calibration process described in this section. The calibration errors will be discussed in the uncertainty analysis section, and form a part of the fluid temperature errors as given by Eq. 14. Because the imaging area of the microscope lens was fixed at 2.56×2.36 mm2, several intensity maps were recorded and later combined to provide the complete picture of variation of intensity along the channel. Figure 4 shows a schematic of the locations at which intensity maps were recorded. These locations were identical to within 1 μm between the calibration and the heated experiments. Note that the locations had significant overlap, with images recorded axially at 1 mm intervals; the data in the regions of overlap were averaged.
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Fig. 4

Schematic of the heat sink indicating the overlapped imaging locations spaced 1 mm apart (not to scale)

For calibration, water at Tf=23.5°C was pumped through the microchannel and intensity maps were recorded at specific locations along the channel (see Fig. 4). These maps were used to determine \( C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) at each location. An average of ten intensity maps at each location recorded at 30 frames s−1 was used to determine local correction factors. These multiple images were later used to determine precision errors in detected intensity as a part of the calibration errors.

Figure 5 shows one such intensity map recorded during calibration, recorded at a distance of x=4.5 mm downstream of the microchannel inlet. Note that the intensity of the background is very uniform, thereby reducing the errors due to spatial variations in background emission. Figure 6 shows \( C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) corresponding to the centerline of the channel in Fig. 5, calculated using Eq. 13 and the known fluid temperature during calibration.
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Fig. 5

Typical intensity map at an axial location of 4.5 mm from the entrance of the microchannel obtained during calibration; Re=251

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Fig. 6

Plot of correction factor, obtained from calibration, along the channel centerline at a location of 4.5 mm from the channel entrance; Re=251

4.2 Temperature measurement procedure

During test conditions a constant electric power of 2.3 W was provided to the heater. The electrical energy input was determined using voltage and current measured with a correction for voltage drop in the heater lead wires. This value of power ensured a minimum rise of 10°C in bulk fluid temperature along the total length of the channel for all test conditions. Overlapping intensity maps that each covered 2.56 mm of axial channel length were recorded at 14 locations spaced 1 mm apart, see Fig. 4. Care was taken to ensure identical traverse locations between the calibration and test conditions. Figure 7 indicates a heated intensity map, recorded at the same location as the calibration map in Fig. 5. The background intensities are of similar magnitude to the fluid temperature and increase in the same direction as the fluid intensity. Hence, the contribution of background radiation is fairly constant spatially. With \( C_{{ij}} \varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \) factor applied to each location along the channel centerline from Fig. 5, the near-wall fluid temperatures along the channel centerline can be determined from Eq. 13, and is shown in Fig. 8.
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Fig. 7

Typical intensity map of the heated Si heat sink at an axial location of 4.5 mm from the channel entrance; Re=251

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Fig. 8

Plot of corrected near-wall fluid temperature at a location of 4.5 mm from the channel entrance based on intensities recorded in image map of Fig. 7 and local correction factor in Fig. 6; Re=251

Figure 9 shows a typical true Tf composite plot obtained from temperature data at the 14 locations for Re=297 test condition. The true temperature data obtained from location adjacent to each other have overlapping regions where the data were averaged to obtain a final Tf value for that position. The averaged temperature data thus obtained were curve fitted using Tablecurve 2D® software. Note that not all data points are shown to retain clarity of the figure. Figure 10 shows the fluid temperature plotted against 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 microchannel.
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Fig. 9

Averaged corrected near-wall fluid temperature profile along the microchannel. Test condition: Re=297; q″=0.89 W cm−2. The unfilled symbols represent true temperature data

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Fig. 10

Axial profile of local fluid temperature Tf with Re

4.3 Uncertainty analysis

Uncertainties in measured and estimated variables are shown in Table 1. The precision error in intensity measurement was determined by analyzing ten images at a fixed location at steady state for different Re. As discussed in Section 2.3, Eq. 14 was used to determine the uncertainty in Tf at each location along the axis. In addition, the error in the curve fit shown in Fig. 9 was also included in the final Tf uncertainty. Because the final value of temperature at each location is based on the curve fit equation, the curve fit error has to be included in temperature uncertainty estimation. Bias error in measurements of spatial location, x, was obtained from manufacturers’ product specifications. The thermocouples were calibrated using a NIST-traceable RTD. Uncertainty in Re was calculated using a sequential perturbation method (Figliola and Beasley 2000). The uncertainties are reported as absolute values and/or as a percentage of local value. Curve fit error was the main contributor of error in temperature measurement.
Table 1

Uncertainties in measured and estimated variables

Measured variable

Total error

Comments

Wetted perimeter

0.0148 μm (0.004%)

Based on deviation from a 50×135 μm rectangular geometry

Channel cross-section

2.0%

Based on deviation from a 50×135 μm rectangular geometry

Dh (μm)

135 μm2 (2.0%)

Based on wetted perimeter and channel cross-section

Camera spatial resolution, x (μm)

10

 

\( \ifmmode\expandafter\dot\else\expandafter\.\fi{m} \) (g s−1)

2.3% (Re=297) to 4.0% (Re=204)

Calibrated using a set flow rate from a syringe pump; data averaged over 20 min

\( C\varepsilon _{{\text{f}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{T}_{{{\text{Si}}}} \)

0.26%

Includes bias and precision errors in intensity and calibration error in thermocouple used for fluid temperature measurement

Tsur (°C)

0.15

Calibration error of thermocouple

Estimated variable

Tf (°C)

0.91 (Re=204)

Based on uncertainties in Eq. 14 and error of curve fit such as that in Fig. 9

1.33 (Re=251)

1.04 (Re=285)

0.60 (Re=297)

Re

3.3% (Re=297) to 4.7% (Re=204)

Includes uncertainty in geometry and flow rate

5 Conclusions

A non-intrusive technique for measurement of near-wall temperature of an IR-opaque fluid has been presented and demonstrated in the context of water flow through a Si microchannel. This technique is equally valid for detection of microchannel wall surface temperature for IR-opaque walls. In either case, the heat sink material needs to be transmissive to IR radiation in the detector bandwidth. The technique offers a way to measure local temperatures in microchannel flows.

A radiation analysis is presented to estimate the role of various energy fluxes that contribute to the thermal signal and noise in the measurement. Both high combined fluid emissivity-net substrate transmittance factor and a low uncertainty in its measurement are important for the implementation of this technique. A detailed calibration was used to accurately estimate this factor, while a broadband, anti-reflective coating was employed to enhance the value of net substrate transmittance. Results indicate that spatially local temperatures can be determined with uncertainties ranging from a low of 0.60°C for Re=297 to a high of 1.33°C for Re=251.

Acknowledgments

Partial support for the thermography system was provided by the Oregon State University through Research Equipment Reserve Fund grants.

Copyright information

© Springer-Verlag 2006