Carbon nanotubes are cylindrical carbon molecules which offer promising applications in nanotechnology due to high thermal conductivity. These carbon allotropes can be utilized as additives in various structural materials. Recent development in numerous technological and industrial sectors such as chemical bonding process, optics, and microelectronics requires a strong need to develop such hybrid fluids which are more operative in terms of heat exchange performance. Keeping in view, this study investigates the influence of velocity slip on flow of water-based carbon nanotubes over a convective vertical wall. Single and multiwall carbon nanotubes are suspended within water-based fluid. The governing partial differential equations are transformed into ordinary differential equation using appropriate similarity transformations. Transformed equations are solved numerically by means of Runge–Kutta–Fehlberg method along with shooting scheme. The variation of velocity and temperature profiles is portrayed. Physical quantity of interest such as skin friction coefficient and local heat flux are determined against carbon nanotubes volume fraction, slip parameter, and Biot number. Velocity, temperature, and the local heat flux elevates with nanotubes volume fraction \( \phi \), or the case of single as well as multiwall carbon nanotubes.

中文翻译：

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滑流通过悬浮在水中的悬浮碳纳米管对流板的热物理传递

碳纳米管是圆柱形碳分子，由于其高导热性而在纳米技术中提供了有希望的应用。这些碳同素异形体可以用作各种结构材料中的添加剂。在诸如化学键合工艺，光学和微电子学之类的许多技术和工业领域中的最新发展，强烈需要开发这种在热交换性能方面更具操作性的混合流体。考虑到这一点，本研究调查了速度滑移对对流垂直壁上水基碳纳米管流动的影响。单壁和多壁碳纳米管悬浮在水基流体中。使用适当的相似性变换，将控制的偏微分方程转换为常微分方程。变换后的方程通过Runge–Kutta–Fehlberg方法以及射击方案进行数值求解。描绘了速度和温度曲线的变化。确定感兴趣的物理量（例如皮肤摩擦系数和局部热通量）与碳纳米管的体积分数，滑移参数和比奥特数。速度，温度和局部热通量随纳米管的体积分数升高\（\ phi \），或者是单壁或多壁碳纳米管。