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Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer

Author

Listed:
  • Yasir Nawaz

    (Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan)

  • Muhammad Shoaib Arif

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Stochastic Analysis and Optimization Research Group, Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan)

  • Kamaleldin Abodayeh

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Mairaj Bibi

    (Department of Mathematics, Comsats University Islamabad, Islamabad 44000, Pakistan)

Abstract

The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering.

Suggested Citation

  • Yasir Nawaz & Muhammad Shoaib Arif & Kamaleldin Abodayeh & Mairaj Bibi, 2022. "Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer," Energies, MDPI, vol. 15(13), pages 1-22, June.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:13:p:4713-:d:849161
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    References listed on IDEAS

    as
    1. Sheikholeslami, M. & Farshad, Seyyed Ali & Shafee, Ahmad & Babazadeh, Houman, 2021. "Performance of solar collector with turbulator involving nanomaterial turbulent regime," Renewable Energy, Elsevier, vol. 163(C), pages 1222-1237.
    2. Mashhour A. Alazwari & Nidal H. Abu-Hamdeh & Marjan Goodarzi, 2021. "Entropy Optimization of First-Grade Viscoelastic Nanofluid Flow over a Stretching Sheet by Using Classical Keller-Box Scheme," Mathematics, MDPI, vol. 9(20), pages 1-22, October.
    3. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Muhammad Usman Ashraf, 2022. "A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study," Energies, MDPI, vol. 15(3), pages 1-15, January.
    4. Constantin Fetecau & Rahmat Ellahi & Sadiq M. Sait, 2021. "Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall," Mathematics, MDPI, vol. 9(1), pages 1-13, January.
    5. Fang Wang & Jinling Liu, 2020. "The First Solution for the Helical Flow of a Generalized Maxwell Fluid within Annulus of Cylinders by New Definition of Transcendental Function," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-15, February.
    6. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Amna Nazeer, 2021. "An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow," Energies, MDPI, vol. 14(12), pages 1-17, June.
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