Specifying time varying Boundary Conditions

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. ¾

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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