An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model

J. Kayalvizhi; A. G. Vijaya Kumar; Ndolane Sene; Ali Akgül; Mustafa Inc; Hanaa Abu-Zinadah; S. Abdel-Khalek; J. Kayalvizhi; A. G. Vijaya Kumar; Ndolane Sene; Ali Akgül; Mustafa Inc; Hanaa Abu-Zinadah; S. Abdel-Khalek

doi:10.3934/math.2023180

AIMS Mathematics

2023, Volume 8, Issue 2: 3542-3560. doi: 10.3934/math.2023180

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An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model

1.
Department of Mathematics, School of Advanced Sciences Vellore Institute of Technology, Vellore-632014, India
2.
Department of Mathematics, Institut des Politiques Publiques, Cheikh Anta Diop University, Dakar Fann, Senegal
3.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
4.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10-Turkey
5.
Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey
6.
Department of Medical Research, China Medical University, 40402 Taichung, Taiwan
7.
University of Jeddah, College of Science, Department of Statistics, Jeddah, Saudi Arabia
8.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 26 June 2022 Revised: 12 October 2022 Accepted: 12 October 2022 Published: 22 November 2022
MSC : 35Q30, 26A33

This paper presents the problem modeled using Caputo fractional derivatives with an accurate study of the MHD unsteady flow of Nanofluid through an inclined plate with the mass diffusion effect in association with the energy equation. H₂O is thought to be a base liquid with clay nanoparticles floating in it in a uniform way. Bousinessq's approach is used in the momentum equation for pressure gradient. The nondimensional fluid temperature, species concentration, and fluid transport are derived together with Jacob Fourier sine and Laplace transforms Techniques in terms of exponential decay function, whose inverse is computed further in terms of Mittag-Leffler function. The impact of various physical quantities interpreted with fractional order of the Caputo derivatives. The obtained temperature, transport, and species concentration profiles show behaviours for $0 < \mathtt{α} < 1$ where $\mathtt{α} $ is the fractional parameter. Numerical calculations have been carried out for the rate of heat transmission and the Sherwood number is swotted to be put in the form of tables. The parameters for the magnetic field and the angle of inclination slow down the boundary layer of momentum. The distributions of velocity, temperature, and concentration expand more rapidly for higher values of the fractional parameter. Additionally, it is revealed that for the volume fraction of nanofluids, the concentration profiles behave in the opposite manner. The limiting case solutions also presented on flow field of governing model.
- nanofluid,
- heat and mass transfer,
- magnetic field,
- Caputo fractional derivative,
- Fourier and integral transforms
Citation: J. Kayalvizhi, A. G. Vijaya Kumar, Ndolane Sene, Ali Akgül, Mustafa Inc, Hanaa Abu-Zinadah, S. Abdel-Khalek. An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model[J]. AIMS Mathematics, 2023, 8(2): 3542-3560. doi: 10.3934/math.2023180

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Abstract

This paper presents the problem modeled using Caputo fractional derivatives with an accurate study of the MHD unsteady flow of Nanofluid through an inclined plate with the mass diffusion effect in association with the energy equation. H₂O is thought to be a base liquid with clay nanoparticles floating in it in a uniform way. Bousinessq's approach is used in the momentum equation for pressure gradient. The nondimensional fluid temperature, species concentration, and fluid transport are derived together with Jacob Fourier sine and Laplace transforms Techniques in terms of exponential decay function, whose inverse is computed further in terms of Mittag-Leffler function. The impact of various physical quantities interpreted with fractional order of the Caputo derivatives. The obtained temperature, transport, and species concentration profiles show behaviours for $0 < \mathtt{α} < 1$ where $\mathtt{α} $ is the fractional parameter. Numerical calculations have been carried out for the rate of heat transmission and the Sherwood number is swotted to be put in the form of tables. The parameters for the magnetic field and the angle of inclination slow down the boundary layer of momentum. The distributions of velocity, temperature, and concentration expand more rapidly for higher values of the fractional parameter. Additionally, it is revealed that for the volume fraction of nanofluids, the concentration profiles behave in the opposite manner. The limiting case solutions also presented on flow field of governing model.

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