An improved single-relaxation-time lattice Boltzmann model of the melting with natural convection in a cavity submitted to an inhomogeneous magnetic field is developed and comparatively investigated in this paper, which can not only reduce the numeric diffusion at the phase boundary obviously but also recover the macroscopic energy equations correctly. Three numerical benchmark cases are performed, including the half-space conduction melting, convection-dominated melting, and natural convection under an inhomogeneous magnetic field. Impacts of the dimensionless magnetic force parameter and the magnetic field inclination angle on the melting process are presented in relation to the average Nusselt number, liquid fraction, temperature profile, melting front and pressure distribution. The results show that the numerical predictions based on the current model agree with analytical solutions and present better accuracy than those reported in previous studies. Like the buoyancy force, the magnetic force also has a vital influence on the natural convection development in the melting process. Compared with the case without a magnetic field, the magnetic field angle can be adjusted to enhance and suppress the melting process by employing the coupling effect of the magnetic force and gravity. Moreover, there exists an optimal magnetic field inclination angle for maximizing the melting heat transfer performance. Besides, increasing the dimensionless magnetic parameter expands the gain of melting enhancement while expanding the range of inclination angles that enhances melting performance.

本文建立了一种改进的单弛豫时间晶格 Boltzmann 模型在非均匀磁场作用下的腔内自然对流熔化，该模型不仅可以明显降低相界处的数值扩散，而且可以恢复宏观能量方程正确。进行了三个数值基准案例，包括半空间传导熔化、对流主导熔化和非均匀磁场下的自然对流。介绍了无量纲磁力参数和磁场倾角对熔化过程的影响，涉及平均努塞尔数、液体分数、温度分布、熔化前沿和压力分布。结果表明，基于当前模型的数值预测与解析解一致，并且比以前的研究报告的精度更高。与浮力一样，磁力对熔化过程中的自然对流发展也有重要影响。与没有磁场的情况相比，利用磁力和重力的耦合效应，可以调节磁场角度来增强和抑制熔化过程。此外，存在一个最佳磁场倾角，以最大限度地提高熔化传热性能。此外，增加无量纲磁参数可以扩大熔化增强的增益，同时扩大增强熔化性能的倾角范围。