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Journal of Applied Nonlinear Dynamics 12(2) (2023) 363--378 | DOI:10.5890/JAND.2023.06.013

Muhammad Shoaib Anwar$^{1}$, V Puneeth$^{2}$, Majid Hussain$^{3}$, Zakir Hussain$^{4}$, Muhammad Irfan$^{5}$

$^{1}$ Department of Mathematics, University of Jhang, Jhang 35200, Pakistan

$^{2}$ Department of Computational Science, CHRIST (Deemed to be University), Ghaziabad 201003, India

$^{3}$ Department of Natural Sciences and Humanities, University of Engineering and Technology Lahore 54890, Pakistan

$^{4}$ Department of Mathematics, University of Baltistan Skardu, Pakistan

$^{5}$ Department of Mathematical Sciences Federal Urdu University of Arts, Sciences & Technology, Islamabad 44000, Pakistan

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Abstract

Modeling of physical phenomena with fractional differential equations is as old as modeling with ordinary differential equations. There are two stages in modeling of a memory process. One of them is short with persistent impact and other is usually governed by fractional mathematical model. It is established that fractional models fit the experimental data for the memory phenomena in better way when compared with the ordinary models, particularly in mechanics, psychology and in biology. Fractional model of viscoelastic nanofluid flow through permeable medium is studied in this communication. Convection parameters in the flow domain are used to account for buoyancy forces. The governing flow equations are computed using a numerical algorithm that combines finite difference and finite element techniques. The governing model's friction coefficient, Sherwood numbers, and Nusselt numbers are calculated. Change in non-integer numbers behave similarly in concentration, temperature, and velocity fields, according to simulations. It is also noted that heat flux, $\delta_{1}$ and mass flux, $\delta_{2}$ numbers have contradictory effects on friction coefficient. Various flow patterns, particularly in the polymer industry and electrospinning for nanofiber manufacture, can be addressed in a similar manner.

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