Sequential Estimation of Thermal Diffusivity for Flash Tests

  • M. Raynaud
  • J. V. Beck
  • R. Shoemaker
  • R. Taylor

Abstract

The estimation of thermal diffusivity using a flash experiment is studied. The sequential estimation method is presented and compared to the original flash method as well as two other methods that account for heat loss. The potential accuracy of the four methods is tested with a numerical simulation. The thermal diffusivity of a stainless steel sample is estimated from experimental data. The estimates given by the different methods are compared and analyzed. The sequential estimation method is shown to be less sensitive to random measurement errors and to provide more information regarding the accuracy of the estimated parameters.

Keywords

Furnace Xenon Biot 

Nomenclature

b

maximum temperature rise - parameter to be estimated

Bi

Biot number

c

specific heat per unit mass

G

denotes Green’ function

h

heat transfer coefficient

k

thermal conductivity

L

thickness of the sample

n

total number of measurement times

S

surface area of the sample

t1/2

half-time

Tj

calculated temperature at time tj

Tm

maximum temperature rise

T

environment temperature

Xjs

sensitivity coefficient at time tj for the parameter βs

Yj

measured temperature at time tj

Greek Letters

α

thermal diffusivity - parameter to be estimated

βs

parameter s to be estimated (Section II)

βm

m’ th root of the trascendental equation Eq. (16)

ρ

density

τ

instant of the impulse

Subscripts

j

index for time tj

m

index for time m

Superscripts

(k)

iteration index

m

index for value calculated with m measurement times (1 ≤ m ≤ n)

n

index for value n measurement times

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References

  1. 1.
    W.J. Parker, R.J. Jenkins, C.P. Butler and G.L. Abbott, “Flash method of determining thermal diffusivity, heat capacity and thermal conductivity,” J. App. Physics 32: 1679-1684 (1961).CrossRefGoogle Scholar
  2. 2.
    R.D. Cowan, “Pulse method of measuring thermal diffusivity at high temperatures,” J. App. Physics 34: 926-927 (1963)CrossRefGoogle Scholar
  3. 3.
    L.M. Clark III and R.E. Taylor, “Radiation loss in the flash method for thermal diffusivity,” J. App. Physics 46: 714-718 (1975).CrossRefGoogle Scholar
  4. 4.
    J.V. Beck and K.J. Arnold, “Parameter Estimation in Engineering and Science,” John Wiley & Sons, NY (1977).Google Scholar
  5. 5.
    J.V. Beck, “Sequential estimation of thermal parameters,” J. Heat Transfer 99C: 314-321 (1977).CrossRefGoogle Scholar
  6. 6.
    J.V. Beck, “Green’s functions and numbering system for transient heat conduction,” AIAA Journal 23: 1609 - 1614 (1986).Google Scholar
  7. 7.
    J.V. Beck, “Green’s function solution for transient heat condition problems,” Int. J. Heat Mass Transfer 27: 1235-1244 (1984).CrossRefGoogle Scholar
  8. 8.
    J.A. Cape and G.W. Lehman, “Temperature and finite pulse-time effects in the flash method for measuring thermal diffusivity,” J. App. Physics 34: 1909-1913 (1963).CrossRefGoogle Scholar

Copyright information

© Purdue Research Foundation 1989

Authors and Affiliations

  • M. Raynaud
    • 1
  • J. V. Beck
    • 2
  • R. Shoemaker
    • 3
  • R. Taylor
    • 3
  1. 1.Department of Mechanical EngineeringNew Mexico State UniversityLas CrucesUSA
  2. 2.Heat Transfer Group Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA
  3. 3.Thermophysical Properties Research LaboratoryPurdue UniversityWest LafayetteUSA

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