# Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media

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## Abstract

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## 1. Introduction

## 2. Mathematical Formulation

## 3. Statement of the Problem

## 4. Problem Solution

## 5. Numerical Results

#### 5.1. Implications of the Nonlocal Coefficient

#### 5.2. The Influence of the Fractional Operators

## 6. Conclusions

- Nonlocal factors have a significant role in changing the behavior of thermomechanical interactions in small-sized semiconductor materials. As a result, when modeling nonlocal microstructures, the value of the nonlocal coefficient must be chosen very carefully.
- The new nonlocal photothermal model predicts smaller amounts than those in the case of the traditional (local) photothermal model. For this reason, nanoscale factors must be included in reducing the mechanical wave behavior of (nonlocal) nanostructures.
- The fractional-order index can be used to reclassify semiconductor materials in terms of photoelectric thermal conductivity. The fractional coefficient of the derivative operator of Atangana and Baleanu slightly affects the rate of temperature fluctuation. Thermoplastic models with fractional derivatives have much larger standard deviations than thermoplastic models. As a result, the fractional coefficient is gaining ground as an excellent thermal indicator.
- When using fractional actuators, the values of the thermo-photophysical fields were found to be lower compared to what would be expected by conventional thermophotometric models. Therefore, by varying the fractional parameter, we may be able to estimate the function that the Atangana and Baleanu derivative operators play in heat transfer regimes and perform more detailed examinations of elastic thermal deformation in rigid mechanics. The method and results from this work can also be used to solve similar problems in thermoelasticity and thermodynamics.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**The dimensionless carrier intensity $N$ under the influence of small-scale coefficient $\xi $.

**Figure 6.**Effect of the AB and RL fractional derivative operators on the dimensionless temperature $\theta $.

**Figure 7.**Effect of the AB and RL fractional derivative operators on the nonlocal thermal stress ${\sigma}_{zz}$.

**Figure 8.**Effect of the CF and RL fractional derivative operators on the dimensionless displacement $w$.

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**MDPI and ACS Style**

Askar, S.; Abouelregal, A.E.; Marin, M.; Foul, A.
Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media. *Symmetry* **2023**, *15*, 656.
https://doi.org/10.3390/sym15030656

**AMA Style**

Askar S, Abouelregal AE, Marin M, Foul A.
Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media. *Symmetry*. 2023; 15(3):656.
https://doi.org/10.3390/sym15030656

**Chicago/Turabian Style**

Askar, Sameh, Ahmed E. Abouelregal, Marin Marin, and Abdelaziz Foul.
2023. "Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media" *Symmetry* 15, no. 3: 656.
https://doi.org/10.3390/sym15030656