Transient Behavior of a Couette Flow

kinematic viscosity

0.1

This Demonstration shows how the Couette flow in a slot develops. Initially the fluid and both walls are stationary. To start the flow the lower wall is brought to a constant velocity

u

0

=1m/s.

The momentum equation and the no-slip boundary condition are

∂u

∂t

=ν

2

∂

u

∂

2

y

, where

ν

is the kinematic viscosity, and

u(1)=0

.

The steady-state solution is the linear velocity profile given by

u(y)=1-y

.

This Demonstration plots the velocity profile at constant time intervals (from

t=0.01s

to

t=1s

) with different colors. You can vary the kinematic viscosity to see how fast this final velocity profile (shown in black) is attained. Indeed, for very small kinematic viscosities, the response is slower. This result is to be expected since the kinematic viscosity unit is

2

cm

/s

just like the diffusion coefficient and the thermal diffusivity. Kinematic viscosity is the important factor for momentum transfer.