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.
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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.
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The second option in COMSOL is to specify the dependant variable as any function of time.
(see Method 2 below)
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.
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3) Click on OK. We will now define the
function, heat_flux(t).
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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
2007 Cornell University
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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 the
function.
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 the Inward Heat Flux, q0.
2007 Cornell University
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