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Unsteady Heat Transfer in Bilayer, and Three-Layer Materials

Toufik Sahabi1,*, Smain Balaska2

1 Physics Department, Faculty of Sciences, University of Saida Dr. Moulay Tahar, Saida, 20000, Algeria
2 Theoretical Physics Laboratory, University of Oran -1- Ahmed Ben Bella, Oran, 31000, Algeria

* Corresponding Author: Toufik Sahabi. Email:

(This article belongs to this Special Issue: Materials and Energy an Updated Image for 2021)

Fluid Dynamics & Materials Processing 2023, 19(4), 977-990.


The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis. An analytical dimensionless analysis is implemented in the framework of a separation of variables method (SVM). This approach leads to an Eigenvalues problem that is solved by the Newton’s method. Two types of dynamics are found: An unsteady condition (in the form of jumps or drops in temperatures depending on the considered case), and a permanent equilibrium (tending to the ambient temperature). The validity and effectiveness of the proposed approach for any number of adjacent layers is also discussed. It is shown that, as expected, the diffusion of the temperature is linked to the ratio of the thermo-physical properties of the considered layers and their number.

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Unsteady Heat Transfer in Bilayer, and Three-Layer Materials


Cite This Article

Sahabi, T., Balaska, S. (2023). Unsteady Heat Transfer in Bilayer, and Three-Layer Materials. FDMP-Fluid Dynamics & Materials Processing, 19(4), 977–990.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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