Spatial Decay Bounds in Time Dependent Pipe Flow of an Incompressible Viscous Fluid

2004 ◽  
Vol 65 (2) ◽  
pp. 458-474 ◽  
Author(s):  
Changhao Lin ◽  
Lawrence E. Payne
Keyword(s):  
Viscous Fluid ◽  
Pipe Flow ◽  
Time Dependent ◽  
Incompressible Viscous Fluid ◽  
Spatial Decay ◽  
Decay Bounds

SPATIAL DECAY BOUNDS IN THE CHANNEL FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID

2004 ◽  
Vol 14 (06) ◽  
pp. 795-818 ◽  
Author(s):  
CHANGHAO LIN ◽  
LAWRENCE E. PAYNE
Keyword(s):  
Laminar Flow ◽  
Viscous Fluid ◽  
Channel Flow ◽  
Exponential Decay ◽  
Transient Flow ◽  
Incompressible Viscous Fluid ◽  
Spatial Decay ◽  
Decay Bounds ◽  
Channel Boundary ◽  
Entrance Velocity

In this paper, we study the transient flow of an incompressible viscous fluid in a semi-infinite channel assuming adherence at the channel boundary. We show that under appropriate restrictions on the data if the fluid is initially at rest and the channel entrance velocity and/or channel width are sufficiently small, the solution will tend exponentially to a transient laminar flow as the distance form the entry section tends to infinity. In fact explicit exponential decay bounds are obtained.

scholarly journals Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 98
Author(s):  
Xuejiao Chen ◽  
Yuanfei Li ◽  
Dandan Li
Keyword(s):  
Pipe Flow ◽  
Nonlinear Boundary ◽  
Energy Analysis ◽  
Nonlinear Boundary Conditions ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Brinkman Equations ◽  
Diffusive Convection ◽  
Decay Bounds ◽  
Double Diffusive

In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived.

SPATIAL DECAY IN THE PIPE FLOW OF A VISCOUS FLUID INTERFACING A POROUS MEDIUM

2001 ◽  
Vol 11 (09) ◽  
pp. 1547-1562 ◽  
Author(s):  
K. A. AMES ◽  
L. E. PAYNE ◽  
J. C. SONG
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Pipe Flow ◽  
Lateral Surface ◽  
Surface Boundary ◽  
Interface Conditions ◽  
Spatial Decay ◽  
Weighted Energy ◽  
Surface Boundary Conditions

This paper establishes exponential decay of weighted energy in the pipe flow of a slowly moving viscous fluid interfacing with a porous medium when homogeneous initial and lateral surface boundary conditions and appropriate interface conditions are applied. This decay requires that the net flow across the intake section of the semi-infinite pipe be zero.

scholarly journals Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

2013 ◽  
Vol 38 ◽  
pp. 61-73
Author(s):  
MA Haque
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Initial Value Problem ◽  
Shooting Method ◽  
Boundary Layer Equation ◽  
Incompressible Viscous Fluid ◽  
Initial Value ◽  
Box Scheme ◽  
Runge Kutta Method ◽  
Dimensional Boundary

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

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