timevary_comsol

8/9/2019 timevary_comsol

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2007 Cornell University

BEE453, Professor Ashim Datta

Authored by Vineet Rakesh

Software: COMSOL Multiphysics 3.3

Specifying time varying Boundary Conditions

Suppose you want to model a flow where the boundary conditions are changing with time. Take the

case of diffusion of drug from a patch into the skin. The drug concentration in the patch falls down with

time and hence we need a time varying flux condition on the skin boundary where the drug is diffusing

into the skin. This is an example of time varying boundary condition applied to the species transfer

equation. The same may be true in case of the energy or the momentum equation. For example, take

the case of air intake through the nose. If a full cycle of inhalation and exhalation is considered, it can

be seen that the velocity of air flowing in varies with time. We can implement these models in

COMSOL. The following example uses heat flux as the variable for the time varying input.

Temperature, species concentration, flux (heat and species), velocity and material property values can

be defined as time varying quantities similarly. These variables will be denoted as dependant

variables in the subsequent discussion.

COMSOL provides us with 2 options to specify time varying boundary conditions.

The dependant variable can be defined as a function of time by specifying a set of data points

(dependant variable vs. time) (see Method 1 below) similar to how we specified properties

varying with temperature for the CRYOSURGERY Tutorial.

The second option in COMSOL is to specify the dependant variable as any function of time.

(see Method 2 below)


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2007 Cornell University 2

Example 1: Specifying Data Points

1) Open the Boundary Settings window:

Physics >> Boundary Settings >> Select

Heat Flux under Boundary Condition from

the drop-down menu for the Boundary you

want to specify the time varying heat flux

for.

2) In the Inward Heat Flux, q0, field, enter

heat_flux(t). heat_flux(t) tells COMSOL that

heat_flux (to be specified in Step 4 later) is

a function of time. heat_flux is any arbitrary

user defined name chosen for the function.

3) Click on OK. We will now define the

function, heat_flux(t).

4) Under Options, click on Functions

5) Click on the New button

6) Next to Function name: type in heat_flux

7) Check Interpolation. By checking this, we

are directing the solver to interpolate values

of heat flux between different times.

8) Select Table next to the Use data from box

9) Click OK

10) Enter the time and the corresponding heat

flux values in the text boxes. The first

column (under x) shows the values of time

and f(x) represents the corresponding heat

flux values. Click on Ok

4

5


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Example 2: Specifying an Exponential Function

1) Open the Boundary Settings window:

Physics >> Boundary Settings >>

Select Heat Flux under Boundary

Condition from the drop-down menu

for the Boundary you want to specify

the time varying heat flux for.

2) In the Inward Heat Flux, q0, field, enter

heat_flux. heat_flux tells COMSOL

that heat_flux (to be specified in Step

4 later) is a function of some other

variables. heat_flux is any arbitrary

user defined name chosen for thefunction.

3) Click on OK. We will now define the

function, heat_flux.

4) Under Options, click on Expressions >>

Global Expressions

5) In the Global Expressions window,

define heat_flux a s function of time. In

this example we say heat_flux =

1.4t+0.7t2. heat_flux can be defined as

a function of any independent

variables using this method.

6) Click Ok.

Note: The expression can directly be input

in theInward Heat Flux, q0.

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timevary_comsol