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# Analysis of Silver Nanoparticles in Engine Oil: Atangana–Baleanu Fractional Model

1 Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan
2 Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam
3 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 70000, Vietnam
4 Department of Mathematics, College of Science Al-Zulfi, Majmah University, Al-Majmah, 11952, Saudi Arabia
5 Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser, 11991, Saudi Arabia

* Corresponding Author: Farhad Ali. Email:

Computers, Materials & Continua 2021, 67(3), 2915-2932. https://doi.org/10.32604/cmc.2021.013757

## Abstract

The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted, generalized Jeffrey nanofluid in a heated rotatory system. The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B0. The medium is porous accepting generalized Darcy’s law. The motion of the fluid is due to the cosine oscillations of the plate. Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil. The problem has been modeled in the form of classical partial differential equations and then generalized by replacing time derivative with Atangana–Baleanu (AB) time-fractional derivative. Upon taking the Laplace transform technique (LTT) and using physical boundary conditions, exact expressions have been obtained for momentum, energy, and concentration distributions. The impact of a number of parameters on fluid flow is shown graphically. The numerical tables have been computed for variation in the rate of heat and mass transfer with respect to rooted parameters. Finally, the classical solution is recovered by taking the fractional parameter approaching unity. It is worth noting that by adding silver nanoparticles in regular engine oil, its heat transfer rate increased by 14.59%, which will improve the life and workability of the engine.

## Keywords

S. Murtaza, F. Ali, N. Ahmad Sheikh, I. Khan and K. Sooppy Nisar, "Analysis of silver nanoparticles in engine oil: atangana–baleanu fractional model," Computers, Materials & Continua, vol. 67, no.3, pp. 2915–2932, 2021. https://doi.org/10.32604/cmc.2021.013757

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