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Modelling heat transfer in heterogeneous media using fractional calculus
Dominik Sierociuk1, Andrzej Dzielinski, Grzegorz Sarwas
1Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland. dsieroci@ee.pw.edu.pl
Summary
This study models heat transfer in heterogeneous media using fractional calculus, accounting for heat flux dispersion. Experimental validation confirms the derived transfer function for predicting temperature distribution.
Area of Science:
- Physics
- Engineering
- Materials Science
Background:
- Heat transfer in solid materials is typically modeled using integer-order differential equations.
- Heterogeneous media present complexities requiring fractional-order differential equations (sub- or hyperdiffusion).
- Heat flux dispersion into the environment is often overlooked in standard models.
Purpose of the Study:
- To develop a heat transfer model for heterogeneous media incorporating heat flux dispersion.
- To derive a new heat transfer equation and its corresponding transfer function.
- To experimentally validate the model using real-world plant data in the frequency domain.
Main Methods:
- Modeling heat transfer using fractional order partial differential equations.
- Modifying the heat flux-temperature relation to include heat flux dispersion.
- Deriving a transfer function to describe heat flux-temperature dependency.
- Experimental frequency domain modeling of a real plant.
Main Results:
- A modified heat transfer equation for heterogeneous media with dispersed heat flux was obtained.
- A transfer function was derived, linking initial heat flux to temperature at a distance.
- Experimental results validated the accuracy of the developed transfer function.
Conclusions:
- Fractional calculus provides a suitable framework for modeling heat transfer in heterogeneous media with dispersion.
- The derived transfer function accurately predicts temperature distribution under these conditions.
- The study offers a novel approach for analyzing heat transfer in complex materials.
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