Abstract
In this paper we study the buoyancy driven flow of a particulate suspension between two inclined walls. The suspension is modeled as a non-linear fluid, where the (shear) viscosity depends on the concentration (volume fraction of particles) and the shear rate. The motion of the particles is determined by a convection-diffusion equation. The equations are made dimensionless and the boundary value problem is solved numerically. A parametric study is performed, and velocity, concentration and temperature profiles are obtained for various values of the dimensionless numbers. The numerical results indicate that due to the non-uniform shear rate, the particles tend to concentrate near the centerline; however, for a small Lewis number (Le) related to the size of the particles, a uniform concentration distribution can be achieved.
Highlights
Fluid flow can occur for various reasons such as applications of external forces, presence of pressure or temperature gradients, natural convection, etc
The numerical results show that the isotherms become elliptic and deviate from the circular pattern which is the typical pattern with isotropic thermal conductivity
We look at a more general situation by considering two parallel walls which are tilted at an angle, giving rise to the possibility that particles may 7 shows the effect particle flux due to gravity
Summary
Fluid flow can occur for various reasons such as applications of external forces, presence of pressure or temperature gradients, natural convection (buoyancy driven flow), etc. Metivier et al (2017) [6] experimentally studied the onset of the Rayleigh-Bénard convection of a concentrated suspension of microgels subject to a temperature gradient. They focused their studies on the no-slip condition and found that the main control parameters for this flow is the ratio between the yield stress and the buoyancy force. The numerical results show that the isotherms become elliptic and deviate from the circular pattern which is the typical pattern with isotropic thermal conductivity
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