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Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 203--216 | DOI:10.5890/DNC.2022.06.002

J. Volkmann$^{1,2}$, N. Suedland$^3$, R. Rablbauer$^1$, A. Wollenberg$^1$, O. Schauerte$^1$, M. Prouvier$^1$, \newline A. Winkler$^1$, M. Frambourg$^1$, F. Klein$^3$, N. Migranov$^4$

$^1$ Group Innovation, Volkswagen AG, 38436 Wolfsburg, Germany

$^2$ International Laboratory of Theoretical and Mathematical Physics of Molecules and Crystals, Ufa Federal

Research Centre, Russian Academy of Sciences, Prospect Octyabrya, 71, Ufa 450054, Russia

$^3$ Aage GmbH, Roentgenstr. 24, 73431 Aalen, Germany

$^4$ Department of Medical Physics, Bashkir State Medical University, Lenin Str. 3, Ufa, 450008, Russia

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Abstract

The variance theorem from the field of statistical analysis is used to evaluate the experimental data set of a classical heat diffusion experiment measuring temperatures as a function of time on a thermocouples prepared aluminium bar. The experimental data set during heating of the bar shows a nonlinear behavior. Known mathematical concepts to describe anomalous diffusion are shortly quoted and subsequent a novel approach of evaluating the data is presented. On the basis of the fundamental solution of the homogenous diffusion equation using finite boundaries defined by the discrete positions of the thermocouples, three different linearly independent momenta: expectation value, variance, and asymmetry are determined. For each momentum the parameter: thermal diffusivity $a$ of the solution equation is calculated. The three values are in the same range and coincide well to the known technical diffusivity of aluminium.

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