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.