Technical Briefs

The Question of Thermal Waves in Heterogeneous and Biological Materials

[+] Author and Article Information
Elaine P. Scott

Director of Engineering Programs, Seattle Pacific University, 3307 Third Avenue West, Suite 307, Seattle, WA 98119-1957scotte@spu.edu

Muluken Tilahun

 Kraft Foods Research and Development, 910 Mayer Avenue, Madison, WI 53704muluken.tilahun@kraft.com

Brian Vick

Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 114-Q Randolph Hall, Blacksburg, VA 24061-0238bvick@vt.edu

J Biomech Eng 131(7), 074518 (Jul 07, 2009) (6 pages) doi:10.1115/1.3167804 History: Received November 03, 2008; Revised June 03, 2009; Published July 07, 2009

In the 1990s, there were two experimental studies that sparked a renewed interest in thermal wave behavior at the macroscale level. Both reported thermal relaxation times of 10 s or higher. However, no further experimental evidence of this behavior has been reported. Due to the extreme significance of these findings, the objectives of this study were to try to reproduce these earlier studies and offer an explanation for the outcome. These two previous studies, one using heterogeneous materials and one using bologna, were repeated following the experimental protocol provided in the studies as closely and as practically as possible. In both cases, the temperature response to a specified boundary condition was recorded. The results from the first set of experiments suggested that the thermal relaxation times presented in the previous study were actually the thermal lag expected from applying Fourier’s law, taking into account the uncertainty of the temperature sensor. In the second set of experiments, unlike the distinct jumps in temperature found previously, no indication of wave behavior was found. Here, the explanation for the previous results was more difficult to ascertain. Possible explanations include problems with either the experimental protocol or the temperature sensors used.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Experiment 1: experimental setup (not to scale)

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Figure 2

Experiment 2: experimental setup (not to scale)

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Figure 3

Experiment 1: temperature response for NaHCO3 during heating (θ=(T−Ti)/(qL/k); sensor at xs=7 mm). Replication 1: Ti=22.2°C, q=394.5 W/m2, k=0.19 W/mK; replication 2: Ti=24.3°C, q=400.8 W/m2, k=0.24 W/mK; replication 1: Ti=24.3°C, q=400.9 W/m2, k=0.30 W/mK.

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Figure 4

Comparison of mean calculated and mean experimental temperatures for experiment 1 with sand, assuming Fourier’s law (θ=(T−Ti)/(qL/k); sensor at xs=7 mm)

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Figure 5

Nondimensional experimental temperature responses for three replications for Experiment 2A (room temperature sample, θ=(T−Ti,r)/(Ti,avg−Ti,r); Ti,avg=(Ti,r+Ti,c)/2; sensor at xs=6 mm). Replication 1: Ti,r=24.4°C, temperature Ti,c=5.5°C; replication 2: Ti,r=21.3°C, temperature Ti,c=3.9°C; replication 3: Ti,r=23.1°C, temperature Ti,c=4.9°C

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Figure 6

Experiment 2A: Comparison of experimental and analytical results for room temperature sample



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