In this article, the free convection flow of second-grade nanofluids based on carbon nanotubes (CNTs) with Prabhakar-like fractional and Newtonian heating over a vertical plate has been studied. The fractional model of governing equations is defined by the time-dependent fractional Prabhakar derivative. Using the Laplace transform method, analytical solutions are determined for the dimensionless thermal and velocity profiles. Prabhakar-like fractional second-grade fluids with generalized thermal transport velocity and heat transfer are compared with ordinary second-grade fluids with ordinary thermal transport and ordinary viscous fluids with classical Fourier thermal flux. The effects of fractional and physical parameters are expressed graphically.

中文翻译：

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碳纳米管类 Prabhakar 分数二级纳米流体在具有牛顿加热的无限板上的自然对流流动

在本文中，研究了基于碳纳米管 (CNT) 的二级纳米流体在垂直板上具有类 Prabhakar 分数和牛顿加热的自由对流流动。控制方程的分数模型由时间相关分数 Prabhakar 导数定义。使用拉普拉斯变换方法，确定无量纲热和速度分布的解析解。将具有广义热传递速度和热传递的类 Prabhakar 分数二级流体与具有普通热传递的普通二级流体和具有经典傅里叶热通量的普通粘性流体进行了比较。分数和物理参数的影响以图形方式表示。