The effect of an external magnetic field on the mixed convection $$\hbox {Fe}_{{3}}\hbox {O}_{{4}}/$$ Fe 3 O 4 / water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles $$0\le \varphi \le 0.05$$ 0 ≤ φ ≤ 0.05 , magnetic numbers $$0\le \hbox {Mn} \le 100$$ 0 ≤ Mn ≤ 100 , Reynolds numbers $$100\le \hbox {Re}\le 500$$ 100 ≤ Re ≤ 500 , Darcy numbers $$\hbox {10}^{{-3}}\le \hbox {Da}\le 10^{{-1}}$$ 10 - 3 ≤ Da ≤ 10 - 1 and porosity parameters $$0.7\le \varepsilon \le 0.9$$ 0.7 ≤ ε ≤ 0.9 while fixing the Grashof number at $$10^{{4}}$$ 10 4 . Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter.

中文翻译：

---

磁场对水平多孔通道中混合对流的影响 $$\hbox {Fe}_{3}\hbox {O}_{{{4}}}/\hbox {water}$$ 铁磁流体流动

外磁场对水平多孔中混合对流的影响 $$\hbox {Fe}_{{3}}\hbox {O}_{{4}}/$$ Fe 3 O 4 / water ferrofluid flow通道进行了数值研究。使用 Darcy-Brinkman-Forchheimer 公式的控制方程通过采用有限体积法求解。计算了一系列纳米颗粒的体积分数 $$0\le \varphi \le 0.05$$ 0 ≤ φ ≤ 0.05 ，磁数 $$0\le \hbox {Mn} \le 100$$ 0 ≤ Mn ≤ 100 , 雷诺数 $$100\le \hbox {Re}\le 500$$ 100 ≤ Re ≤ 500 , 达西数 $$\hbox {10}^{{-3}}\le \hbox {Da}\le 10 ^{{-1}}$$ 10 - 3 ≤ Da ≤ 10 - 1 和孔隙度参数 $$0.7\le \varepsilon \le 0.9$$ 0.7 ≤ ε ≤ 0.9 同时将 Grashof 数固定为 $$10^{{4} }$$ 10 4 . 结果表明，在开尔文力的影响下，在磁源附近形成了回流区。它随着磁数的增加而增长。摩擦因数随着磁数的增加而增加，随着达西数的增加而减少。随着磁场增强，流动加速。通过增加纳米颗粒的体积分数和磁数，传热速率增加。通过增加雷诺数和达西数，磁场对铁磁流体流动的流体动力学和热行为的影响显着增强。在雷诺数、渗透率和/或孔隙率参数值较高时，铁磁纳米颗粒和磁场对传热增强率的综合影响变得更加明显。