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ABSTRACT
The natural convection of non-Newtonian power-law fluids in a rectangular cavity in the presence of wall vibrations has been investigated by the lattice Boltzmann method. The longitudinal and transverse vibrations are applied to the horizontal walls of the cavity separately, and the two vertical walls are set as high and low temperatures, respectively. The velocity fields and temperature distributions of power-law fluids are visualized with respect to the streamlines and isotherm contours. The heat transfer characteristics are interpreted in terms of averaged Nusselt number () near the surface of heated wall. The effects of power-law index n in the range of 0.5–1.2 on momentum transport and heat transfer are investigated for Rayleigh number (Ra) in the range of 103–105 and Prandtl number (Pr) of 10.
near the hot wall is increased significantly with the fluid exponent increase at high Ra, but it is smaller than that without wall vibrations. Moreover, wall vibrations show slight and even no influence on
of power-law fluids at low Ra. The maximum velocity components of shear-thinning fluids are both decreased under wall vibrations with increasing n, but it is unchanged in shear-thickening fluids. The velocity components along the central lines of the cavity are decreased significantly for power-law fluids under wall vibrations. It is concluded that wall vibrations influence the streamlines, isotherm contours, and heat transfer characteristics of power-law fluids significantly at high Ra (∼105). In addition, it has been found that the heat transfer rate is decreased as both aspect ratio and Pr increase.
Nomenclature
| c | = | discrete particle velocity |
| k | = | consistency of fluid |
| cs | = | speed of sound |
| n | = | fluid exponent |
| = | local shear rate | |
| = | averaged Nusselt number | |
| e | = | strain rate |
| Pr | = | Prandtl number |
| f | = | buoyancy force |
| R | = | gas constant |
| F | = | body force |
| Ra | = | Rayleigh number |
| f | = | density distribution function |
| T | = | temperature |
| g | = | gravity |
| t | = | time |
| G | = | pressure gradient |
| u | = | fluid velocity |
| g | = | temperature distribution function |
| V* | = | reference velocity |
| H | = | height of cavity |
| x | = | particle coordinate |
| Greek symbols | = | |
| α | = | thermal diffusion coefficient |
| ρ | = | fluid density |
| β | = | thermal expansion coefficient |
| τ | = | relaxation time |
| δ | = | expansion parameter |
| μ | = | dynamic viscosity |
| ε | = | internal energy |
| ν | = | kinematic viscosity |
| Superscripts | = | |
| eq | = | equilibrium state |
| neq | = | nonequilibrium state |
| Subscripts | = | |
| c | = | temperature index |
| s | = | speed index |
| eff | = | effective |
| ν | = | density index |
| i | = | discrete direction |
Nomenclature
| c | = | discrete particle velocity |
| k | = | consistency of fluid |
| cs | = | speed of sound |
| n | = | fluid exponent |
| = | local shear rate | |
| = | averaged Nusselt number | |
| e | = | strain rate |
| Pr | = | Prandtl number |
| f | = | buoyancy force |
| R | = | gas constant |
| F | = | body force |
| Ra | = | Rayleigh number |
| f | = | density distribution function |
| T | = | temperature |
| g | = | gravity |
| t | = | time |
| G | = | pressure gradient |
| u | = | fluid velocity |
| g | = | temperature distribution function |
| V* | = | reference velocity |
| H | = | height of cavity |
| x | = | particle coordinate |
| Greek symbols | = | |
| α | = | thermal diffusion coefficient |
| ρ | = | fluid density |
| β | = | thermal expansion coefficient |
| τ | = | relaxation time |
| δ | = | expansion parameter |
| μ | = | dynamic viscosity |
| ε | = | internal energy |
| ν | = | kinematic viscosity |
| Superscripts | = | |
| eq | = | equilibrium state |
| neq | = | nonequilibrium state |
| Subscripts | = | |
| c | = | temperature index |
| s | = | speed index |
| eff | = | effective |
| ν | = | density index |
| i | = | discrete direction |