In this study, numerical analysis and optimization in a single and multiple walled carbon nanotube-water nanofluid filled lid driven cavity having an inner elliptic obstacle were performed by using finite element method and COBYLA optimization solver. The top wall is moving with constant speed and vertical walls are kept at constant temperatures. An optimal size of the inner elliptic obstacle was determined by using an optimization study to maximize the average heat transfer along the hot wall of the cavity. Numerical simulation was performed by for various values of Richardson numbers (between 0.05 and 50) and various solid particle volume fraction (between 0 and 0.06) for single and multiple-walled carbon nanotubes water nanofluid. A larger obstacle (higher values of radii in the major and minor axis) with lower values of Richardson number results in higher heat transfer rates. The average Nusselt number versus solid particle volume fraction shows a linear trend and the discrepancy between the average Nusselt number for the cavity with the optimized obstacle and other obstacles becomes higher with higher particle volume fraction. The average heat transfer enhances significantly which is about 120.20% for single wall carbon nanotube -water nanofluid at solid volume fraction of 0.06 when compared to pure water. The discrepancy between the average Nusselt number for single and multiple walled carbon nanotubes becomes higher for higher values of Richardson number and solid particle volume fraction. A polynomial type correlation was proposed for the average Nusselt number along the hot wall which is fifth order for Richardson number an first order for nanoparticle volume fraction.

在这项研究中，通过使用有限元方法和COBYLA优化求解器，对具有内椭圆形障碍的单壁和多壁碳纳米管-水纳米流体填充盖驱动腔进行了数值分析和优化。顶壁以恒定的速度移动，垂直壁保持恒定的温度。通过使用优化研究来确定内部椭圆形障碍物的最佳尺寸，以使沿着腔体热壁的平均热量传递最大化。通过对单壁和多壁碳纳米管水纳米流体的理查森数的各种值（0.05到50之间）和各种固体颗粒体积分数（0到0.06之间）进行数值模拟。较大的障碍物（长轴和短轴的半径值较高）和理查森数的值较低会导致较高的传热速率。平均努塞尔数相对于固体颗粒体积分数显示出线性趋势，并且具有最佳障碍物的腔体的平均努塞尔数与其他障碍物之间的差异随着更高的颗粒体积分数而变得更高。与纯水相比，在固体体积分数为0.06的情况下，单壁碳纳米管-水纳米流体的平均热传递显着增强，约为120.20％。对于更高的理查森数和固体颗粒体积分数，单壁和多壁碳纳米管的平均努塞尔数之间的差异变得更高。