Effect of Thermophoresis and Brownian Motion on Natural Convection of Yield Stress Nanofluids

Document Type : Original Research Paper


1 Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

2 Arts et Métiers ParisTech, 2 Boulevard du Ronceray, BP 93525, F-49035 Angers cedex 01, France.


This paper analyzes the effects of yield stress and nanoparticles transport on the natural convection of viscoplastic Casson nanofluids. The non-linear coupled partial differential equations are solved numerically using Buongiorno’s mathematical model. The governing parameters for the problem are the Rayleigh number (Ra), yield number (Y), and thermophoresis and Brownianmotion parameters (N t&Nb). The effects of these parameters on the fluid flow, heat and mass transfer, and the shape of yielded and unyielded regions are examined and discussed in detail. The results demonstrate that the heat and mass transfer rates increase as the Rayleigh number increases, while the opposite behaviors are observed with increasing the yield number. The fluid is difficultly yielded at low Rayleigh number. The heat and mass transfer are primarily due to conduction at the high values of the yield number. The main effect of thermophoresis and Brownian motion parameters is on temperature and concentration distribution in the cavity. These parameters also show significant impacts on critical heat and mass transfer.


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