heat1_2
TRANSCRIPT
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COMSOL 4.2 Tutorial
COMSOL Multiphysics (formerly FEMLAB) is a finite element analysis, solver
and Simulation software / FEA Software package for various physics and
engineering applications, especially coupled phenomena, or multiphysics.
COMSOL Multiphysics also offers an extensive interface to MATLAB and its
toolboxes for a large variety of programming, preprocessing and postprocessing
possibilities. The packages are cross-platform (Windows, Mac, Linux,Unix.) In
addition to conventional physics-based user-interfaces, COMSOL Multiphysics
also allows for entering coupled systems of partial differential equations (PDEs).
How to create a new model in COMSOL
1. Start COMSOL Multiphysics
2. Work through the COMSOL Model Wizard which will require you to select the
coordinate system for the model, the relevant physics to the problem, and the type
of study you wish to perform (Time dependant or stationary).
3. Define the parameters, equations and variables pertinent to the model (sub
directory (Global Definitions).
4. Define the geometry of the model (Geometry).
5. Select the materials you wish to use in your model (Materials).
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6. Select the boundary, bulk and initial conditions for your system for each physics
you are using (This will be entered separately for each different physics you are
using e.g. you will need to enter these for Laminar Flow and again for Heat
Transfer if you are using both ).
7. Choose the element size to be used (Mesh).
8. Adjust solver parameters and compute (Study).
10. Display the desired results in the most meaningful way (Results).
Not all of these steps are always necessary when building a model. The order is
also variable depending on the complexity of the model.
Example 1. (Heat transfer) Consider a cylindrical heating rod which is sheathed by a concentric tube of
thickness 0.05 m and which starts 0.05 m away from the center. The entire
assembly is immersed in a fluid and the system is at steady-state, as shown below.
We wish to determine the temperature distribution within the sheath. After
thinking about the problem, assume that we arrived at the following
approximations (make sure you understand how we arrived at following
approximations for your future quiz and test): The temperature of the heater is
constant at 400K. The temperature at R1 is the same as the temperature of the
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heater, 400K. The fluid temperature is constant at 300K and this is the temperature
of the surrounding sheath at R2.
Given that heat diffusion should be the same at any given it is reasonable to
define this problem in 2D as follows.
Solution using COMSOL:
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Startup
1. Start COMSOL by clicking the COMSOL Multiphysics 4.2 icon.
2. When COMSOL starts, the Model
Wizard will be open automatically.
This wizard asks you to define the
spatial dimension youll be using for
the model as well as the applicable
physics and the type of study you wish
to perform (either time dependant or stationary). For this problem start by selecting
2D, continue by clicking the
blue, right pointing arrow at the
top right of the Model Wizard
screen.
3. Next select the applicable
physics for the model. In this
case heat transfer in solids will
be selected. This can be found
under the Heat Transfer module.
Click the triangle to the left of
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the Heat Transfer module to see the drop down menu which contains Heat Transfer
in Solids, left click this so that it is highlighted then click the blue, right pointing
arrow at the top right of the Model Wizard menu screen. Multiple physics can be
added to a single model by left clicking the physics to add and then left clicking
the blue + sign at the bottom left of the Model Wizard menu screen.
4. The final step in the Model
Wizard is to select the type of
study you would like to
perform on our model. In our
case stationary will be
sufficient to find the steady
state solution to this problem.
As with the physics add the
stationary study by left clicking
on Stationary below the
preset studies icon. Click the
finish flag at the top right of the
Model Wizard to finish startup.
Model Builder and Saving
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Now that we are finished with the Model Wizard we will turn our attention to the
Model Builder portion of the program. This
is just to the left of where the Model
Wizard had been. Before we continue with
the Model Builder let us take a second to
save our model. This is done by clicking
File at the top left of the screen and then
selecting Save As as is the case with most programs. This file will be named
Heat Transfer Example. By default COMSOL will save all COMSOL files in a
folder it creates called COMSOL42 however this folder name will change with the
version of COMSOL being used. After giving our file a name and clicking the save
button seen in the above image notice that the first icon within the model builder
now has the name of our file. From
this point on we can essentially just work our way down the Model Builders list of
options filling in values and conditions where we need them.
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Geometry
Now we are ready to add the geometry of
the model. This is very simple because our
assumptions have placed the problem into
only 2 dimensions. Our geometry consists
of only of a rectangle.
1. To create this rectangle first find the
geometry icon in the model builder menus
and right click it, this will bring up the
menu shown at right.
