A comparative study for fractional simulations of Casson nanofluid flow with sinusoidal and slipping boundary conditions via a fractional approach

Ali Raza; Umair Khan; Aurang Zaib; Wajaree Weera; Ahmed M. Galal; Ali Raza; Umair Khan; Aurang Zaib; Wajaree Weera; Ahmed M. Galal

doi:10.3934/math.20221092

AIMS Mathematics

2022, Volume 7, Issue 11: 19954-19974. doi: 10.3934/math.20221092

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A comparative study for fractional simulations of Casson nanofluid flow with sinusoidal and slipping boundary conditions via a fractional approach

1.
Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
2.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia
3.
Department of Mathematics and Social Sciences, Sukkur IBA University, Sukkur 65200, Sindh Pakistan
4.
Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Gulshan-e-Iqbal Karachi-75300, Pakistan
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
6.
Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam bin Abdulaziz University, Saudi Arabia
7.
Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O 35516, Mansoura, Egypt

Received: 03 July 2022 Revised: 13 August 2022 Accepted: 19 August 2022 Published: 09 September 2022
MSC : 26A33, 76A05, 76R10

This paper addresses a mixed and free convective Casson nanofluid flowing on an oscillating inclined poured plate with sinusoidal heat transfers and slip boundaries. As base fluid water is supposed and the suspension of nanofluid is formulated with the combination of individual copper $ \left(Cu\right) $, titanium dioxide $ \left(Ti{O}_{2}\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ as nanoparticles, the dimensionless governing equations are generalized based on Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional operators for developing a fractional form. Then, for the semi-analytical solution of the momentum and thermal profiles, the Laplace transformation is utilized. To discuss the influences of various pertinent parameters on governing equations, graphical tablecomparison of the Nusselt number and skin friction is also inspected at different times and numerical schemes. As a result, it has been concluded that both the momentum and energy profiles represent the more significant results for the AB-fractional model as related to the CF-fractional model solution. Furthermore, water-based titanium dioxide $ \left(Ti{O}_{2}\right) $ has a more progressive impact on the momentum as well as the thermal fields as compared to copper $ \left(Cu\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ nanoparticles. The Casson fluid parameter represents the dual behavior for the momentum profile, initially momentum field decreases due to the Casson parameter but it then reverses its impact and the fluid flow moves more progressively.
- fractional derivatives,
- nanofluids,
- AB-fractional derivative,
- slip boundary,
- sinusoidal conditions
Citation: Ali Raza, Umair Khan, Aurang Zaib, Wajaree Weera, Ahmed M. Galal. A comparative study for fractional simulations of Casson nanofluid flow with sinusoidal and slipping boundary conditions via a fractional approach[J]. AIMS Mathematics, 2022, 7(11): 19954-19974. doi: 10.3934/math.20221092

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Abstract

This paper addresses a mixed and free convective Casson nanofluid flowing on an oscillating inclined poured plate with sinusoidal heat transfers and slip boundaries. As base fluid water is supposed and the suspension of nanofluid is formulated with the combination of individual copper $ \left(Cu\right) $, titanium dioxide $ \left(Ti{O}_{2}\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ as nanoparticles, the dimensionless governing equations are generalized based on Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional operators for developing a fractional form. Then, for the semi-analytical solution of the momentum and thermal profiles, the Laplace transformation is utilized. To discuss the influences of various pertinent parameters on governing equations, graphical tablecomparison of the Nusselt number and skin friction is also inspected at different times and numerical schemes. As a result, it has been concluded that both the momentum and energy profiles represent the more significant results for the AB-fractional model as related to the CF-fractional model solution. Furthermore, water-based titanium dioxide $ \left(Ti{O}_{2}\right) $ has a more progressive impact on the momentum as well as the thermal fields as compared to copper $ \left(Cu\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ nanoparticles. The Casson fluid parameter represents the dual behavior for the momentum profile, initially momentum field decreases due to the Casson parameter but it then reverses its impact and the fluid flow moves more progressively.

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