This study deals with the roles of a magnetic field and circular rotation of a circular cylinder on the dissemination of solid phase within a nanofluid-filled square cavity. Two wavy layers of the non-Darcy porous media are situated on the vertical sides of a cavity. An incompressible smoothed particle hydrodynamics (ISPH) method was endorsed to carry out the blending process concerning solid phase into nanofluid and porous media layers. Initially, the solid phase is stationed in a circular cylinder containing two open gates. Implications of a buoyancy ratio (N = −2: 2), Hartmann number (Ha = 0: 100), rotational frequency $\left(\omega =1 : 10\right)$, Darcy parameter $\left(Da={10}^{-2}:{10}^{-5}\right)$, Rayleigh number $\left(Ra={10}^3:{10}^6\right)$, nanoparticles parameter $\left(\phi =0:0.06\right)$, and amplitude of wavy porous layers $\left({\rm A}=0.05:0.15\right)$ on the lineaments of heat/mass transport have been carried out. The results revealed that the diffusion of the solid phase is permanently moving toward upward except at opposing flow mode $\left(N<0\right)$ toward downward. The lower Rayleigh number reduces the solid-phase diffusions. A reduction in a Darcy parameter lessens the nanofluid speed and solid-phase diffusions in the porous layers. A reduction in $Da$ from ${10}^{-3}$ to ${10}^{-5}$ diminishes the maximum of streamlines ${\left|\mathbf{\psi }\right|}_{\mathbf{max}}$ by 13.19% at $N=-2$, by 46.75% at $N=0$, and by 74.75% at $N=2$.

这项研究涉及磁场和圆柱体的圆形旋转对纳米流体填充方形腔内固相扩散的作用。非达西多孔介质的两个波浪层位于空腔的垂直侧。不可压缩的光滑粒子流体力学 (ISPH) 方法被认可用于将固相混合到纳米流体和多孔介质层中。最初，固相被放置在一个包含两个开放门的圆柱体中。浮力比 ( N = -2: 2)、哈特曼数 ( Ha = 0: 100)、旋转频率的含义$\left(\omega =1 ： 10\right)$, 达西参数 $\left(D\mathrm{一种}={10}^{-2}：{10}^{-5}\right)$, 瑞利数 $\left(\mathrm{电阻}\mathrm{一种}={10}^3：{10}^6\right)$, 纳米颗粒参数 $\left(\phi =0：0.06\right)$, 和波状多孔层的振幅 $\left({\rm A}=0.05：0.15\right)$已经进行了热/质量传输的线路。结果表明，除逆流模式外，固相的扩散是永久向上移动的$\left(N<0\right)$向下。较低的瑞利数减少了固相扩散。Darcy 参数的减小会降低多孔层中的纳米流体速度和固相扩散。减少$D\mathrm{一种}$ 从 ${10}^{-3}$ 到 ${10}^{-5}$ 减少流线的最大值 ${\left|\mathbf{\psi }\right|}_{\mathbf{最大限度}}$ 13.19% 在 $N=-2$, 46.75% 在 $N=0$，并且在 74.75% $N=2$.