Temperature Dependent Thermal Conductivity Measurement on Biological Materials by Solving Inverse Heat Conduction Problem: A Theoretical Study

Knowledge of thermal properties of biomaterials is very important for understanding the heat transfer processes in biological materials. Even though some techniques can be used to measure thermal conductivity of materials at fixed temperature, such as self-heated thermistor technique, few methods are available for measuring temperature dependent thermal conductivity of materials. In this paper, an analytical solution of the IHCP (inverse heat conduction problem) has been developed, based on which temperature dependent thermal conductivity of materials can be determined. In this inverse problem we are concerned about an infinite region with a constant linear heat source at the center. Assuming the material has a known constant thermal diffusivity and temperature dependent thermal conductivity. First, by employing the Kirchhoff transfromation. the heat conduction problem is linearised. Then the analytical solution of this inverse heat conduction problem can be developed by applying Hankel transformation and the corresponding inversion transformation. This solution if we can measure the temperature profile at an arbitrary space location, the temperature dependent thermal conductivity can be obtained. This is also the theoretical foundation of the new technique for measuring temperature dependent thermal conductivity of biomaterials.