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Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation

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  • M.M. Khader
  • A. Eid
  • M. Adel

Abstract

Theoretical investigation of magnetohydrodynamics (MHD) Casson and Williamson fluid flow and heat and mass transfer in laminar flow through a stretching sheet in the presence of heat generation is carried out in this study. The convective wall temperature and convective wall mass boundary condition are taken into account in this study. A study is also provided, which looks into the impact of viscous dissipation. Except for a temperature‐dependent thermal conductivity, all properties of the proposed model are assumed to be constants in the study. The spectral collocation method based on the shifted Vieta–Lucas polynomials is used to give an approximate formula for the n‐order derivative and solve numerically the coupled momentum, energy, and mass equations. This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. This system is built as a restricted optimization problem and optimized to obtain the series solution’s unknown coefficients. Some theorems are provided to investigate the method’s convergence. The statistics, which are given visually, were compared to the results of other researchers’ theoretical analysis.

Suggested Citation

  • M.M. Khader & A. Eid & M. Adel, 2022. "Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3257808
    DOI: 10.1155/2022/3257808
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    References listed on IDEAS

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    1. M. M. Khader & M. Adel, 2020. "Numerical and theoretical treatment based on the compact finite difference and spectral collocation algorithms of the space fractional-order Fisher’s equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-13, September.
    2. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    3. Ahmed M. Megahed, 2020. "Steady flow of MHD Williamson fluid due to a continuously moving surface with viscous dissipation and slip velocity," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-12, January.
    4. W. Abbas & Ahmed M. Megahed, 2021. "Numerical solution for chemical reaction and viscous dissipation phenomena on non-Newtonian MHD fluid flow and heat mass transfer due to a nonuniform stretching sheet with thermal radiation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(09), pages 1-20, September.
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    1. M. M. Khader & M. M. Babatin & Ahmed M. Megahed & A. Eid, 2022. "Implementing the Galerkin Method Associated with the Shifted Vieta‐Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms over a Slippery Stretching Sheet," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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