Numerical approach has been employed to model the effect of permeability and Lorentz terms on buoyant flow of nanomaterial within a tank with one sinusoidal hot element. Although managing the system in thermal view is important, scrutinizing the irreversibility should be considered to reach the optimized unit. CVFEM with involving vorticity formulation was selected and sources terms of Lorentz and permeability was involved in vorticity transportation. Outcomes were summarized in terms of 3D distributions for Nu, Be and contours. Although increasing Ha leads to higher temperature of inner wavy wall, temperature gradient reduces which causes Nu to reduce and Be to increase. These effects are attributed to lower strength of circulation cell with rise of Ha which makes isotherms become parallel to each other and friction factor do not allow the nanomaterial to move faster inside the tank. With reduce of Da, resistance term becomes superior than convection term and nano particles cannot migrate easier and consequently Nu declines with reduce of permeability. Lower Da leads to higher share of S_gen,th and Be increases and same trend was reported for Ra. Stronger buoyancy force cause more complex isotherms and temperature of hot elements declines, so Nu enhances while reduction in temperature gradient leads to lower Be. Although augment of Ha can enhance the Be about 17.9% while it makes Nu to reduce about 24.7%. As Ra augments, Be declines about 75.22% while Nu for greater Ra is 2.79 times greater than that of Ra = 10³. Temperature of inner wall declines about 62.5% and 25% with growth of Ra and Da, respectively. Besides, as Ha increases, temperature augments about 33.33%. S_gen,th declines about 18.18% with rise of Ra.

已经采用数值方法来模拟渗透率和洛伦兹项对具有一个正弦热元素的储罐内纳米材料的浮力流动的影响。尽管从热学角度管理系统很重要，但应考虑仔细检查不可逆性以达到最佳单位。选择了具有涡度公式化的CVFEM，并且洛伦兹和渗透率的来源条件参与了涡度传输。结果根据Nu，Be和轮廓的3D分布进行了总结。尽管增加Ha会导致内部波状壁的温度升高，但温度梯度会降低，这会导致Nu减少和Be增加。这些效应归因于随着Ha的增加循环池强度降低，这使得等温线变得彼此平行，并且摩擦系数不允许纳米材料在槽内更快地移动。随着Da的减少，电阻项变得优于对流项，并且纳米粒子不能更容易迁移，因此Nu随渗透率的降低而下降。较低的Da导致较高的S份额_gen，th和Be增加，并且Ra的趋势相同。较强的浮力会导致更复杂的等温线，并且热元素的温度会下降，因此Nu会增加，而温度梯度的降低会导致Be的降低。尽管增加Ha可以使Be提高约17.9％，而使Nu降低约24.7％。随着Ra的增加，Be下降约75.22％，而更大Ra的Nu则是Ra = 10 ^3的2.79倍。随着Ra和Da的增加，内壁温度分别下降了约62.5％和25％。此外，随着Ha的增加，温度升高约33.33％。随着Ra的增加，S _gen，th下降约18.18％。