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Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet
Institution:1. School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan;2. Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan;3. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan;4. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;2. Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia;3. Department of Mathematics, International Islamic University, Islamabad 44000, Pakistan;1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;2. School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China;1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Mathematics Department, Faculty of Science, South Valley University, Qena, Egypt;2. Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt;1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 Pakistan;2. Mechanical and Materials Engineering, Spencer Engineering Building, Room 3055, University of Western Ontario, London, Ontario, Canada;3. Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa, Pakistan;4. DBS&H, CEME, National University of Sciences and Technology, Islamabad, Pakistan
Abstract:This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet.
Keywords:Nanofluid  Axisymmetric flow  Non-linear stretching sheet  Optimal homotopy analysis method  Keller–Box method
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