Problem Specification
This example analyzes the process of cryogenic wart treatment by optimizing the temperature and the duration of liquid jet that is applied to the surface of common warts. The goal is to destroy as much of the wart as possible while damaging as little healthy skin as possible. In the following figure, the area of application with a convective boundary is shown in red and the zero flux boundaries are in aqua.
Figure 1. Schematic, where radius of wart is 0.002 m, depth of skin is 0.002 m, and width of skin is 0.008 m.
Assumptions:
The wart is represented as a semi-spherical protrusion from a flat skin surface. For simplicity, the geometry was considered in two dimensions so that the wart becomes a semicircle attached to a flat skin slab. The model assumes homogenous properties and perfectly symmetrical geometry of the wart and skin. Therefore, the model used is axis-symmetric and can be swept 360 degrees around the axis to obtain a three-dimensional representation. In addition, the skin is considered to be semi-infinite.
The skin and the wart areas were defined as separate entities and meshed independently. The skin mesh was a uniform mesh. The wart area was meshed using a paved algorithm due to its curved geometry. The skew for both the skin and wart meshes was minimal.
Conductivity and Specific Heat
Conductivity and specific heat will be modeled by the following curves:
Figure 2. Thermal conductivity and specific heat as a function of temperature
Step 1: Run the software GAMBIT to create the geometry and to mesh it
1) In the Command Prompt, type: gambit –id wart
2) Now Gambit is launched. Click on Solver menu at the top of the Gambit window and choose FIDAP.
Step 2: Create Geometry and Mesh in GAMBIT
Create the vertices outlining the geometry
The coordinates of the vertices of the rectangle are (0, 0, 0), (0.002, 0, 0), (0.004, 0, 0), (.004, 0.004, 0), (0.002, 0.004, 0), (0.002, 0.002, 0), (0.0015, 0.002, 0). The vertex (0.00175, 0.00025, 0) is the center of the quarter circle in the geometry.
1) Under the Operations panel, click on the Geometry command button
2) Under the Geometry panel, click on the Vertex command button
3) Under the Vertex panel, click on Create Vertex. Create Real Vertex Window pops up.
4) In the Create Real Vertex Window, type in the coordinates of the vertex (0, 0, 0) in the text boxes
5) Click on Apply
6) Repeat for the other vertices: ((0.002, 0, 0), (0.004, 0, 0), (.004, 0.004, 0), (0.002, 0.004, 0), (0.002, 0.002, 0), (0.0015, 0.002, 0), (0.00175, 0.00025, 0).
1) Click on Fit to Window to see the zoomed view
Your window should look like this:
Create the edges
1) Under the Geometry panel, click on the Edge command button
2) Under the Edge panel, right click and hold on the Create Edge drop-down menu and choose Straight
3) In the Graphics window, Shift-left-click on the vertices A, B, C, D, E, F, G (See Figure) (in the given order) to select these vertices.
4) In the Create Straight Egde window, click on Apply
5) In the Graphics window, Shift-left-click on the vertices B and F
6) In the Create Straight Egde window, click on Apply
7) Under the Edge panel, right click and hold on the Create Edge drop-down menu and choose Arc
8) In the Create Real Circular Arc window, click on the text field next to Center.
9) In the Graphics window, Shift- Left- Click on the vertex H to select it as the center of the arc.
10) In the Create Real Circular Arc window, click on the text field next to End- Points.
11) In the Graphics window, Shift- Left- Click on the vertices A and G to select them as the end points of the arc.
12) Click on Apply.
The edges should look like this:
http://www.cadfamily.com/html/Article/FIDAP-Cryosurgery_607_1.htm
http://www.cadfamily.com/html/Article/FIDAP-Cryosurgery_607_2.htm
http://www.cadfamily.com/html/Article/FIDAP-Cryosurgery_607_3.htm
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