On the blowup criteria and global regularity for the non-diffusive Boussinesq equations with temperature-dependent viscosity coefficient

2016 ◽  
Vol 144 ◽  
pp. 93-109 ◽  
Author(s):  
Ming He
Keyword(s):  
Global Regularity ◽  
Boussinesq Equations ◽  
Viscosity Coefficient ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Buoyancy-driven convection in cylindrical geometries

1969 ◽  
Vol 36 (2) ◽  
pp. 239-258 ◽  
Author(s):  
S. F. Liang ◽  
A. Vidal ◽  
Andreas Acrivos
Keyword(s):  
Numerical Solutions ◽  
Perturbation Expansion ◽  
Boussinesq Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cylindrical Cell ◽  
Prandtl Numbers ◽  
Buoyancy Driven Convection ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.

scholarly journals One-dimensional compressible heat-conducting gas with temperature-dependent viscosity

2016 ◽  
Vol 26 (12) ◽  
pp. 2237-2275 ◽  
Author(s):  
Tao Wang ◽  
Huijiang Zhao
Keyword(s):  
Initial Data ◽  
Vacuum Solution ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
One Dimensional ◽  
The One ◽  
Dependent Viscosity

We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.

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