Eulerian–Lagrangian analysis of solid particle distribution in an internally heated and cooled air-filled cavity

• The Eulerian–Lagrangian method was used to study free convection in a cavity.
• Particle deposition and distribution for this problem is investigated.
• Effects of different forces are investigated using a sensitivity analysis approach.
• Thermophoretic force can significantly affect the distribution of particles with dp = 1 μm.
• It is also found that at low Rayleigh numbers the particle distribution is strongly non-uniform.

A parametric study has been conducted to investigate particle deposition on solid surfaces during free convection flow in an internally heated and cooled square cavity filled with air. The cavity walls are insulated while several pairs of heaters and coolers (HACs) inside the cavity lead to free convection flow. The HACs are assumed to be isothermal heat source and sinks with temperatures Th and Tc (Th > Tc). The problem is numerically investigated using the Eulerian–Lagrangian method. Two-dimensional Navier–Stokes and energy equations are solved using finite volume discretization method. Applying the Lagrangian approach, 5000 particles, distributed randomly in the enclosure, were tracked for 150 s. Effects of drag, lift, gravity, buoyancy, pressure gradient, shear stress terms, thermophoresis and Brownian forces on particles movements are considered. Furthermore, effects of various design parameters on the heat transfer rate and deposition of particles such as Rayleigh number (104⩽Ra⩽107104⩽Ra⩽107) as well as orientation and number of the HACs are investigated. Our simulations indicate that thermophoretic force can significantly affect the distribution of particles of dp=1dp=1 μm diameter. It is also found that at low Rayleigh numbers the particle distribution is strongly non-uniform. Moreover, it was observed that by increasing number of the HACs and changing orientation of the HACs from vertical to horizontal, deposition rate of the solid particles increases significantly.