Department of Mathematics, Air University, Sector E-9, P.A. F Complex, Islamabad, 44000, Pakistan.
Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
Sci Rep. 2023 Mar 14;13(1):4190. doi: 10.1038/s41598-023-30609-9.
The prime motive to conduct this communication is to explicate hydrothermal attributes of water by inducing new composition of nanoparticles termed as ternary particles. For this purpose, two differently natured groups one with lesser densities (Carbon nanotubes, Graphene and Aluminium oxide) and with higher densities (Copper oxide, Copper and Silver) are accounted. A 3D permeable surface is considered as a physical configuration of problem by providing dual stretching. Initially, mathematical structuring in dimensional representation expressing the constitutive relations for mass, momentum and energy conservation is manifested. Later on, a set of similar variables are executed to express attained coupled system into ordinary form. Numerical simulations are performed to find solution by employing shooting and RK-4 methods in conjunction. Description about change is displayed through graphical visualization. Subsequently, temperature distribution and heat flux coefficient against sundry variables are also measured and comprehensively discussed in pictorial and tabular format. Wall drag coefficients along (x, y) directions are also computed. It is inferred from the outcomes that velocity, temperature and concentration of base fluid is higher for ternary group 1 containing particles of low densities than for group 2 with more denser particles. It is also deduced that elevation in temperature of fluid is revealed against Soret number whereas contrary aspects is observed in view of concentration distribution. Dufour number has declining impact on temperature profile whereas it upsurges the mass distribution. It is depicted that skin friction in case of group containing particles with less densities are more than other group.
进行本次交流的主要动机是通过引入新的纳米粒子组合——三元粒子，来阐明水的热液属性。为此，我们考虑了两组具有不同密度的物质，一组密度较低（碳纳米管、石墨烯和氧化铝），另一组密度较高（氧化铜、铜和银）。通过提供双重拉伸，将 3D 可渗透表面视为问题的物理配置。首先，以维度表示形式表现出质量、动量和能量守恒的本构关系的数学结构。之后，通过执行一组类似的变量，将获得的耦合系统表达为常微分方程形式。通过结合打靶法和 RK-4 方法进行数值模拟以找到解。通过图形可视化显示关于变化的描述。随后，还测量并以图形和表格形式综合讨论了各种变量下的温度分布和热流系数。还计算了沿（x，y）方向的壁面阻力系数。结果表明，与包含高密度粒子的第二组相比，包含低密度粒子的第一组三元粒子的基液速度、温度和浓度更高。还可以推断出，流体温度随索雷特数的升高而升高，而在浓度分布方面则相反。杜弗尔数对温度分布有下降的影响，而对质量分布则有上升的影响。结果表明，在包含低密度粒子的组中，摩擦系数比其他组更大。
