0
RESEARCH PAPER: Conduction

Heat flux determination from measured heating rates using thermographic phosphors

[+] Author and Article Information
D. G. Walker

Department of Mechanical Engineering,  Vanderbilt University, Nashville, TN 37235-1592greg.walker@vanderbilt.edu

J. Heat Transfer 127(6), 560-570 (Oct 05, 2004) (11 pages) doi:10.1115/1.1915389 History: Received August 19, 2003; Revised October 05, 2004

A new method for measuring the heating rate (defined as the time rate of change of temperature) and estimating heat flux from the heating rate is proposed. The example problem involves analytic heat conduction in a one-dimensional slab, where the measurement location of temperature or heating rate coincides with the location of the estimated heat flux. The new method involves the solution to a Volterra equation of the second kind, which is inherently more stable than Volterra equations of the first kind. The solution for heat flux from a measured temperature is generally a first kind Volterra equation. Estimates from the new approach are compared to estimates from measured temperatures. The heating rate measurements are accomplished by leveraging the temperature dependent decay rate of thermographic phosphors (TGP). Results indicate that the new data-reduction method is far more stable than the usual minimization of temperature residuals, which results in errors that are 1.5–12 times larger than those of the new approach. Furthermore, noise in TGP measurements was found to give an uncertainty of 4% in the heating rate measurement, which is comparable to the noise introduced in the test case data. Results of the simulations and the level of noise in TGP measurements suggest that this novel approach to heat flux determination is viable.

Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 4

The exact temperature response to a triangular heat flux profile (see Fig. 5). The noisy signal has a normally distributed random noise with standard deviation σ=0.02.

Grahic Jump Location
Figure 5

The heat flux history estimates are derived from the temperatures in Fig. 4. The estimate from noisy data, QYn, demonstrate how small errors become amplified. The lines merely guide the eye.

Grahic Jump Location
Figure 1

The temperature response to a zero heat flux is shown with and without added noise. The normally distributed random noise has a standard deviation of σ=0.02. Lines are added to guide the eye.

Grahic Jump Location
Figure 2

The heating rate response to a zero heat flux is shown with and without added noise. The normally distributed random noise (Hn) has a standard deviation of 0.08, and a central differencing of the noisy temperature Yn is used to produce Hd, which has a standard deviation of 0.94. The lines connecting the points merely guide the eye.

Grahic Jump Location
Figure 3

The heat flux estimates of the zero flux case from temperature measurements Yn, heat rate measurements Hn and differenced temperatures Hd. The lines connecting the estimates merely guide the eye.

Grahic Jump Location
Figure 6

Heat flux estimates derived from heating rate data using an exact matching scheme. Noise in the measured data is not amplified as in case of temperature data. The lines merely guide the eye.

Grahic Jump Location
Figure 7

Heating rate measurement data for the triangular case with an without added noise are shown. The lines merely guide the eye.

Grahic Jump Location
Figure 8

Temperature solution to a sin wave heat flux with and without added noise

Grahic Jump Location
Figure 9

Heating rate measurements of the sinusoidal heat flux with and without noise

Grahic Jump Location
Figure 10

Error in the heat flux estimates derived from temperature measurements for the sinusoidal case

Grahic Jump Location
Figure 11

Error in the heat flux estimates derived from heating rate data for the sinusoidal case

Grahic Jump Location
Figure 12

Temperature solution to a square wave heat flux with and without added noise

Grahic Jump Location
Figure 13

Heating rate measurements of the square heat flux with and without noise

Grahic Jump Location
Figure 14

The heat flux history estimates are derived from the temperatures in Fig. 1. The estimate from noisy data, QYn, demonstrate how small errors become amplified. The lines merely guide the eye.

Grahic Jump Location
Figure 15

Heat flux estimates derived from heating rate data (see Fig. 1) using an exact matching scheme. Noise in the measured data is not amplified as in case of temperature data. The lines merely guide the eye.

Grahic Jump Location
Figure 16

Norm of the error for estimates derived from the measurements indicated on a log–log scale. Errors are normalized with the total number of samples.

Grahic Jump Location
Figure 17

Phosphor emission from La2O2S:Eu after LED excitation was turned off. The data was translated so that the peak emission occurs at t=0ms. Fitting parameters are shown in Table 4.

Grahic Jump Location
Figure 18

Fit of fabricated noisy emission data using the constant and linear decay models

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In