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Brownian motion and thermophoretic effects on non-Newtonian nanofluid flow via Crank–Nicolson scheme

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Abstract

Herein, we examined the impact of Brownian motion and thermophoresis on MHD stagnation-point nanofluid flow toward vertical stretching surface using the non-Newtonian Prandtl fluid model. The governing mathematical model consists of a set of nonlinear partial differential equations along with associated boundary conditions. The similarity conversion technique is adopted to convert them to nonlinear ordinary differential equations, which are then solved numerically using the Finite-Difference Crank–Nicolson Method. The simulation is performed to examine flow, heat and mass transfer due to changes in physical parameters. The study revealed that, in the buoyancy opposing flow region, the heat transfer rate increases, and the mass transfer rate decreases due to an increase in Brownian motion. Moreover, augmentation in thermophoresis effects enhances the mass transfer rate, while the heat transfer rate is not dominantly affected. It is further noticed that the FDM-based Crank–Nicolson scheme is well matched and efficient to deal with the solution of such kinds of nonlinear physical models arising in mechanics.

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Acknowledgement

The authors would like to thank the referees for their valuable suggestions that help improve the manuscript's content. The corresponding author (M. Hamid) is sincerely grateful to Fudan University for providing research opportunities through the Postdoctoral International Exchange Fellowship. China Postdoctoral Science Foundation supported this work (No. 2020M681135).

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Authors and Affiliations

  1. Department of Basic Sciences and Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Larkana, Pakistan

    Feroz Ahmed Soomro

  2. Department of Electrical Engineering, Bahria University, Islamabad Campus, Islamabad, Pakistan

    Rizwan Ul Haq

  3. Department of Mechanics and Engineering Science, Fudan University, Shanghai, 200433, China

    Muhammad Hamid

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  1. Feroz Ahmed Soomro
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  2. Rizwan Ul Haq
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Soomro, F.A., Haq, R.U. & Hamid, M. Brownian motion and thermophoretic effects on non-Newtonian nanofluid flow via Crank–Nicolson scheme. Arch Appl Mech 91, 3303–3313 (2021). https://doi.org/10.1007/s00419-021-01966-6

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