Numerical simulations of solid particles dispersion during double-diffusive convection of a nanofluid in a cavity with a wavy source

This study attempts to address the dispersion of the solid particles in nanofluid flow throughout the double-diffusive convection under the impacts of buoyancy ratio, magnetic field and three different boundary conditions. The main target of this study is to examine the mixing processes between solid particles and nanofluid flow at natural convection flow. An incompressible scheme of smoothed particle hydrodynamics (ISPH) is applied to study the dispersion processes of solid particles through the nanofluid flow. The mesh-free nature of ISPH method is helpful in handling the interactions between solid and fluid particles in an easy way. The sidewalls are wavy walls, and the solid particles are embedded in an open circular cylinder positioned in the cavity center. The numerical simulations are performed for various values of buoyancy ratio -2≤N≤2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( { - 2 \le N \le 2} \right)$$\end{document}, Hartman parameter 0≤Ha≤100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {0 \le {\text{Ha}} \le 100} \right)$$\end{document}, Lewis number 0≤Le≤50\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {0 \le {\text{Le}} \le 50} \right)$$\end{document}, nanoparticles parameter 0≤ϕ≤0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {0 \le \phi \le 0.1} \right)$$\end{document}, wave amplitude 0.05≤A≤0.15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {0.05 \le A \le 0.15} \right)$$\end{document} and wave undulation number 2≤κ≤10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {2 \le \kappa \le 10} \right)$$\end{document}. Results show that the variations on the boundary conditions of heat and mass differentiate dramatically the direction of solid particles dispersion in a cavity. Buoyancy ratio is playing a main role in direction of the solid particles dispersion, and Hartman parameter reduces the solid particles dispersion.