scholarly journals Diffusion Creep and Grain Growth in Forsterite +20 vol% Enstatite Aggregates: 2. Their Common Diffusional Mechanism and Its Consequence for Weak-Temperature-Dependent Viscosity

2018 ◽  
Vol 123 (11) ◽  
pp. 9513-9527 ◽  
Author(s):  
T. Nakakoji ◽  
T. Hiraga
Keyword(s):  
Grain Growth ◽  
Diffusion Creep ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Diffusional Mechanism ◽  
Dependent Viscosity

scholarly journals Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Boundary ◽  
Galerkin Approximation ◽  
Large Data ◽  
Temperature Dependent ◽  
Weak Formulation ◽  
Temperature Dependent Viscosity ◽  
Pipeline Network ◽  
Flux Boundary Conditions ◽  
Creeping Flows ◽  
Dependent Viscosity

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

Elastic Effects on Rayleigh-Be´nard-Marangoni Convection in Liquids With Temperature-Dependent Viscosity

2009 ◽  
Author(s):  
G. N. Sekhar ◽  
G. Jayalatha
Keyword(s):  
Stress Relaxation ◽  
Variable Viscosity ◽  
Relaxation Parameter ◽  
Oscillatory Convection ◽  
Tight Coupling ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Viscoelastic Liquids ◽  
Retardation Parameter

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.

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