2007 Cornell University BEE453, Professor Ashim Datta Authored by Vineet Rakesh Software: COMSOL Multiphysics 3.3

Specifying a Parabolic Inlet Velocity Profile

Let us take the example of the flow of blood through the capillaries. Suppose we want to model a

section of a capillary with blood entering on side and flowing out on the other side (Figure 1).

Figure 1. Blood flowing through a capillary

At the inlet, the velocity profile of the blood is parabolic as shown in Figure 2.

Figure 2. Velocity profile at the inlet

As can be seen from Figure 2, the velocity is given by the following equation.

)1( 2

2

max Rruuz −= (1)

We see that the velocity is zero at both the walls (substituting r = R) and it is equal to umax at r = 0.

0=zu at r = R (2)

maxuuz = at r = 0 (3)

Let us assume that uz is 10 ms-1 and R is 0.5 m. We substitute these values in equation (1).

)5.0

1(10 2

2ruz −=

or 24010 ruz −= (4)

We can model this boundary condition in COMSOL using the following steps.

2007 Cornell University 2

Step 1: Activate the momentum equation Model Navigator >> Application Modes >> COMSOL Multiphysics >> Fluid Dynamics (Select the

convective term option by specifying the coefficient, as described earlier, if you want the solver to

solve for convection in the heat transfer or species transfer equations)

Step 2: Specify the Parabolic Inlet velocity Boundary Condition

1) Open the Boundary Settings

window: Physics >> Boundary

Settings >> Select

Inflow/Outflow Velocity under

Boundary Conditions from the

drop-down menu for the

Boundary you want to specify

the parabolic velocity profile

for.

2) Specify the parabolic velocity

expression in the appropriate

(x or y) velocity field. Here we

specify the x-velocity as a

parabolic velocity profile.

3) Click on OK.