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Sci Rep. 2019 Jan 24;9(1):562. doi: 10.1038/s41598-018-37267-2.

On the convective heat and zero nanoparticle mass flux conditions in the flow of 3D MHD Couple Stress nanofluid over an exponentially stretched surface.

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Department of Computer Science, Bahria University, Islamabad Campus, Islamabad, 44000, Pakistan.
Department of Mechanical Engineering, Sejong University, Seoul, 143-747, Korea.
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran.
Department of Mathematics, Allama Iqbal Open University, Islamabad, 44000, Pakistan.
Department of Mechanical Engineering, Sejong University, Seoul, 143-747, Korea.


Three dimensional problems reflect more imperative understanding to real world issues in comparison to two dimensional problems. Keeping this fact in mind, a mathematical model is designed to deliberate the 3D magnetohydrodynamic couple stress nanofluid flow with joule heating and viscous dissipation effects past an exponential stretched surface. The analysis is performed keeping in mind the physical effects of Brownian motion and thermophoresis combined with convective heat condition. This paper also distinctly introduces a more realistic boundary constraint for nanoliquid flow model. For instance, zero mass flux condition has been instituted for the first time for 3D couple stress nanofluid model as far as the exponential stretched surface is concerned. Self-similar transformations are engaged to obtain a system of ordinary differential equations possessing high nonlinearity from the system of boundary layer partial differential equations. Analytic solution is constructed in the form of series using Homotopy Analysis Method (HAM). Numerically calculated values of Skin friction and local Nusselt number are also given with suitable analysis. Moreover, the influences of sundry parameters on velocity distribution, and heat and mass transfer rates are deliberated and depicted through relevant graphs. The results obtained clearly show that the Biot number and Hartmann number possess increasing effect on temperature distribution. To authenticate our obtained results, a comparison in limiting case is also given.

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