A boundary value problem of heat transfer within DBD-based plasma jet setups

P. Vafeas; A. Skarlatos; P. K. Papadopoulos; P. Svarnas; N. Sarmas; P. Vafeas; A. Skarlatos; P. K. Papadopoulos; P. Svarnas; N. Sarmas

doi:10.3934/mbe.2023815

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18345-18367. doi: 10.3934/mbe.2023815

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A boundary value problem of heat transfer within DBD-based plasma jet setups

1.
Department of Chemical Engineering, University of Patras, 26504 Patras, Greece
2.
Université Paris-Saclay, CEA, List, 91120 Palaiseau, France
3.
Department of Mechanical Engineering & Aeronautics, University of Patras, 26504 Patras, Greece
4.
High Voltage Laboratory, Department of Electrical & Computer Engineering, University of Patras, 26504 Patras, Greece

Academic Editor: Feliz Manuel Barrão Minhós

Received: 01 April 2023 Revised: 15 September 2023 Accepted: 20 September 2023 Published: 25 September 2023

We claim an analytical solution for the thermal boundary value problem that arises in DBD-based plasma jet systems as a preliminary and consistent approach to a simplified geometry. This approach involves the outline of a coaxial plasma jet reactor and the consideration of the heat transfer to the reactor solids, namely, the dielectric barrier and the grounded electrode. The non-homogeneous initial and boundary value thermal problem is solved analytically, while a simple cut-off technique is applied to deal with the appearance of infinite series relationships, being the outcome of merging dual expressions. The results are also implemented numerically, supporting the analytical solution, while a Finite Integration Technique (FIT) is used for the validation. Both the analytical and numerical data reveal the temperature pattern at the cross-section of the solids in perfect agreement. This analytical approach could be of importance for the optimization of plasma jet systems employed in tailored applications where temperature-sensitive materials are involved, like in plasma biomedicine.
- dielectric barrier discharge,
- cold plasma jet systems,
- thermal non-homogeneous boundary value problem,
- analytical methodology,
- finite integration technique
Citation: P. Vafeas, A. Skarlatos, P. K. Papadopoulos, P. Svarnas, N. Sarmas. A boundary value problem of heat transfer within DBD-based plasma jet setups[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18345-18367. doi: 10.3934/mbe.2023815

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Abstract

We claim an analytical solution for the thermal boundary value problem that arises in DBD-based plasma jet systems as a preliminary and consistent approach to a simplified geometry. This approach involves the outline of a coaxial plasma jet reactor and the consideration of the heat transfer to the reactor solids, namely, the dielectric barrier and the grounded electrode. The non-homogeneous initial and boundary value thermal problem is solved analytically, while a simple cut-off technique is applied to deal with the appearance of infinite series relationships, being the outcome of merging dual expressions. The results are also implemented numerically, supporting the analytical solution, while a Finite Integration Technique (FIT) is used for the validation. Both the analytical and numerical data reveal the temperature pattern at the cross-section of the solids in perfect agreement. This analytical approach could be of importance for the optimization of plasma jet systems employed in tailored applications where temperature-sensitive materials are involved, like in plasma biomedicine.

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