Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 1. Analysis and bifurcations

1999 ◽  
Vol 398 ◽  
pp. 61-85 ◽  
Author(s):  
S. A. SUSLOV ◽  
S. PAOLUCCI
Keyword(s):  
Mixed Convection ◽  
Open Systems ◽  
Landau Equation ◽  
Vertical Channel ◽  
Variable Density ◽  
Special Treatment ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Weakly Nonlinear ◽  
Wide Range

The weakly nonlinear theory for modelling flows away from the bifurcation point developed by the authors in their previous work (Suslov & Paolucci 1997) is generalized for flows of variable-density fluids in open systems. It is shown that special treatment of the continuity equation is necessary to perform the analysis of such flows and to account for the potential total fluid mass variation in the domain. The stability analysis of non-Boussinesq mixed convection flow of air in a vertical channel is then performed for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. A cubic Landau equation, which governs the evolution of a disturbance amplitude, is derived and used to identify regions of subcritical and supercritical bifurcations to periodic flows. Equilibrium disturbance amplitudes are computed for regions of supercritical bifurcations.

Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 2. Mean flow characteristics

1999 ◽  
Vol 398 ◽  
pp. 87-108 ◽  
Author(s):  
S. A. SUSLOV ◽  
S. PAOLUCCI
Keyword(s):  
Mixed Convection ◽  
Mass Flux ◽  
Flow Characteristics ◽  
Vertical Channel ◽  
Physical Nature ◽  
Reynolds Numbers ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Mean Flow ◽  
Wide Range

Based on amplitude expansions developed in Part 1 (Suslov & Paolucci 1999), we examine the mean flow characteristics of non-Boussinesq mixed convection flow of air in a vertical channel in the vicinity of bifurcation points for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. The constant mass flux and constant pressure gradient formulations are shown to lead to qualitatively similar, but quantitatively different, results. The physical nature of the distinct shear and buoyancy disturbances is investigated, and detailed mean flow and energy analyses are presented. The variation of the total mass of fluid in a flow domain as disturbances develop is discussed. The average Nusselt number and mass flux are estimated for supercritical regimes for a wide range of governing parameters.

scholarly journals Bistable fully developed mixed convection flow with viscous dissipation in a vertical channel

2018 ◽  
Vol 5 (7) ◽  
pp. 171880
Author(s):  
M. Miklavčič
Keyword(s):  
Mixed Convection ◽  
Thermal Radiation ◽  
Pressure Gradient ◽  
Viscous Dissipation ◽  
Vertical Channel ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Radiation Model ◽  
Stable Solutions ◽  
Stable Flow

It is shown that unstable dual solutions in fully developed mixed convection flow in a vertical channel disappear in the presence of relatively strong thermal radiation. In this case, we have a unique stable flow at each pressure gradient. When the effect of thermal radiation is weak another branch of stable solutions is created, resulting in bistable flows. In this case, the flow exhibits hysteresis with variation of the pressure gradient. Optically, a thin radiation model is used.

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