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Supplementary Material
Heat flux concentration through polymeric thermal lenses
R.S. Kapadia and P.R. Bandaru
Department of Mechanical Engineering,
University of California, San Diego, La Jolla, CA 92093, USA
Test Specimen
Radiation
Shield
I. Temperature imaging and comparison with FEA simulations to obtain heat flux (Q)
FLIR IR
Camera
Figure S1. Scheme for measuring temperature profiles along the surface of a thermal lens.
A contactless method, employing an infrared (IR) camera (FLIR A15SC): Figure S1, was
used for imaging the temperature profiles, as the typical use of RTDs (resistance temperature
detectors) or heat flux sensors perturbs the heat flow. For high fidelity imaging, the images surfaces
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were coated with a thin layer of lampblack acrylic paint (DecoArt Inc.) with an emissivity ~ 0.95. It
was assumed that this layer is a reliable indicator of the temperature of the underlying polymer.
Additionally, the radiative and convective losses from the other surfaces were reduced through
coating of a low-emissivity (< 0.2) paint (LO/MIT-II, from Solec Energy Corp) and the use of
shields placed close (< 5 mm) to the setup. The measured temperature profiles were correlated to
those obtained from COMSOL, and Q was quantitatively deduced. The confidence in the obtained
Q was increased through close correspondence with analytical estimates as well as through
calibration by the use of simpler geometries. Additionally, the conservation of Q was always
ensured, e.g., see Figure S2. The plots of Q in the figure represent the variation across four parallel
and representative cross-sections corresponding to the PTL: Figure S2(a), and the CTL
configurations: Figure S2(b).
Figure S2. Simulated heat flux profiles along the (a) planar thermal lens (PTL), and the (b) concave
thermal lens (CTL) were used for comparison with experiment and ensuring that the heat flux was
conserved across various interfaces of the thermal lens. A high heat flux concentration is evident
through the use of the CTL.
While the computed area under the plots was constant at ~ 11.2 W/m for both the samples, the Q
profiles clearly indicate the flux concentration in the CTL case.
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II. Calibration of thermoelectric generators (TEG), used to transduce the concentrated
thermal energy and heat flux (Q) to voltage
Figure S3. A thermoelectric generator (TEG) used for transducing the thermal energy, obtained
through heat flux focusing to electrical voltage. (a) The set up for the calibration, (b) The measured
voltage as a function of the temperature difference (T)
A TEG (Digikey, Laird Technologies, Model: 430701-501) was placed on a copper plate on
a Peltier Cooler: Figure S1(a). Using two surface mount K-type thermocouples (precision fine wire
0.01” dia., from Omega Inc.), the temperature on the top of the TEG and the surface of the copper
plate was monitored. By increasing the power to the Peltier cooler, the voltage generated was
measured through a digital multimeter (Keithley 2700, cold-junction compensated) and plotted as a
function of the temperature difference: Figure S3 (b). The data was fit to a slope of 14.5 mV / K,
and has been used to convert the measured data of Figure 4(c) and 4(d).
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III. Extraction of temperature values from TEG measurements and FEA simulations
From the TEG measurements, the measured ratio of the temperature difference between
the hot and the cold sides (ΔT) at the center and the side: ΔTcenter / ΔTside was ~ 1.43.
Through
comparison with FEA simulations, the equivalent ratio was found to be ~ 1.3. It was assumed that
the cold side temperature was constant for all the three TEGs as they were in contact with the large
conforming copper block (Figure 4 (a) and (c)). Alternately, it was noted, e.g., in Figure 4(a), that
the TEGs (in the center, and the sides) were placed in contact with three nanocomposite layers, with
an averaged center ~ 0.53 W/mK and side ~ 0.36 W/mK, the ratio of which is ~ 1.47.