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Article

Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

by
Amir Abbas
1,
Muhammad Ashraf
1,
Yu-Ming Chu
2,3,
Saqib Zia
4,
Ilyas Khan
5,* and
Kottakkaran Sooppy Nisar
6
1
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha 40100, Pakistan
2
Department of Mathematics, Huzhou University, Huzhou 313000, China
3
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China
4
Department of Mathematics, COMSATS University Islamabad, Islamabad 40100, Pakistan
5
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
6
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Molecules 2020, 25(11), 2694; https://doi.org/10.3390/molecules25112694
Submission received: 30 April 2020 / Revised: 3 June 2020 / Accepted: 4 June 2020 / Published: 10 June 2020
(This article belongs to the Special Issue Applications of Computational Fluid Dynamics)
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Abstract

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.
Keywords: thermophoretic; mixed convection; finite difference method; sphere; primitive variable formulation thermophoretic; mixed convection; finite difference method; sphere; primitive variable formulation

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MDPI and ACS Style

Abbas, A.; Ashraf, M.; Chu, Y.-M.; Zia, S.; Khan, I.; Nisar, K.S. Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere. Molecules 2020, 25, 2694. https://doi.org/10.3390/molecules25112694

AMA Style

Abbas A, Ashraf M, Chu Y-M, Zia S, Khan I, Nisar KS. Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere. Molecules. 2020; 25(11):2694. https://doi.org/10.3390/molecules25112694

Chicago/Turabian Style

Abbas, Amir, Muhammad Ashraf, Yu-Ming Chu, Saqib Zia, Ilyas Khan, and Kottakkaran Sooppy Nisar. 2020. "Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere" Molecules 25, no. 11: 2694. https://doi.org/10.3390/molecules25112694

APA Style

Abbas, A., Ashraf, M., Chu, Y.-M., Zia, S., Khan, I., & Nisar, K. S. (2020). Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere. Molecules, 25(11), 2694. https://doi.org/10.3390/molecules25112694

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