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Article

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

1
Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
2
Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia
3
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
4
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, Malaysia
5
Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
6
Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Energies 2019, 12(7), 1268; https://doi.org/10.3390/en12071268
Received: 12 January 2019 / Revised: 18 February 2019 / Accepted: 19 February 2019 / Published: 2 April 2019
(This article belongs to the Special Issue Numerical Simulation of Convective-Radiative Heat Transfer)
The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution. View Full-Text
Keywords: nanofluid; stagnation sheet; three-dimensional flow; slip condition; stability analysis nanofluid; stagnation sheet; three-dimensional flow; slip condition; stability analysis
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MDPI and ACS Style

Khashi’ie, N.S.; Md Arifin, N.; Nazar, R.; Hafidzuddin, E.H.; Wahi, N.; Pop, I. A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip. Energies 2019, 12, 1268. https://doi.org/10.3390/en12071268

AMA Style

Khashi’ie NS, Md Arifin N, Nazar R, Hafidzuddin EH, Wahi N, Pop I. A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip. Energies. 2019; 12(7):1268. https://doi.org/10.3390/en12071268

Chicago/Turabian Style

Khashi’ie, Najiyah S.; Md Arifin, Norihan; Nazar, Roslinda; Hafidzuddin, Ezad H.; Wahi, Nadihah; Pop, Ioan. 2019. "A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip" Energies 12, no. 7: 1268. https://doi.org/10.3390/en12071268

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