Heat Content Asymptotics

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Most discussions of heat transfer address primarily the steady state solution, the long-term solution to heat flow that is measured once the function has stabilized. The Heat Asymptotics Research Project (HARP) addresses instead the transient solution, the very short-term function that appears before settling into the steady state solution.

Mathematical discussions of the subject (see Resources) show that the transient solution for the heat flow depends on the topological features of the object. For example, a cube in a water bath should show different heat flow, in the very short term, on an edge than on a face. However, this discussion has been almost exclusively in the realm of mathematics, with so far very little physical experimentation to corroborate the mathematical models.


The overarching goal of the Heat Asymptotics Research Project is to provide physical data that is relevant to the question of whether transient heat flow depends on the shape of an object. This question will be addressed in three parts: with macroscopic objects using thermocouple sensors, with macroscopic objects using an interferometer, and with microscopic objects using the optical tweezers.

A peripheral goal of this project is to collect and organize secondary research relevant to the subject, in order to better understand the specific field of heat flow studies and to learn from others’ similar experiments, if any.

Macroscopic Objects Measured with Thermocouples

Experimental Setup: Part one of the research project involves taking data from several differently shaped aluminum objects (a cube, cylinder, sphere, torus, and tetragon) submerged in a water bath, whose temperature is controlled by a chiller. The objects have small holes drilled into them at various faces, edges, and vertices within which T-type thermocouples are attached. The objects will enter the water via a spring mechanism in order to minimize the time that they are in contact with the water but not fully submerged, and an amplifier is required to make the data from the thermocouples taken on a nanosecond timescale readable. A trigger is attached to the spring mechanism to trigger the oscilloscope to take data upon the cubes entry of the water. All electronic components have been thermally isolated from the environment to reduce signal drift due to ambient temperature. (the amplifier is in a refrigerator, the water is in a cooler, the oscilloscope is in another room)

Things to check before taking data: -Battery voltage for amplifier

-Temp of oscilloscope (run temp calibration on the scope)
-Reading on the amp thermister
-Steady temperature of cooler water (the re-circulator switches on and off to try to maintain steady temp, so temp should be brought just 
below then the flow valve closed, then allow water to come to desired temp)
-Temp inside fridge

Procedure: For each shape the first step is to calibrate the thermocouples. To do this the water is chilled to a known temperture and the object submersed in it. The voltages from the thermocouple are then recorded. Adjust the temperature and repeat. This data can then be used to plot voltage vs temperature. This curve can be used to tell you the temperature of the thermocouple based off its voltage reading. Once calibration is complete data will be collected.

Microscopic Objects Measured with Optical Tweezers

This part of the project involves trapping microscopic objects of different shapes using the lab's Optical Tweezers setup. To date, groups have:

  • determined that a 980 nm laser could be used to trap microscopic objects and a 1550 nm laser could be used to heat them by coupling both wavelengths into a corresponding WDM and out along the same optical path in the system.
  • characterized trap strength for a 980 nm wavelength fiber-coupled laser.
  • determined that Thorlabs FGB67 bandpass filter (colored glass) will be a good candidate for the material of the microscopic objects because it absorbs 1550 nm and transmits 980 nm light.
  • been informed from the manufacturer that the existing Olympus UPLFLN 100xO2 objective lens will transmit at best 28% of incident 1550 nm light.
  • observed that the path of 1550 nm light coupled into the system will diverge from the path of similarly coupled 980 nm light after passing through the two lenses of the beam expander.

Summer 2015 presentation:[1]

Summer 2015 report:[2]

Future groups will have to:

  • connectorize the fiber-coupled 980 nm and 1550 nm laser outputs into the appropriate WDM to combine the wavelengths in one output fiber.
  • acquire an output coupler that can collimate both 980 nm and 1550 nm light.
  • confirm that both wavelengths of light travel identical paths through the system.
  • acquire an objective lens that can transmit both wavelengths of light efficiently.
  • fabricate micro-objects out of the Thorlabs colored glass using the focused ion beam (FIB) in CAMCOR.
  • integrate a quadrant photodiode into the system to accurately track object position for short timescales.
  • heat micro-objects using the 1550 nm laser which are trapped by the 980 nm laser and determine their transient heat flow characteristics dependent on object topology.