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Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

Rabha W. Ibrahim1,*, Ahmed M. Ajaj2, Nadia M.G. Al-Saidi3, Dumitru Balean4,5,6

1 Institute of Electrical and Electronics Engineers, Kuala Lumpur, Malaysia
2 Department of Islamic Finance and Banking, College of Islamic Sciences, Iraqi University, Adhamiyah, Iraq
3 Department of Applied Sciences, University of Technology, Baghdad, Iraq
4 Department of Mathematics, Cankaya University, Ankara, Turkey
5 Institute of Space Sciences, Magurele-Bucharest, Romania
6 Department of Medical Research, China Medical University, Taichung, Taiwan

* Corresponding Author: Rabha W. Ibrahim. Email: email

(This article belongs to this Special Issue: Recent Trends in Nanofluids: Modelling and Simulations)

Computer Modeling in Engineering & Sciences 2022, 130(1), 221-232.


The science of strategy (game theory) is known as the optimal decision-making of autonomous and challenging players in a strategic background. There are different strategies to complete the optimal decision. One of these strategies is the similarity technique. Similarity technique is a generalization of the symmetric strategy, which depends only on the other approaches employed, which can be formulated by altering diversities. One of these methods is the fractal theory. In this investigation, we present a new method studying the similarity analytic solution (SAS) of a 3D-fractal nanofluid system (FNFS). The dynamic evolution is completely given by the concept of differential subordination and majorization. Subordination and majorization relationships are the sets of observable individualities. Game theory can simplify the conditions under which particular sets combine. We offer an explicit construction for the complex possible velocity, energy and thermal functions of two-dimensional fluid flow (the complex variable is suggested in the open unit disk, where the disk is selected at a constant temperature and concentration with uniform velocity). We establish that whenever the 3D-fractal nanofluid system is approximated by a fractal function, the solution has the same property, so a class of fractal tangent function gives SAS. Finally, we demonstrate some simulations and examples that give the consequences of this methodology.


Cite This Article

Ibrahim, R. W., Ajaj, A. M., Al-Saidi, N. M., Balean, D. (2022). Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function. CMES-Computer Modeling in Engineering & Sciences, 130(1), 221–232.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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