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Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation

Author

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  • Muhammad Shoaib Arif

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

  • Wasfi Shatanawi

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan)

  • Yasir Nawaz

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

Abstract

This study addresses heat and mass transfer of electrical magnetohydrodynamics (MHD) Williamson fluid flow over the moving sheet. The mathematical model for the considered flow phenomenon is expressed in a set of partial differential equations. Later, linear and nonlinear ordinary differential equations (ODEs) are obtained. The finite element method tackles a reduced system of ODEs with boundary conditions. Galerkin weighted residuals and constructs of weak formulations constitute the basis of this method. An iterative procedure is considered for handling nonlinear terms in a given system of ODEs. Some results acquired using the finite element method are compared with those reported in previous research via the Matlab solver bvp4c in order to validate the obtained solutions of ODEs. It is seen that the velocity profile is decayed by enhancing the Wiesenberg number. The finite element method also converges to an accurate solution by increasing the number of elements, whereas Matlab solver bvp4c produces accurate results on small grid points. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures.

Suggested Citation

  • Muhammad Shoaib Arif & Wasfi Shatanawi & Yasir Nawaz, 2023. "Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation," Energies, MDPI, vol. 16(6), pages 1-19, March.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:6:p:2778-:d:1099593
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    References listed on IDEAS

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    1. Stanford Shateyi & Sandile Sydney Motsa, 2009. "Thermal Radiation Effects on Heat and Mass Transfer over an Unsteady Stretching Surface," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-13, January.
    2. Doaa Rizk & Asad Ullah & Ikramullah & Samia Elattar & Khalid Abdulkhaliq M. Alharbi & Mohammad Sohail & Rajwali Khan & Alamzeb Khan & Nabil Mlaiki, 2022. "Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface," Energies, MDPI, vol. 15(8), pages 1-16, April.
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