In this study, for the first time, a nanofluid's natural convection heat transfer in a two-dimensional square cavity has been numerically investigated by use of the lattice Boltzmann method with the constant heat flux boundary condition. The horizontal walls of the cavity are insulated, and the vertical walls are kept at a constant heat flux. The diameters of the nanoparticles inside the cavity are the same and have a homogeneous distribution, and there is no chemical reaction between the particles. The flow is also assumed to be the steady state and two-dimensional. Constant temperature, streamlines, velocity, and average Nusselt have been investigated for different nanoparticle volume fractions and Rayleigh numbers. The results showed that the lattice Boltzmann method efficiently analyzes the natural heat transfer of nanofluids; moreover, by use of nanofluid in the cavity increases the heat transfer rate. With the increase in the nanoparticle volume fraction, the average Nusselt number on the right wall of the cavity increased. For a volume fraction of 20% with Grashof number 10⁵, the average Nusselt number increased by almost 50% compared to the base fluid at the same Grashof number. It has been observed that as the volume fraction of nanoparticles in the fluid increases, the fluid’s viscosity also increases; consequently, the velocity of the fluid is found to decrease.

在这项研究中，首次利用恒定热通量边界条件的格子玻尔兹曼方法对纳米流体在二维方形腔内的自然对流换热进行了数值研究。腔体的水平壁是隔热的，垂直壁保持恒定的热通量。空腔内纳米粒子直径相同且分布均匀，粒子间不发生化学反应。还假设流动是稳态和二维的。研究了不同纳米颗粒体积分数和瑞利数的恒定温度、流线、速度和平均努塞尔特。结果表明，格子玻尔兹曼方法有效地分析了纳米流体的自然传热；此外，通过在腔体中使用纳米流体提高了传热速率。随着纳米颗粒体积分数的增加，空腔右壁的平均努塞尔数增加。对于体积分数为 20%、格拉霍夫数为 10 ^{5 的}情况，与相同格拉霍夫数的基液相比，平均努塞尔数增加了近 50%。据观察，随着流体中纳米粒子体积分数的增加，流体的粘度也增加；因此，发现流体的速度降低。