On the quasi-static theory of space-time fractional thermoelasticity in the unbounded domains

Mourad, Noha; Abdella, Mohamed; Awad, Emad

doi:10.21608/jealex.2025.337944.1060

On the quasi-static theory of space-time fractional thermoelasticity in the unbounded domains

Document Type : Original Article

Authors

Faculty of Education, Alexandria University

10.21608/jealex.2025.337944.1060

Abstract

The thermal conduction phenomenon is known to be strongly dependent on the temperature and the inner structure of materials. In some materials that include impurities and/or voids, thermal conductivity deviates from the conventional behaviour. In this work, anomalous thermal conductivity that deviates from the classical definition is mathematically expressed through a space-time fractional Fourier law of heat conduction. A quasi-static theory of fractional thermoelasticity that uses a fractional space-time fractional Fourier law is considered in this work. An initial value problem is solved on the unbounded domain with initial conditions on the temperature and stresses concentrated on the middle plane that separates the two half-spaces constituting the full unbounded space. It is found that such initial conditions need an additional boundary condition in the infinity so that the initial value problem transforms into an initial boundary value problem. Exact solutions for the temperature and displacement are derived in terms of the Fox H-function. Graphical representations for the temperature and displacement show that the anomalous thermal conductivity proposed in this work has a significant effect on both the temperature and displacement distribution.

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References

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