Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha 40100, Pakistan.
Department of Mathematics, Huzhou University, Huzhou 313000, China.
Molecules. 2020 Jun 10;25(11):2694. doi: 10.3390/molecules25112694.
The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.
本研究的主要目的是研究球体表面的热泳输运和混合对流的耦合机制。为了分析存在热泳输运时的热和流体流动特性，我们根据守恒定律建立了一个非线性耦合偏微分方程组的数学模型。此外，通过实施有限差分法和内置的 BVP4C 边界值问题四阶代码，对所提出现象的数学模型进行了逼近。本文的新颖之处在于，引入了原始变量公式将偏微分方程组转换为原始形式，从而使算法的线条更加平滑。其次，在质量方程中引入了热泳输运项，从而可以在球体的不同位置计算热泳输运的影响。基本上，在这项研究中，我们找到了球体周围的一些位置，在这些位置可以同时计算速度场、温度分布、质量浓度、表面摩擦和传热速率，而无需对球体表面的流动进行任何分离。
