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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

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Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator

Oprzędkiewicz Krzysztof

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 1

art. no. e135843

In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.

Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator

Oprzędkiewicz K., Dziedzic K., Więckowski Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 5

905--914

The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.