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

Amir Abbas,Yu-Ming Chu,Muhammad Ashraf,Kottakkaran Sooppy Nisar,Ilyas Khan,Saqib Zia

doi:10.3390/molecules25112694

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.

Highlights

The present work deals with the analysis of the coupled mechanism of thermophoretic transportation and mixed convection around the surface of a sphere
Simulation was performed for different values of the controlling parameters, including the Prandtl number Pr, mixed convection parameter λt, Schmidt number Sc, thermophoresis parameter Nt, thermophoretic coefficient κ, and modified mixed convection parameter λC on the velocity field U, temperature field θ, concentration distribution φ, and thermophoretic velocity Vt around different positions of the surface of the sphere
The details of the obtained numerical solutions along with parameters, including the Prandtl number Pr, mixed convection parameter λt, Schmidt number Sc, thermophoresis parameter Nt, thermophoretic coefficient κ, and modified mixed convection parameter λC on the velocity field U, temperature field θ, concentration distribution φ, and thermophoretic velocity Vt around different positions of the surface of the sphere

Summary

Introduction

The present work deals with the analysis of the coupled mechanism of thermophoretic transportation and mixed convection around the surface of a sphere. A sphere is working as a heat source with a constant surface temperature, and the exact velocity components at the solid surface of a sphere are considered to be zero and approach an ambient condition far from the surface. The sphere is a source of heat, which transmits its energy to its surroundings, where submicron particles are in motion and have low energy. These small particles receive energy from the sphere and Molecules 2020, 25, 2694; doi:10.3390/molecules25112694 www.mdpi.com/journal/molecules. The phenomenon of heat convection around the surface of a sphere takes place due to a temperature difference and thermophoretic motion

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