2. Find the Rectangle button in this new
menu and left click this.
3. At this point the rectangle has been added, however the dimensions of this
rectangle need to be changed to fit the dimensions in the problem. We do this by
left clicking the white rectangle just to the left of the geometry icon. This will
expand the geometry tab to show all the sub tabs contained within geometry. If you
added the rectangle correctly you will see the tab called Rectangle 1. This contains
all the information regarding this object and to adjust the dimensions and position
of this rectangle this is where we do so. Left click the tab labeled Rectangle 1.
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4. If you have completed the above steps successfully your screen should resemble
the one above. Notice that by default the corner of the rectangle has been placed at
the origin (position x= 0, y =0) and given width and height of 1m. For this problem
the height needs to be 5 cm (0.05 m) and the width needs to be 30 cm (0.3 m).
Enter these values into the designated fields and press the blue building icon at the
top right of the rectangle menus. This is the Build All button and will add your
rectangle to the model.
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5. To get the graphical interface of COMSOL to center on the rectangle and adjust
the axis bounds click the Zoom Extents button
Materials
To give the rectangle thermal properties such as heat capacity and thermal
conductivity we can either add these directly under the Heat Transfer tab or by
selecting a material to build the rectangle from. In this problem we will make our
rectangle out of copper and we will do this using the Materials tab.
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1. Left click on Materials tab and then left click Materials Browser. Your
screen should look like the screen below.
2. As can be seen above the Material Browser has a search bar that allows you to
enter the name of the material in question and COMSOL will find any matches
within its database. Enter copper into the search bar and click search.
3. Open the Built-In tab and then right click Copper. Your screen should now
look like the one below. Left click Add Material to Model. You have now added
copper to all domains by default which means the rectangle now has the properties
of solid copper.
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Heat Transfer
It is under the Heat Transfer tab that the boundary, bulk and initial conditions for
the equations of heat conduction can be input. In our case we only have boundary
conditions. Initial conditions are used in conjunction with time dependant studies
and bulk conditions apply to the entire domain, not just a boundary. In our case we
have on boundary in contact with the heated rod which is at 400k and all other
boundaries in contact with the thermostat bathe at 300k.
1. To input these boundary conditions first open the Heat Transfer tab by left
clicking the white triangle to the left of the Heat Transfer icon. Your screen should
look like this.
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2. Right click the Heat Transfer icon to open a menu containing the various types
of bulk and boundary conditions. Go through this menu and select Temperature
by left clicking. A new icon will now appear under initial values that says
Temperature this is where we will input one of our two temperature conditions.
3. Add another temperature boundary condition by repeating step 2.
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4. After adding the two temperature boundary
conditions your
screen should
look like the image to the right. We now
need to specify a value and a location for
our temperature boundary conditions. Lets
start with the warm surface. Start by left
clicking Temperature 1. The interface
region of COMSOL should now look like
the image at left. We need to do 2 things
here. The first is to add the surface to which
we wish to apply this boundary condition and the second is to give a value to this
temperature. We will choose the bottom of our rectangle as the location for our
boundary condition. In the graphical interface left click this boundary (which
should then turn red as seen below and click the button to add. Now set the
temperature to 400 k by typing 400 into the To field.
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If done properly your screen should look like this.
5. We now need to apply the cooler boundary condition. Do this by clicking
Temperature 2 to open the interface and select the top and side boundaries to
apply the boundary condition. Then enter 300 into the To field. Your screen should
look the one below. This concludes our activities within the Heat Transfer tab we
can now proceed to calculate the solution.
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Study
To calculate the solution to our PDE we simply right click on the Study tab and
click the green equals sign .
After solving the PDE the
temperature profile will be
displayed as shown below.
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Results
To display the temperature at a given point left click the point you wish to probe
and the result will be displayed under the results tab as shown below.
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To make a graph showing the temperature profile along a line we will need to add
a cut line to our solution and display the temperature along it. This may be done
as follows.
1. Right click data sets under the results
tab and select 2D cut line from the
menu which will pop up.
2. The two points defining the cut line
need to be selected. In this case we will
have our cut line start at point (0.15,0) and end at point (0.15,0.05). To do this
enter these coordinates into
the cut line 2D screen
that will come up after left
clicking on the Cut line
2D icon under the data
sets tab. Your screen should
look like the one at left.
3. Press the paint brush button in the top right of the Cut line 2D screen to
have the cut line displayed. Your cut line should look like the one below.
