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

• Published in: Applied mathematics and computation Vol. 430; p. 127255
• Main Authors: Liu, Yi, Chi, Xiaoqing, Xu, Huanying, Jiang, Xiaoyun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2022
• Subjects: Fast method; Fractional coupled model; Magnetohydrodynamic flow and heat transfer; Stability and convergence; Weighted and shifted Grünwald difference method; Magnetohydrodynamic flow and heat transfer; Weighted and shifted Grünwald difference method; Fast method; Fractional coupled model; Stability and convergence
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127255

•A fractional Maxwell fluid model is built to study the flow and heat transfer.•The weighted and shifted Grnwald difference method is used to discretize.•A fast algorithm is proposed to reduce the time and the memory requirements.•The stability and convergence of the scheme with the fast method are proved.•The efficiency of scheme is verified and the effects of parameters are discussed. 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.