Heat trnasfer

Short Introduction to Comsol Multiphysics
Michael Hanke June 1, 2006
Comsol Multiphysics is an integrated environment for solving systems of timedependent or stationary second order in space partial differential equations in one, two, and three dimensions. Moreover, such equations may be coupled in an almost arbitrary way. Comsol Multiphysics provides sophisticated (and convenient) tools forgeometric modeling. Therefore, for many standard problems, there exist predefined so-called application modes which act like templates in order to hide much of the complex details of modeling by equations. The application modes make use of the language used in the respective engineering discipline. For our purposes, it is sufficient to work with the core equation model because we do not need to usethe advanced features of Comsol Multiphysics. There are two forms of the partial differential equations available, the coefficient form and the general form. They read ∂u + ∇ · (−c∇u − αu + γ) + β · ∇u + au = f da ∂t and ∂u da + ∇ · Γ = F, ∂t respectively. We will stick to the coefficient form. It can only be used for mildly nonlinear problems. For most nonlinear problems, the general form needs to beused. The coefficients of the coefficient form may depend both on x, t, and u. Observe that a dependence on u is not recommended. Example. As a running example take the one-dimensional heat equation ∂ ∂ ∂u − ( u) = Q. ∂t ∂x ∂x Here we have da = 1, c = 1, f = Q, and all other coefficients are vanishing.

Starting Comsol Multiphysics
Comsol Multiphysics is available at NADA on all supportedplatforms. Under Solaris or Linux, issue the command 1

> module add comsol in order to get access to the system. If you are using Comsol Multiphysics in other installations, please follow the instructions coming with the installation CD. In order to invoke Comsol Multiphysics, go to a directory of your choice and run the command: > comsol & You will be confronted with the Model Navigator. Here youcan select the space dimension of the problem (1, 2, or 3), the application mode, the name of the dependent variable(s) (this may be more than one if you have a system of equations), and the type of the finite element to be used. I recommend that you do not change the name of the application mode. The Multiphysics button leads to the more advanced features of Comsol Multiphysics.1 If you want to loadyour own model, press OK without selecting a new application mode. Example. Let us continue with our heat equation. We set the space dimension to 1D. Even if there is a predefined application mode for the heat equation, we will use the coefficient form for demonstration purposes. So select Comsol Multiphysics --> PDE Modes --> PDE, Coefficient Form --> Time-Dependent Analysis On the right-hand sideof the window, the form of the equation will be displayed. Do not touch all other parameters. The name of the unknown function will be u while the independent variables are x and t.

Define your problem
After you have accepted your choice in the Model Navigator, the main window of Comsol Multiphysics will appear. Its main contents is the a graphics window displaying the domain underconstruction (of course, it is empty in the beginning). The menu contains the main steps to be taken in obtaining a solution. Below the main menu, there is a button line providing shortcuts to the most important submenu items. If you stop with the mouse over a button, a bubble help will appear. As a rule of thumb, you have to traverse the main menu (or the button line) from left to right. In the File menu,you can save your project at any time, and reload it if you want to continue.
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Indeed, multiphysics is one of the main strengths of Comsol Multiphysics!

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Options
In the Options menu, you can define some global settings. The most important points are probably • Axes/Grid Setting: Here you can define the area to be displayed in the graphics window. • Constants: Very often, a problem...