[1] The planform of sublithospheric convection is studied by a 3-D linear stability analysis of longitudinal rolls in the presence of vertical shear. Rayleigh numbers up to 10 are considered. The transition Rayleigh number over which longitudinal rolls are unstable is derived as a function of surface velocity. Effects of nonlinear vertical shear are shown to be insignificant unless nonlinearity...

natural convection heat transfer has many applications in different fields of industry; such as cooling industries, electronic transformer devices and ventilation equipment; due to simple process, economic advantage, low noise and renewed retrieval. recently, heat transfer of nanofluids have been considered because of higher thermal conductivity coefficient compared with those of ordinary fluid...

[1] At the temperatures and stresses associated with the onset of convection in an ice I shell of the Galilean satellites, ice behaves as a non-Newtonian fluid with a viscosity that depends on both temperature and strain rate. The convective stability of a non-Newtonian ice shell can be judged by comparing the Rayleigh number of the shell to a critical value. Previous studies suggest that the c...

We report experimental measurements of heat transport in rotating Rayleigh-Bénard convection in a cylindrical convection cell with an aspect ratio of Γ=1/2. The fluid is helium gas with a Prandtl number Pr=0.7. The range of control parameters for Rayleigh numbers 4×10^{9}<Ra<4×10^{11} and for Ekman numbers 2×10^{-7}<Ek<3×10^{-5} (corresponding to Taylor numbers 4×10^{9}<Ta<1×10^{14} and convect...

[1] We investigate the physics of multiscale convection in Earth’s mantle, characterized by the coexistence of large-scale mantle circulation associated with plate tectonics and small-scale sublithospheric convection. In this study, conditions for the existence of smallscale convection beneath oceanic lithosphere are investigated by deriving a scaling law for the onset of convection in a fluid ...

The three-dlmensional, incompressible Navler-Stokes and energy equations with the Bousslnesq assumption have been directly simulated at a Rayleigh number of 3.8 x 105 and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were applied. A spectral/finite difference numerical method was used to simulate the flow. At t...

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

Steady state natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity and thermal expansion coefficient of Al2O3–water nanofluid. This study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ Φ ≤ 7%), enclosure aspect ratios (0.5 ≤ AR ≤ 2) and temperature differences between the cold...