Computational aspects of hot-wire identification of thermal conductivity and diffusivity under high temperature

Development of advanced materials resistant to high temperature, needed namely for the design of heat storage for low-energy and passive buildings, requires simple, inexpensive and reliable methods of identification of their temperature-sensitive thermal conductivity and diffusivity, covering both well-advised experimental setting and implementation of robust and effective computational algorithms. Special geometrical configurations offer a possibility of quasi-analytical evaluation of temperature development for direct problems, whereas inverse problems of simultaneous evaluation of thermal conductivity and diffusivity must be handled carefully, using some least-squares (minimum variance) arguments. This paper demonstrates the proper mathematical and computational approach to such model problem, thanks to the radial symmetry of hot-wire measurements, including its numerical implementation.