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Gegenbauer wavelets collocation-based scheme to explore the solution of free bio-convection of nanofluid in 3D nearby stagnation point

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Abstract

In the current article, we investigated a three-dimensional nanofluid bio-convection model near a stagnation attachment. The set of governing equations, with a set of similarity variables, expressing the conservation of momentum, total mass, microorganisms, thermal energy and nanoparticles are reduced to nonlinear ODEs set. The obtained nonlinear system is tackled via collocation-based Gegenbauer wavelets technique. The purpose of this extension is to reduce the computational work as compared to the traditional Gegenbauer wavelets method. Additionally, the suggested trial solutions must satisfy the boundary conditions. Convergence analysis shows an excellent agreement. The graphical plots for various physical parameters are illustrated. Additionally, the significant physical quantities of viable interests and the impact of different physical parameters on the dissemination of the motile microorganisms are also included in our study. The error and convergence analyses are endorsing that the proposed method is well efficient and could be extended to other nonlinear problems.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Muhammad Usman & Muhammad Hamid

  2. Department of Civil Engineering, School of Engineering, University of Birmingham, Birmingham, UK

    Mohammad Mehdi Rashidi

Authors
  1. Muhammad Usman
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  2. Muhammad Hamid
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  3. Mohammad Mehdi Rashidi
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Correspondence to Muhammad Usman.

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Usman, M., Hamid, M. & Rashidi, M.M. Gegenbauer wavelets collocation-based scheme to explore the solution of free bio-convection of nanofluid in 3D nearby stagnation point. Neural Comput & Applic 31, 8003–8019 (2019). https://doi.org/10.1007/s00521-018-3625-8

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  • DOI: https://doi.org/10.1007/s00521-018-3625-8

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