Determination of thermal conductivity distribution from internal temperature distribution measurements

Although various useful techniques exist for nondestructively measuring homogeneous thermal properties, a few useful type techniques for measuring inhomogeneous thermal properties are reported such that there are many structures, materials, substances, and living things whose thermal properties cannot be measured. The temperature distribution of a target, however, can be nondestructively measured with a very high accuracy using infrared, pyroelectric, ultrasound, or magnetic resonance sensors. In this report, we describe an inverse problem technique for determining in situ the thermal conductivity distribution of a target having an arbitrary geometry using only internal steady temperature distribution measurements. The target distribution is directly determined by linearly solving heat transfer equations as the first-order partial differential equations in which temperature distributions and reference thermal conductivities of the region of interest are used as inhomogeneous coefficients. Under proper configurations of reference regions and thermal sources/sinks, this technique enables the determination of the conductivity distribution without disturbing the temperature distribution. A stable numerical solution that considers measurement noise and improper configurations of reference regions and thermal sources/sinks is also described. Technique feasibility is confirmed using two-dimensional problems through simulations and experiments using conventional infrared thermography.