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TECHNICAL PAPERS: Conduction

Determining Anisotropic Film Thermal Properties Through Harmonic Surface Heating With a Gaussian Laser Beam: A Theoretical Consideration

[+] Author and Article Information
Ted D. Bennett

Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106

J. Heat Transfer 126(3), 305-311 (Jun 16, 2004) (7 pages) doi:10.1115/1.1735758 History: Received March 11, 2003; Revised February 20, 2004; Online June 16, 2004
Copyright © 2004 by ASME
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References

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Cowan  , 1963, “Pulse Method of Measuring Thermal Diffusivity at High Temperature,” J. Appl. Phys., 46, pp. 714–719.
Choy,  C. L., Yang,  G. W., and Wong,  Y. W., 1997, “Thermal Diffusivity of Polymer Films by Pulsed Photothermal Radiometry,” J. Polym. Sci., Part B: Polym. Phys., 35(10), pp. 1621–1631.
Rosencwaig,  A., and Gersho,  A., 1976, “Theory of the Photoacoustic Effect With Solids,” J. Appl. Phys., 47(1), pp. 64–69.
Hu,  H., Wang,  X., and Xu,  X., 1999, “Generalized Theory of the Photoacoustic Effect in a Multilayer Material,” J. Appl. Phys., 86(7), pp. 3953–3958.
Boccara,  A. C., Fournier,  D., and Badoz,  J., 1980, “Thermo-Optical Spectroscopy: Detection by the ‘Mirage Effect’,” Appl. Phys. Lett., 36(2), pp. 130–132.
Aamodt,  L. C., and Murphy,  J. C., 1981, “Photothermal Measurements Using a Localized Excitation Source,” J. Appl. Phys., 52(8), pp. 4903–5400.
Kuo,  P. K., Sendler,  E. D., Favro,  L. D., and Thomas,  R. L., 1986, “Mirage Effect Measurement of Thermal Diffusivity. II. Theory,” Can. J. Phys., 64(9), pp. 1168–1671.
Salazar,  A., Sanchez-Lavega,  A., Ocariz,  A., Guitonny,  J., and Pandey,  J. C., 1995, “Novel Results on Thermal Diffusivity Measurements on Anisotropic Materials Using Photothermal Methods,” Appl. Phys. Lett., 67(5), pp. 626–628.
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Myers, G. E., 1998, Analytical Methods in Conduction Heat Transfer, 2nd ed. AMCHT Publications, Madison, WI.

Figures

Grahic Jump Location
Mathematical problem posed by an anisotropic film heated with a Gaussian beam. The Laplacian operator is given by: ∇2≡kr/kz(L/R)2(∂2/∂r2+(1/r)∂/∂r)+∂2/∂z2.
Grahic Jump Location
Illustrative solution for the complex temperature amplitude and phase, using l =2, b=1/2, γ=2, asub=2, and cfilm=1/2. The left panel shows dimensionless amplitude, while the right panel shows phase in units of radians.
Grahic Jump Location
Map of temperature phase sensitivity to the unknown thermal properties of the film. Sensitivity to any variable “X” is defined as ∂θ̃(0,0)/∂X. The map uses asub=2,cfilm=1/2, and γ=2 for the nominal film parameters.
Grahic Jump Location
Surface temperature phase for the limiting case of large beam diameter b/l≫1 as a function of thermal penetration depth and effusivity contrast parameter
Grahic Jump Location
Relationship between the surface temperature phase extremum (left abscissa), the effusivity contrast parameter γ (ordinate), and the corresponding thermal penetration depth (right abscissa), for the beam diameter b/l≫1 case. The surface temperature phase extremum corresponds to the laser frequency ω* at which ∂/∂l arg{θ̃b/l≫1(0)}=0.
Grahic Jump Location
The surface-center temperature phase plotted as a function of the beam diameter made dimensionless by the radial thermal diffusion length R/[αr]film/ω for the limiting case of small thermal penetration depth l ≪1
Grahic Jump Location
Convergence of the surface-center temperature phase to the limiting case of l ≪1 for measurements made with constant Rω

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