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4. We now need to add a 1D plot group to the results. As you may be beginning
to realize COMSOL uses a right click
interface for addition of most options. So
right click Results and left click the 1D
plot group.
5. We want to add a line graph to our 1D plot group, so to do this right click on
1D Plot Group and choose
Line Graph from the menu.
This will add a line graph under the 1D plot group
6. Finally left click on Line graph and for data select Cut Line 2D, this will
take the temperature everywhere
along the cut line we created. To
create the graph left click the paint
brush button . You should
obtain the following result.
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As can be seen the temperature decreases linearly from the heated surface to the
cooled surface.
Adjusting The Problem
At this point it is a simple matter to go back and change some of our boundary or
bulk conditions. We will do so now.
We will start by changing the lateral surfaces to perfect insulators. We do this as
follows:
1. Go back to Heat Transfer and left click the arrow just to the right of this icon
to open all of the options.
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2. Go to the boundary condition Temperature 2 and de-select the lateral surfaces
so that now only the upper surface is at constant 300 k. You de-select a sub-
domain by left clicking it and then pressing the minus button . If done correctly
your constant temperature condition should look like the one below. By default
now the lateral surfaces will be insulated.
3. Right click on Study and press compute. The below result should appear.
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Notice how only the region of the rectangle close to the lateral surfaces has
changed from before. If you check the temperature profile along the cut line you
shouldnt see much of a change because this cut line was exactly in the middle of
our rectangle where the side effects were minimal.
We will now add a heat generation term. This is a bulk condition and can be added
in a similar way as the temperature boundary conditions.
1. Go back up to Heat Transfer and right click to open the list of possible
boundary and bulk conditions. Left click on
Heat Source, this will add a Heat Source
1 icon within Heat Transfer menu. Left
click this to open the interface.
2. We need to add the domain over which this condition applies, and as a bulk
condition it will apply over the entire geometry. So left click the rectangle and then
left click the plus sign as done previously.
3. Now a value for a per volume heat generation term needs to be added. We will
use 100,000,000 W/m3 as shown below.
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4. Again after changing any boundary or bulk condition(s) a new solution must be
found so right click on Study and press compute. The below result should be
obtained.
It is elucidating to examine the temperature profile for this solution so click on your previously made line graph displaying the temperature across the cut line. This should look like the one below.
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Note how this differs from the solution without heat generation, the maximum temperature is no longer at the heated surface, but instead near the center of the rectangle because of the large amount of heat being produced throughout the entire volume.
Example 1.1 (2D Axisymmetric Heat Transfer) We will now solve the same problem as in example 1, but this time without the reduction of the problem into rectangular coordinates. To avoid redundancy only the steps that are significantly different from those in example 1 will be explained in detail.
Startup
1. You will need to start a new model either be restarting COMSOL or by clicking New in the File menu.
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2. You will now select 2D Axisymmtric instead of simply 2D. This will take whatever geometry you create and rotate it about an axis and is ideal for problems with symmetry about an axis.
3. You will select Heat Transfer as your physics and Stationary as your study as before.
Geometry
We will now create our geometry, this is the where the biggest differences exist between this model and the previous one.
1. Right click geometry and add a rectangle.
2. Have the corner placed at z=0m and r=0.05m. Notice that our geometry will be spun around the line r=0.
3. Click Build All and obtain the following result.
Materials
Select Copper as the material and apply this to the geometry as before.
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Heat Transfer
We will use the same boundary conditions as before. Namely that
@ r=R1 T=400k
@ r=R2 T=300k
@ z=0 T=300k and @ z= 0.3m T=300k
This means that as before we will need to add two different temperature conditions. This is done by right clicking on heat transfer and clicking temperature. Enter the appropriate temperatures in the temperature field and select the appropriate surfaces to apply these boundaries (same as before). Study
Now that the model has been built we are ready to examine the solution. Right click Study and left click compute. The below result should be obtained.
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This is a pretty image but does not tell us much about the actual solution. To get a better understanding of the temperature profile we will add a Cut Line as before.
1. Right click on Data Sets under the Results tab. Click Cut Line 2D
2. Set the two points for the cut line as (r=0.05m,z=0.15m) and (r=0.10,z=0.15m) 3. Right click on Results and add a 1D plot group.
4. Right click on 1D plot group and add a line graph.
5. In the line graph interface select Cut line 2D as the data source and click the paintbrush icon to have the graph generated. The below result should be obtained.
Compare this solution to the solution from example 1.