tlist = linspace(0, tf, nt); % time, tf is final time, nt is number of time steps
use the following function for a linear equation
u1 = parabolic(u0, tlist, file_b', p, e, t, c, a, f, d);
Note that for heat transfer for Equations (6) and (7), c corresponds to thermal conductivity, a and
f can be used to account for a heat source, and d corresponds to the density times the specific
heat capacity which can be seen by comparing to Equations (1) and (2).
References
In addition to this document there is help available online from within MATLAB. Under the
Contents tab within the help browser window there is a section titled Partial Differential
Equation Toolbox that contains many resources. In particular, there are several tutorials and a
manual available in PDF format called the Partial Differential Equation Toolbox User’s Guide.
The manual contains all the details about the GUI, functions, and the PDE toolbox’s
implementation of the finite element method.
Getting Started with SolidWorks Simulation
To get started, launch SolidWorks by double-clicking the icon on the desktop. For the following
instructions, a basic working knowledge of the steps necessary to create simple geometry in
SolidWorks is assumed. Please consult with the instructor if you are not familiar with this solids
modeling software package and need assistance.
To create a new file, from the toolbar at the top use the File pull-down menu to select New, then
Part, and then click OK. Next, from the same toolbar use the Tools pull-down menu to select
Add-Ins and insure that SolidWorks Simulation is selected as one of the Active Add-ins and then
click OK. Finally, use the same Tools pull-down menu to select Options and then under the
Document Properties tab select Units and set the Unit System to MKS and then click OK.
Geometry and Material Properties
To create the geometry, from the Features tab select Extruded Boss/Base. In the drawing
window select the Front Plane. From the Sketch tab select the Corner Rectangle button and draw
a rectangle with the lower left hand corner starting at the origin. Use the Smart Dimension button
to make the rectangle dimensions 1 m by 1 m. Use the Exit Sketch button to close the sketch, set
the depth or D1 to 0.1 m, and click the green check mark to finish creating the part. Finally,
change the part name from Boss-Extrude1 to “brick” in the Feature Manager Design Tree.
To set the material properties for your brick, in the Feature Manager Design Tree right click on
Material and select Edit Material from the pop-up menu. In the Material window right click on
Custom Materials, select New Category, and name it ME 554 Materials. Right click on your new
category and select New Material, change the name to “ceramic,” set density to 1 kg/m
3
, thermal
conductivity to 1 W/m•K, specific heat to 1 J/kg•K, and then click Save, Apply and Close.
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