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Article

A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

1
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
2
Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, Hungary
3
Basrah Education Directorate, Ministry of Education, Basrah 61001, Iraq
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Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
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Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen
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Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
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Departamento de Aeronáutica, FCEFyN, Instituto de Estudios Avanzados en Ingeniería y Tecnología (IDIT), Universidad Nacional de Córdoba and CONICET, Córdoba 5000, Argentina
8
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego Str., 90-924 Lodz, Poland
*
Authors to whom correspondence should be addressed.
Symmetry 2022, 14(4), 682; https://doi.org/10.3390/sym14040682
Submission received: 1 March 2022 / Revised: 22 March 2022 / Accepted: 23 March 2022 / Published: 25 March 2022
(This article belongs to the Section Physics)

Abstract

In this recent work, the continuous dependence of double diffusive convection was studied theoretically in a porous medium of the Forchheimer model along with a variable viscosity. The analysis depicts that the density of saturating fluid under consideration shows a linear relationship with its concentration and a cubic dependence on the temperature. In this model, the equations for convection fluid motion were examined when viscosity changed with temperature linearly. This problem allowed the possibility of resonance between internal layers in thermal convection. Furthermore, we investigated the continuous dependence of this solution based on the changes in viscosity. Throughout the paper, we found an “a priori estimate” with coefficients that relied only on initial values, boundary data, and the geometry of the problem that demonstrated the continuous dependence of the solution on changes in the viscosity, which also helped us to state the relationship between the continuous dependence of the solution and the changes in viscosity. Moreover, we deduced a convergence result based on the Forchheimer model at the stage when the variable viscosity trends toward a constant value by assuming a couple of solutions to the boundary-initial-value problems and defining a difference solution of variables that satisfy a given boundary-initial-value problem.
Keywords: Forchheimer model; double diffusive; salinization; stability; variable viscosity; convergence Forchheimer model; double diffusive; salinization; stability; variable viscosity; convergence

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MDPI and ACS Style

Ali, A.H.; Meften, G.A.; Bazighifan, O.; Iqbal, M.; Elaskar, S.; Awrejcewicz, J. A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model. Symmetry 2022, 14, 682. https://doi.org/10.3390/sym14040682

AMA Style

Ali AH, Meften GA, Bazighifan O, Iqbal M, Elaskar S, Awrejcewicz J. A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model. Symmetry. 2022; 14(4):682. https://doi.org/10.3390/sym14040682

Chicago/Turabian Style

Ali, Ali Hasan, Ghazi Abed Meften, Omar Bazighifan, Mehak Iqbal, Sergio Elaskar, and Jan Awrejcewicz. 2022. "A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model" Symmetry 14, no. 4: 682. https://doi.org/10.3390/sym14040682

APA Style

Ali, A. H., Meften, G. A., Bazighifan, O., Iqbal, M., Elaskar, S., & Awrejcewicz, J. (2022). A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model. Symmetry, 14(4), 682. https://doi.org/10.3390/sym14040682

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