In this paper, a two-phase model is administered to investigate natural convection of Fe₃O₄–water ferrofluid in a square cavity and under turbulent regime. Ferrofluid flow is exposed to magnetic fields which are induced by two parallel current-carrying wires. The left and right walls of the cavity are maintained at constant temperatures of \({T}_{h}\) and \({T}_{c}\) respectively, while the other walls are insulated. In this study, Buongiorno’s two-phase model is modified for considering the nanoparticle diffusion via turbulent eddies and magnetophoresis effects. The Reynolds-averaged Navier–Stokes equations are treated based on v²–f model and the governing equations are solved by the SIMPLE-based finite volume method. The computations are performed for various Rayleigh numbers (\({10}^{7}\), \(5\times 10^{7}\) and \({10}^{8}\)), nanoparticle's volume fraction (\(0\le {\phi }_{m}\le 0.06\)) and magnetic numbers ranging from 0 to \(3.4 \times {10}^{11}\). Numerical results indicate that heat transfer rate and turbulence intensity can be significantly enhanced by the applied magnetic fields. However, the effect of employed magnetic field on heat transfer increment is more pronounced at low Rayleigh numbers.

本文采用两相模型研究Fe ₃ O _{4 –}水铁磁流体在方腔内和湍流条件下的自然对流。铁磁流体流暴露于磁场，该磁场由两条平行的载流导线感应。空腔的左壁和右壁分别保持在恒定温度\（{T} _ {h} \）和\（{T} _ {c} \），而其他壁则保持绝缘。在这项研究中，对Buongiorno的两相模型进行了修改，以考虑通过湍流和磁泳效应产生的纳米粒子扩散。根据v ²处理雷诺平均Navier-Stokes方程-f模型和控制方程由基于SIMPLE的有限体积法求解。对各种瑞利数（\（{10} ^ {7} \），\（5×10 ^ {7} \）和\（{10} ^ {8} \））进行计算，纳米粒子的体积分数（\（0 \ le {\ phi} _ {m} \ le 0.06 \））和磁数范围从0到\（3.4 \ times {10} ^ {11} \）。数值结果表明，通过施加磁场可以显着提高传热速率和湍流强度。但是，在低瑞利数下，所用磁场对传热增量的影响更为明显。