A new anisotropic, two-dimensional, transient heat flux-temperature integral relationship for half-space diffusion

作者：Frankel J I^*; Keyhani M; Elkins B; Arimilli R V

来源：Zeitschrift fur Angewandte Mathematik und Mechanik, 2010, 90(2): 161-170.

DOI：10.1002/zamm.200900326

• Integral relationship
• inverse analysis
• heating rate sensors
• heat flux

This paper presents a new heat flux-temperature integral relationship for anisotropic materials in the two-dimensional, semi-infinite, planar geometry defined by x > 0, y is an element of (-infinity, infinity) which is useful for experimental Studies requiring determination of internal heat fluxes in short, run-time or large-domain experiments. This new relationship provides the in-depth heat flux perpendicular to the surface using in-depth data collected parallel to the surface without knowledge of the surface boundary condition This relationship explicitly illustrates that the accurate depiction of the time rate of change of temperature is important for the stable and accurate recovery of heat flux A unified mathematical treatment is proposed utilizing operational and transform methods; and, singular integral equation regularization. The diffusion operator provides sufficient mathematical insight for choosing the novel regularization operator The resulting integral relationship does not require the specification of temperature gradients in the orthogonal coordinate system. This paper offers a novel time-domain viewpoint for reconstructing the heat flux based on implementing both conservation of energy and the constitutive law This methodology is particularly appealing for anisotropic materials where Fourier's law of heat flux requires temperature gradients to be specified in multiple coordinate directions. Finally, time-domain an

• 出版日期2010-2