In this paper, a numerical research for the problem of unsteady space fractional magnetohydrodynamic (MHD) free convective flow and heat transfer with Hall effects is investigated. We firstly establish a space fractional MHD flow and heat transfer model, which is coupled by the incompressible space fractional Navier–Stokes equations and the heat conduction equation. Then we develop a finite difference spectral decomposition method based on the pressure correction algorithm to solve this nonlinear coupled model. The validity of the proposed numerical scheme is verified and some flow field, temperature field are obtained. We also detailedly analyze the effects of relevant parameters on the space fractional MHD flow and heat transfer.

本文对具有霍尔效应的非稳态空间分数磁流体动力自由对流和传热问题进行了数值研究。我们首先建立了空间分数MHD流动和传热模型，该模型由不可压缩的空间分数Navier–Stokes方程和热传导方程耦合。然后，我们基于压力校正算法开发了一种有限差分谱分解方法，以解决该非线性耦合模型。验证了所提出数值方案的有效性，并获得了一些流场，温度场。我们还详细分析了相关参数对空间分数MHD流动和传热的影响。