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Research Papers: Conduction

Estimating Two Heat-Conduction Parameters From Two Complementary Transient Experiments

[+] Author and Article Information
Robert L. McMasters

Department of Mechanical Engineering,
Virginia Military Institute,
Lexington, VA 24450
e-mail: mcmastersrl@vmi.edu

Filippo de Monte

Department of Industrial and Information
Engineering and Economics,
University of L'Aquila,
Via G. Gronchi n. 18,
L'Aquila 67100, Italy

James V. Beck

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 26, 2017; final manuscript received October 16, 2017; published online March 30, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(7), 071301 (Mar 30, 2018) (8 pages) Paper No: HT-17-1507; doi: 10.1115/1.4038855 History: Received August 26, 2017; Revised October 16, 2017

A desirable feature of any parameter estimation method is to obtain as much information as possible with one experiment. However, achieving multiple objectives with one experiment is often not possible. In the field of thermal parameter estimation, a determination of thermal conductivity, volumetric heat capacity, heat addition rate, surface emissivity, and convection coefficient may be desired from a set of temperature measurements in an experiment where a radiant heat source is used. It would not be possible to determine all of these parameters from such an experiment; more information would be needed. The work presented in the present research shows how thermal parameters can be determined from temperature measurements using complementary experiments where the same material is tested more than once using a different geometry or heating configuration in each experiment. The method of ordinary least squares is used in order to fit a mathematical model to a temperature history in each case. Several examples are provided using one-dimensional conduction experiments, with some having a planar geometry and some having a cylindrical geometry. The parameters of interest in these examples are thermal conductivity and volumetric heat capacity. Sometimes, both of these parameters cannot be determined simultaneously from one experiment but utilizing two complementary experiments may allow each of the parameters to be determined. An examination of confidence regions is an important topic in parameter estimation and this aspect of the procedure is addressed in the present work. A method is presented as part of the current research by which confidence regions can be found for results from a single analysis of multiple experiments.

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References

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Figures

Grahic Jump Location
Fig. 2

Temperature and thermal diffusivity sensitivity coefficient curves at r = 0 for the R01B1T0 case. The maximum scaled sensitivity coefficient is 0.5683 at t̃= 0.1965.

Grahic Jump Location
Fig. 1

Temperature and sensitivity coefficient curves at x = L for the X22B10T0 case

Grahic Jump Location
Fig. 4

Temperature and sensitivity coefficients for the x = 0 and L locations for the X22B10T0 case. The maximum Δ+ = 0.00588 at t̃max=0.65.

Grahic Jump Location
Fig. 3

The minimum scaled C-sensitivity is at about t̃≈0.405 and is the value of −0.2983 and the C-sensitivity at the same time is −0.4033. The maximum Δ+ = 0.0111 at t̃max=2.94 for the X21B10T0 case.

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