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Impact of Thermal Radiation and Heat Source/Sink on MHD Time-Dependent Thin-Film Flow of Oldroyed-B, Maxwell, and Jeffry Fluids over a Stretching Surface
Open AccessArticle

Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan
2
Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan
3
KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
4
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
5
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Processes 2019, 7(5), 262; https://doi.org/10.3390/pr7050262
Received: 3 April 2019 / Revised: 27 April 2019 / Accepted: 28 April 2019 / Published: 6 May 2019
(This article belongs to the Special Issue Thin Film Processes)
The boundary-layer equations for mass and heat energy transfer with entropy generation are analyzed for the two-dimensional viscoelastic second-grade nanofluid thin film flow in the presence of a uniform magnetic field (MHD) over a vertical stretching sheet. Different factors, such as the thermophoresis effect, Brownian motion, and concentration gradients, are considered in the nanofluid model. The basic time-dependent equations of the nanofluid flow are modeled and transformed to the ordinary differential equations system by using similarity variables. Then the reduced system of equations is treated with the Homotopy Analysis Method to achieve the desire goal. The convergence of the method is prescribed by a numerical survey. The results obtained are more efficient than the available results for the boundary-layer equations, which is the beauty of the Homotopy Analysis Method, and shows the consistency, reliability, and accuracy of our obtained results. The effects of various parameters, such as Nusselt number, skin friction, and Sherwood number, on nanoliquid film flow are examined. Tables are displayed for skin friction, Sherwood number, and Nusselt number, which analyze the sheet surface in interaction with the nanofluid flow and other informative characteristics regarding this flow of the nanofluids. The behavior of the local Nusselt number and the entropy generation is examined numerically with the variations in the non-dimensional numbers. These results are shown with the help of graphs and briefly explained in the discussion. An analytical exploration is described for the unsteadiness parameter on the thin film. The larger values of the unsteadiness parameter increase the velocity profile. The nanofluid film velocity shows decline due the increasing values of the magnetic parameter. Moreover, a survey on the physical embedded parameters is given by graphs and discussed in detail. View Full-Text
Keywords: entropy generation; second-grade fluid; nanofluid; liquid films; thin film; time depending stretching surface; magnetic field; HAM entropy generation; second-grade fluid; nanofluid; liquid films; thin film; time depending stretching surface; magnetic field; HAM
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MDPI and ACS Style

Ullah, A.; Shah, Z.; Kumam, P.; Ayaz, M.; Islam, S.; Jameel, M. Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation. Processes 2019, 7, 262. https://doi.org/10.3390/pr7050262

AMA Style

Ullah A, Shah Z, Kumam P, Ayaz M, Islam S, Jameel M. Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation. Processes. 2019; 7(5):262. https://doi.org/10.3390/pr7050262

Chicago/Turabian Style

Ullah, Asad; Shah, Zahir; Kumam, Poom; Ayaz, Muhammad; Islam, Saeed; Jameel, Muhammad. 2019. "Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation" Processes 7, no. 5: 262. https://doi.org/10.3390/pr7050262

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