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Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid

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  • Liu, Yi
  • Chi, Xiaoqing
  • Xu, Huanying
  • Jiang, Xiaoyun

Abstract

This work investigates the unsteady magnetohydrodynamic (MHD) flow and heat transfer of fractional Maxwell fluids in a square cavity, which is under the influence of the Hall effect and radiation heat. The coupled model is formed from the momentum equation based on the fractional constitutive relationship and the fractional heat-conduction equation derived from the Fourier law. The fractional coupled model is solved numerically by combining the weighted and shifted Grünwald difference method in the temporal direction with the spectral method based on Lagrange-basis polynomials in the spatial direction. In addition, we propose a fast method to reduce the computational time and the memory requirements of the actual calculation. We also prove the stability and convergence of the numerical scheme with the fast method. Furthermore, a numerical example is given to verify the efficiency of the numerical method and of the theoretical analysis. An example of non-smooth solutions is dealt with by adding correction terms. Finally, an example is considered to discuss the effects of the Hartmann number, the Hall parameter, and the thermal radiation parameter on the MHD flow and heat transfer of a fractional Maxwell fluid in a square cavity.

Suggested Citation

  • Liu, Yi & Chi, Xiaoqing & Xu, Huanying & Jiang, Xiaoyun, 2022. "Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003290
    DOI: 10.1016/j.amc.2022.127255
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    References listed on IDEAS

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    1. Pal, Dulal & Mandal, Gopinath & Vajravalu, Kuppalapalle, 2016. "Soret and Dufour effects on MHD convective–radiative heat and mass transfer of nanofluids over a vertical non-linear stretching/shrinking sheet," Applied Mathematics and Computation, Elsevier, vol. 287, pages 184-200.
    2. Jian, Huan-Yan & Huang, Ting-Zhu & Ostermann, Alexander & Gu, Xian-Ming & Zhao, Yong-Liang, 2021. "Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Chi, Xiaoqing & Jiang, Xiaoyun, 2021. "Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.
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    Cited by:

    1. Li, Nan & Wang, Xiaoping & Xu, Huanying & Qi, Haitao, 2024. "Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 291-305.

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