Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.
Comput Methods Programs Biomed. 2020 Jul;191:105342. doi: 10.1016/j.cmpb.2020.105342. Epub 2020 Jan 27.
Nanofluids are known for better heat transfer characteristics in many heat exchanger devices due to their enhanced heat transfer abilities. Recently, scientists give the idea of nanofluid which is the mixture of base fluid and solid nanoparticles having very small size. For physical phenomenon of conventional fluids by mean of suspensions of nanoparticles in base fluids and prompted produce a new composite known as "nanofluids". These composite contain the nanoparticles with 1-100 nm sized which are suspended in the base fluids. Here we have considered a subclass of non-Newtonian fluid called Oldroyd-B fluid. The fluid motion over the disk surface is produced due to the rotation as well as radially stretching of disk. Further, the impact of non-linear thermal radiation and heat generation/absorption is introduced to visualize the heat transfer behavior. The convective boundary is also taken into consideration in order to investigate the fluid thermal characteristics. The novel features of thermophoresis and Brownian motion during the nanoparticles movement in fluid motion are studied with revised Buongiorno model. The physical problem is modeled with the concept of classical Fourier's and Fick's laws. The von Karman variables are used to convert the partial differential equations (PDEs) into non-dimensional ordinary differential equations (ODEs).
The system of governing ordinary differential equations (ODEs) with boundary conditions (BCs) are highly non-linear in nature. To handle these non-linear ODEs, we use a numerical technique called BVP Midrich scheme which uses the midpoint method to acquire the numerical solution of the governing problem. The solutions of the governing problem are obtained by utilizing Maple software.
Effect of different involved controlling parameters on the velocity profiles, temperature and concentration distributions are analyzed graphically. Additionally, the numerical data for local Nusselt and Sherwood numbers are also tabulated. The reduction in heat transfer rate at the wall is noticed against thermoporesis and Brownian motion parameters, respectively. The concentration gradient at the wall reduces with an increment in mass transfer parameter.
由于纳米流体具有增强的传热能力，因此在许多换热器设备中，它们以更好的传热特性而闻名。最近，科学家提出了纳米流体的想法，即由具有非常小尺寸的基液和固体纳米粒子组成的混合物。通过在基液中悬浮纳米粒子来实现常规流体的物理现象，并促使产生一种新的复合材料，称为“纳米流体”。这些复合材料包含 1-100nm 尺寸的纳米粒子，悬浮在基液中。在这里，我们考虑了一种称为 Oldroyd-B 流体的非牛顿流体子类。由于盘的旋转和径向拉伸，在盘表面上产生了流体运动。此外，引入了非线性热辐射和热生成/吸收的影响，以可视化传热行为。为了研究流体的热特性，还考虑了对流边界。在流体运动中，纳米粒子的运动过程中研究了热泳和布朗运动的新颖特征，并采用修正的 Buongiorno 模型进行了研究。该物理问题是基于经典傅立叶定律和菲克定律的概念建模的。使用 von Karman 变量将偏微分方程（PDE）转换为无量纲常微分方程（ODE）。
具有边界条件（BC）的常微分方程组（ODE）本质上是高度非线性的。为了处理这些非线性 ODE，我们使用了一种称为 BVP Midrich 方案的数值技术，该技术使用中点法来获取控制问题的数值解。使用 Maple 软件获得控制问题的解。
以图形方式分析了不同控制参数对速度分布、温度和浓度分布的影响。此外，还列出了局部努塞尔数和舍伍德数的数值数据。分别通过热泳和布朗运动参数，观察到壁处的传热速率降低。随着传质参数的增加，壁处的浓度梯度减小。
