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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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.
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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.
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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.
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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
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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.
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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
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Convergence of the surface-center temperature phase to the limiting case of l ≪1 for measurements made with constant Rω




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