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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Beck, J. , and Arnold, K. , 1977, Parameter Estimation, Wiley, New York.
Parker, W. , Jenkins, R. , Butler, C. , and Abbott, G. , 1961, “ Flash Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity,” J. Appl. Phys., 32(9), pp. 1679–1684. [CrossRef]
Wagner, R. , and Clauser, C. , 2005, “ Evaluating Thermal Response Tests Using Parameter Estimation for Thermal Conductivity and Thermal Capacity,” J. Geophys. Eng., 2(4), pp. 349–356. [CrossRef]
Shonder, J. , and Beck, J. V. , 1999, “ Determining Effective Soil Formation Thermal Properties From Field Data Using a Parameter Estimation Technique,” ASHRAE Trans., 105(Pt. 1), pp. 458–466.
Bozzoli, F. , Pagliarini, G. , Rainieri, S. , and Schiavi, L. , 2011, “ Estimation of Soil and Grout Thermal Properties Through a TSPEP (Two-Step Parameter Estimation Procedure) Applied to TRT (Thermal Response Test) Data,” Energy, 36(2), pp. 839–846. [CrossRef]
Wagner, B. J. , 1992, “ Simultaneous Parameter Estimation and Contaminant Source Characterization for Coupled Groundwater Flow and Contaminant Transport Modelling,” J. Hydrol., 135(1–4), pp. 275–303. [CrossRef]
Van der Merwe, R. , and Wan, E. , 2001, “ The Square-Root Unscented Kalman Filter for State and Parameter-Estimation,” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Salt Lake City, UT, May 7–11, pp. 3461–3464.
Wang, S. , and Xu, X. , 2006, “ Parameter Estimation of Internal Thermal Mass of Building Dynamic Models Using Genetic Algorithm,” Energy Convers. Manage., 47(13), pp. 1927–1941. [CrossRef]
Chen, T. , and Athienitis, A. , 2003, “ Investigation of Practical Issues in Building Thermal Parameter Estimation,” Build. Environ., 38(8), pp. 1027–1038. [CrossRef]
Dewson, T. , Day, B. , and Irving, A. , 1993, “ Least Squares Parameter Estimation of a Reduced Order Thermal Model of an Experimental Building,” Build. Environ., 28(2), pp. 127–137. [CrossRef]
Dowding, K. , Beck, J. , and Blackwell, B. , 1996, “ Estimation of Directional-Dependent Thermal Properties in a Carbon-Carbon Composite,” Int. J. Heat Mass Transfer, 39(15), pp. 3157–3164. [CrossRef]
Jarny, Y. , Ozisik, M. N. , and Bardon, J. P. , 1991, “ A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction,” Int. J. Heat Mass Transfer, 34(11), pp. 2911–2919. [CrossRef]
Cohen, E. , Yehudith, B. , Mannheim, C. , and Saguy, I. , 1994, “ Kinetic Parameter Estimation for Quality Change During Continuous Thermal Processing of Grapefruit Juice,” J. Food Sci., 59(1), pp. 155–158. [CrossRef]
Jurkowski, T. , Jarny, Y. , and Delaunay, D. , 1997, “ Estimation of Thermal Conductivity of Thermoplastics Under Moulding Conditions: An Apparatus and an Inverse Algorithm,” Int. J. Heat Mass Transfer, 40(17), pp. 4169–4181. [CrossRef]
Mejias, M. , Orlande, H. , and Ozisik, M. , 1999, “ A Comparison of Different Parameter Estimation Techniques for the Identification of Thermal Conductivity Components of Orthotropic Solids,” Third International Conference on Inverse Problems in Engineering, Port Ludlow, WA, June 13–18, Paper No. HT14.
Beck, J. , and Woodbury, K. , 1998, “ Inverse Problems and Parameter Estimation: Integration of Measurements and Analysis,” Meas. Sci. Technol., 9(9), p. 839. [CrossRef]
Dantas, L. , Orlande, H. , and Cotta, R. , 2002, “ Estimation of Dimensionless Parameters of Luikov's System for Heat and Mass Transfer in Capillary Porous Media,” Int. J. Therm. Sci., 41(3), pp. 217–227. [CrossRef]
Mehra, R. , 1974, “ Optimal Input Signals for Parameter Estimation in Dynamic Systems—Survey and New Results,” IEEE Trans. Autom. Control, 19(6), pp. 753–768. [CrossRef]
Burnham, A. , and Dinh, L. , 2007, “ A Comparison of Isoconversional and Model-Fitting Approaches to Kinetic Parameter Estimation and Application Predictions,” J. Therm. Anal. Calorim., 89(2), pp. 479–490. [CrossRef]
Emery, A. , Blackwell, B. , and Dowding, K. , 2002, “ The Relationship Between Information, Sampling Rates, and Parameter Estimation Models,” ASME J. Heat Transfer, 124(6), pp. 1192–1199. [CrossRef]
Beck, J. V. , de Monte, F. , and Amos, D. E. , 2017, “ Optimum Design of Complementary Transient Experiments for Estimating Thermal Properties,” Ninth International Conference on Inverse Problems in Engineering (ICIPE), Waterloo, ON, Canada, May 23–26, Paper No. 11T.
Haji-Sheikh, A. , de Monte, F. , and Beck, J. V. , 2013, “ Temperature Solutions in Thin Films Using Thermal Wave Green's Function Solution Equation,” Int. J. Heat Mass Transfer, 62, pp. 78–86. [CrossRef]
de Monte, F. , and Haji-Sheikh, A. , 2017, “ Bio-Heat Diffusion Under Local Thermal Non-Equilibrium Conditions Using Dual-Phase Lag-Based Green's Functions,” Int. J. Heat Mass Transfer, 113, pp. 1291–1305. [CrossRef]
Beck, J. V. , Mishra, D. , and Dolan, K. , 2017, “ Utilization of Generalized Transient Heat Conduction Solutions in Parameter Estimation,” Ninth International Conference on Inverse Problems in Engineering (ICIPE), Waterloo, ON, Canada, May 23–26, Paper No. 05T.
Cole, K. , Beck, J. , Haji-Sheikh, A. , and Litkouhi, B. , 2011, Heat Conduction Using Green's Functions, 2nd ed., Hemisphere Press, New York.
Cole, K. D. , Beck, J. V. , Woodbury, K. A. , and de Monte, F. , 2014, “ Intrinsic Verification and a Heat Conduction Database,” Int. J. Therm. Sci., 78, pp. 36–47. [CrossRef]
Beck, J. , McMasters, R. , Dowding, K. , and Amos, D. , 2006, “ Intrinsic Verification Methods in Linear Heat Conduction,” Int. J. Heat Mass Transfer, 49(17–18), pp. 2984–2994. [CrossRef]


Grahic Jump Location
Fig. 1

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

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. 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.

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.



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.

Related Journal Articles
Related eBook Content
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