Rayleigh-Bénard Convection of Non-Newtonian Power-Law Fluids with Temperature-Dependent Viscosity

Abstract

Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0 ≤ m ≤ 10), the flow behaviour index (0.6 ≤ n ≤ 1.4), and the Rayleigh number (0 < Ra ≤ 10 5 ), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

Numerical nonlinear analysis of subcritical Rayleigh-Bénard convection in a horizontal confined enclosure filled with non-Newtonian fluids

“…Kaddiri et al 22 studied the Rayleigh-Bénard convection of thermo-dependent power-law fluids confined in a square enclosure heated from below and cooled from the top with uniform heat fluxes. The effects of the governing parameters on the onset of convection, flow structure, and heat transfer were investigated.…”

Steady Natural Convection of Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure

“…The natural convection of a non-Newtonian fluid over enclosures such as a cylindrical enclosure or a heated plate has received more attention [7][8][9][10][11][12][13][14]. Several methodologies including analytical [7], numerical [8], and experimental [9] approaches have been employed in most of these studies, and the results indicated that the free convection features are considerably affected by the rheological properties of the fluid.…”

Simulating Complex Fluids with Smoothed Particle Hydrodynamics

“…Additionally, the thermal model can be paired with the momentum equation by introducing temperaturedependent rheological parameters, as in Kaddiri et al [2012], which alters the behavior of the convective cell as shown in Figure 4. The bottom plate is at temperature T b = 100 K and the top plate at T t = 0 K. Considering a Pearson constant m = 10, the kinematic viscosity at temperature T = T b is ν b = 20m 2 /s while at temperature T = T t is ν t ≈ 10 -3 m 2 /s.…”