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Entropy
Volume 27
Issue 9
10.3390/e27090946
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Article

Analytic Solutions and Entropy Production of the Double-Diffusive Equation System

by
Imre Ferenc Barna
1,*,† and
László Mátyás
2,†
1
Hungarian Research Network, Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary
2
Department of Bioengineering, Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia Hungarian University of Transylvania, Libertăţii sq. 1, 530104 Miercurea Ciuc, Romania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Entropy 2025, 27(9), 946; https://doi.org/10.3390/e27090946
Submission received: 14 July 2025 / Revised: 27 August 2025 / Accepted: 9 September 2025 / Published: 10 September 2025
(This article belongs to the Special Issue Dissipative Physical Dynamics)
Versions Notes

Abstract

We investigate the partial differential equation system which describes the double-diffusion convection phenomena with the reduction formalism. Double-diffusion refers to when two scalar quantities with different diffusivity, such as heat and solute concentration, contribute to density gradients within a fluid under the influence of gravity. The time-dependent self-similar trial function is applied and analytic results are presented for the dynamical variables and analyzed in detail. Additionally, the entropy production was derived as well. In the second part of the study we investigate the role of an additional heat source.
Keywords: self-similar method; double-diffusion; salty fingers; fluid flow; heat conduction self-similar method; double-diffusion; salty fingers; fluid flow; heat conduction

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MDPI and ACS Style

Barna, I.F.; Mátyás, L. Analytic Solutions and Entropy Production of the Double-Diffusive Equation System. Entropy 2025, 27, 946. https://doi.org/10.3390/e27090946

AMA Style

Barna IF, Mátyás L. Analytic Solutions and Entropy Production of the Double-Diffusive Equation System. Entropy. 2025; 27(9):946. https://doi.org/10.3390/e27090946

Chicago/Turabian Style

Barna, Imre Ferenc, and László Mátyás. 2025. "Analytic Solutions and Entropy Production of the Double-Diffusive Equation System" Entropy 27, no. 9: 946. https://doi.org/10.3390/e27090946

APA Style

Barna, I. F., & Mátyás, L. (2025). Analytic Solutions and Entropy Production of the Double-Diffusive Equation System. Entropy, 27(9), 946. https://doi.org/10.3390/e27090946

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