Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate

Mushtaq Ahmad; Muhammad Imran Asjad; Ali Akgül; Dumitru Baleanu; Mushtaq Ahmad; Muhammad Imran Asjad; Ali Akgül; Dumitru Baleanu

doi:10.3934/math.2021142

AIMS Mathematics

2021, Volume 6, Issue 3: 2344-2358. doi: 10.3934/math.2021142

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Research article

Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate

1.
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan
2.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3.
Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey
4.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
5.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
6.
Department of Medical Research, China Medical University Taichung 40402, Taiwan

Received: 21 August 2020 Accepted: 03 December 2020 Published: 16 December 2020
MSC : 26A33, 74F10

This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.
- Casson fluid,
- Clay nanoparticles,
- new,
- vertical plate,
- heat transfer,
- hybrid fractional derivative
Citation: Mushtaq Ahmad, Muhammad Imran Asjad, Ali Akgül, Dumitru Baleanu. Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate[J]. AIMS Mathematics, 2021, 6(3): 2344-2358. doi: 10.3934/math.2021142

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Abstract

This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.

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