This study aims at finding the linear theory for the onset of ferromagnetic convective flow in a heterogeneous Brinkman porous layer with uniformly distributed internal heat source in the presence of vertical magnetic field. The resulting critical values are obtained numerically using the Galerkin technique for isothermal/insulated rigid-ferromagnetic boundaries for different forms of vertical heterogeneity permeability function $F(z)$. The results converge for six terms in the Galerkin expansion. The effect of types of $F(z)$ and $N_s$ is found to either delay or speedup the flow of the ferrofluids. The stability of the system for the model $F4$ is more stable and least stable for the model $F1$ in the presence of $N_s$. For different forms of $F(z)$, the results show that the critical Rayleigh number increases with increasing $Da$, while decreases with increasing $R_m$ and $M_3$. The values of $a_c$ increase with $R_m$, but they decrease with increasing $M_3$ and $Da$. Besides, isothermal boundaries are found to be more stabilizing when compared to insulated boundaries.

本研究旨在寻找在存在垂直磁场的情况下具有均匀分布的内部热源的异质 Brinkman 多孔层中铁磁对流开始的线性理论。对于不同形式的垂直非均质性渗透率函数，使用 Galerkin 技术对等温/绝缘刚性-铁磁边界以​​数值方式获得由此产生的临界值$F(z)$. 结果在 Galerkin 展开式中收敛了六个项。类型的影响$F(z)$和${否}_{秒}$被发现延迟或加速铁磁流体的流动。模型的系统稳定性$F\mathrm{4个}$对于模型来说更稳定和最不稳定$F\mathrm{1个}$在......的存在下${否}_{秒}$. 对于不同形式的$F(z)$，结果表明，临界瑞利数随着$丁\mathrm{一个}$, 而随着增加而减少$R_{米}$和${米}_{\mathrm{3个}}$. 的价值观${\mathrm{一个}}_C$增加与$R_{米}$, 但随着增加而减少${米}_{\mathrm{3个}}$和$丁\mathrm{一个}$. 此外，与绝热边界相比，等温边界被发现更稳定。