Simultaneous estimation of spatially distributed thermal conductivity, heat capacity and surface heat transfer coefficient in thermal tomography

Abstract

In thermal tomography, the thermal properties of a target are estimated as spatially distributed parameters based on non-invasive measurements of surface temperatures. In the measurement setup, the target is sequentially heated at different source locations and the induced temperature evolutions are measured at several measurement locations on the surface. In [V. Kolehmainen, J. Kaipio, H. Orlande, Reconstruction of thermal conductivity and heat capacity using a tomographic approach, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5150–5160], it was demonstrated with simulations that simultaneous estimation of spatially distributed thermal conductivity and volumetric heat capacity from transient boundary data is feasible when the boundary heat flux from the target to the surrounding medium is known all over the target boundary. In this article, we extend the computational methods towards the more practical setup of imaging targets, where the boundary heat flux from the target to the surrounding medium is not known. We model the surface heat transfer coefficient as a spatially distributed parameter on the target boundary and estimate it simultaneously with the spatially distributed thermal conductivity and volumetric heat capacity using the statistical (Bayesian) inversion framework. The feasibility of the approach is evaluated with simulations.