Analytical Modeling of Modulated Heating for Three-Dimensional Anisotropic Optical Thermometry of Multilayered Cylinders

Abstract

Thermally relevant cylindrical geometries are used in a plethora of applications with thermal property differences depending significantly on material complexity. Manu- facturing processes also induce substantial anisotropy ratios resulting in directionally dependent thermal transport. However, for cylindrical specimens, current thermal metrology resolves only isotropic thermal properties, assumes perfect thermal inter- faces, and offers no formulation for temperature spatial dependence. In this work, we present an analytical framework that models the frequency dependent thermal transport of orthotropic arbitrary layered cylinders to be used as a forward model for existing optical thermometry techniques. This formulation captures the effects of non-negligible thermal boundary conductance and offers the first closed-form solution of a projected Gaussian laser, a common form of heating in thermal metrology, hav- ing a finite elliptic spot size on a curved surface. The novel anisotropic cylindrical model was compared with literature derivations involving two-dimensional isotropic transport for cylinders by applying simplifying assumptions. For single- and two- layerisotropicsamples, thethree-dimensionalmodelagreedwithestablishedsolutions with negligible error, while predictions for orthotropic multilayer samples agreed with finite-element simulations within 1.5% across a range of material properties and laser geometries. Comparison with anisotropic planar models identified conditions under which a planar approximation can reduce computation time. These results estab- lish the first forward model for noncontact characterization of anisotropic thermal properties in arbitrarily layered cylinders.