When you are done you should see Dirichlet boundary conditions colored red and Neumann and
mixed boundary conditions colored blue. For this laboratory, make the bottom and side borders a
fixed temperature of 0 ˚C and the top border a fixed temperature of 100 ˚C.
When you have completed the geometry and boundary conditions export them to the MATLAB
environment by going to the Boundary menu item and selecting Export Decomposed Geometry,
Bound. Cond’s. Accept the default variables for export which are g for the decomposed geometry
matrix and b for the boundary condition matrix. If you now switch over to the MATLAB
environment you will find g and b in your workspace as matrices. To get more information for
each of these matrices refer to the online help for the function decsg for g and function assemb
for b. Unfortunately, the exporting process is one command that MATLAB does not save to a
script file, so you will have to do this manually every time you run a problem from the GUI.
PDE specification
To define the governing equation, go to PDE on the menu bar and select PDE mode. Then
double-click on the domain for which you wish to specify the PDE. If there are multiple domains
with different properties you can select each one separately. For heat transfer, an elliptic equation
describes steady state conduction while a parabolic equation describes transient conduction. For
a steady state problem, specify the thermal conductivity of the medium (referred to in the PDE
Specification window as Coeff. of heat conduction). Q represents internal heat generation per
unit volume. h and T
ext
represent convection heat transfer on the faces of the domain parallel to
the display. They are set to 0 for insulated faces or for a domain that is long in the z-direction.
For a transient problem the density,
ρ
, and the specific heat, C, must also be specified. For this
laboratory, specify an elliptic equation, k = 1 W/m•K, Q = 0, h = 0, and T
ext
= 0 ˚C.
Mesh
The next step is to define the mesh that divides the geometry into discrete elements. The PDE
toolbox does this automatically for you. Go to the Mesh menu item and select Initialize Mesh.
This creates an unstructured mesh with triangular elements. You can further refine the mesh by
going to the Mesh menu item and selecting Refine Mesh. The mesh should be refined to the point
that a regular array of mesh elements covers the irregularities in the geometry (with “good
resolution") but not to the point that there are so many elements that you get marginally better
answers for increased solution time (“point of diminishing returns”). You can also jiggle the
mesh to knock the triangular elements into better arrangement by going to the Mesh menu item
and selecting Jiggle Mesh. You can start over by selecting Initialize Mesh from the Mesh menu
item at any time. To control the mesh size more select Parameters from the Mesh menu item and
set the maximum edge size to 0.05 m and select OK. Now select Initialize Mesh from the Mesh
menu item and observe the changes. Note that you can also use the mesh growth rate in the Mesh
Parameters window to control the Refine mesh step away from small features in the geometry.
When you have completed the mesh, export the mesh to the MATLAB environment by going to
the Mesh menu item and selecting Export Mesh, so that you can post-process your results.
Accept the default variables for export which are p, e, and t. If you now switch over to the
(292 páginas)
Manymanuals.com
Manymanuals.de
Manymanuals.fr
Manymanuals.it
Manymanuals.pl
Manymanuals.cz
Manymanuals.es
Manymanuals-pt.com
Comentários a estes Manuais