Fractional Mathematical Modeling of Ternary Nanofluid Flow Through an Inclined Artery

Hamza Saleh Zakari¹ , Aminu Barde² , Isah Abdullahi³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.57-63, Jun-2024

Online published on Jun 30, 2024

Copyright © Hamza Saleh Zakari, Aminu Barde, Isah Abdullahi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this study, we examined the fractional order flow of Casson tri-nanofluid through an inclined artery, integrating gold (Au), copper (Cu), and alumina (Al2O3) nanoparticles into blood to form the tri-nanofluid. The flow was modelled as highly pulsatile. The mathematical formulation used differential forms of the conservation laws of mass, momentum, and energy, with the electric potential along the arterial wall accurately described by the Poisson-Boltzmann equation. The classical problem was converted into its fractional equivalents using the Caputo time-fractional derivative. Exact solutions for these transformed equations were derived using a combination of Laplace and finite Hankel transforms, with results computed and graphically presented using Mathcad software. The purpose of incorporating the tri-nanofluid was to enhance heat transfer by improving the fluid`s thermal conductance. The findings revealed that the velocity profiles of the blood flow decreased with an increasing radiation parameter, while the opposite effect was observed with increasing porosity parameter. The temperature profile arose with higher fractional parameter values. This study holds potential for applications in targeted drug delivery using magnetic nanoparticles

Key-Words / Index Term :
Nano Particles, Inclined Artery, Ternary nanofluid, Time-Fractional Derivative

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