General solution for the thermal wave scattering in fiber composites

In this article we present a general solution for the ac temperature field generated from a modulated heating in an opaque material containing a series of aligned subsurface cylinders. The model includes the multiple scattering effects suffered by the plane thermal wave, generated by a planar heat source, when interacting with the cylinders and with the sample surfaces. A series solution to the heat diffusion equation and a matrix formulation to solve the scattering coefficients are used. There are no restrictions on the cylinders number, on their size and position inside the material, nor on the thermal properties of cylinders and sample. For completeness the case of coated cylinders is also investigated. Numerical calculations for the case of nonconducting cylinders illustrate the effect of the multiple scattering of the incident thermal wave on the sample surface temperature. A specific case of interest of the model is its application to the thermal characterization and nondestructive evaluation of fiber reinforced composites.