thermal conductivity; heat transfer; Bessel functions
The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is
useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical
standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions,
neglecting everything except the first terms of the decomposition of related exponential integrals to infinite series, and least-squares based data fitting; such approach reduces the validity of results and obstructs the simultaneous evaluation of heat capacity. This paper demonstrates that substantial improvements can be obtained without
any requirements to additional measurements, both i) under the assumption of a wire of zero-thickness and an infinite sample (following the valid Czech technical standard) with proper exponential integrals and ii) for a more realistic geometrical configuration
and physical simplification (taking into account the thermal characteristics of the wire), based on the properties of Bessel functions. The suggested algorithms have been implemented in the MATLAB environment.