MATHEMATICAL MODEL FOR NANOFIBERS’ DIFFUSION IN A NANOFLUID AND NUMERICAL SIMULATION

Xuejuan Li, Xinyue Yang, Ye-Cheng Luo and Ying Wang
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Xuejuan Li: School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China
Xinyue Yang: School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China
Ye-Cheng Luo: ��School of Jia Yang, Zhejiang Shuren University, Hangzhou, Zhejiang 310015, P. R. China
Ying Wang: School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-15

Abstract: The diffusion process of the nanofibers in a nanofluid displays a combination of diffusion and wave characteristics. The wave-like behavior is attributed to the large aspect ratio of the nanofiber, which can be modeled as a bead-spring chain system, exhibiting wave-like properties. In order to describe this mixed diffusion-wave phenomenon, a fractional diffusion-wave equation is proposed, wherein multiple time fractional derivatives are employed. By appropriately regulating the fractional time terms, the model can be transformed into either the traditional diffusion equation or the traditional wave equation, as required. A numerical schedule is developed through the implementation of suitable time and space discretization, and a stability analysis is conducted. The numerical results substantiate the reliability of the numerical schedule and its applicability to other fractional differential equations.

Keywords: Fractional Derivative; Generalized Finite Difference; Spectral Galerkin Method; Variational Principle; Nanofluid; Boundary Layer (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501445

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