**Krishan Kumar Bhatia **

Finite-element-software Comsol Multiphysics 3.3 allows simulating a wide variety of physical phenomena. In fact, the program can model just about anything that can be described mathematically. It includes equations for some of the most common problems such as stress analysis, fluid transport, heat transfer, and mass diffusion. Users can also type in the governing partial differential equations (PDEs) for problems that describe phenomena not already included in the software.

What really sets 3.3 apart, however, is that it allows coupling various equations together to solve multiphysics problems. A simple example comes from a problem involving thermal-induced stresses in a machine part. A more complex example is a hydrogen-fuel cell, which involves simultaneous mass transport by way of diffusion, fluid flow, and electrochemical reactions.

Users can quickly modify governing PDEs to suit their needs. For example, after learning how to do a simple conduction heat-transfer analysis, a user can, in a matter of minutes, modify the equations to account for spatial and time-varying thermal conductivity throughout the part. All it takes is simply specifying a mathematical function to describe the parameter's variation. Many FE programs do not have this feature. Comsol is flexible enough to model just about everything from the deformation of nonlinear material to species distribution and concentration in a stirred reactor vessel.The program's graphical environment lets users model 2D or 3D geometry, mesh it, apply boundary conditions, and solve the problem. It's also possible to build CAD models of complex geometries, but this can be frustrating for users familiar with modern parametric solid-modeling CAD software. A better method is to import complex files. Comsol imports CAD files in a variety of common formats. An option is a separate CAD-import module that provides a link with SolidWorks.

In addition, nearly a dozen other optional modules are available for disciplines including acoustics, heat transfer, and chemical engineering. They make 3.3 more flexible yet for solving complex problems. For example, to perform an analysis involving fluid-flow-induced stresses and deformation in a machine part (fluid-structural interaction), users could program the coupling in the base Comsol module. However, that might take several hours. The Structural Mechanics Module saves users time because it already includes the necessary multiphysics coupling.

On the downside, the modules cost extra. At least one additional module is probably necessary for most users performing multiphysics coupling in a particular area. Nevertheless, the optional modules work seamlessly with the base module and cut time off projects.

The software is fairly intuitive and easy to learn. Individuals needing hands-on training might attend the free workshops offered regularly or the annual Users Conference held at various global locations. Tutorials, models from other users, and examples for typical problems are available online. They help quickly bring users unfamiliar with the software up to speed. Comsol documentation is also helpful as is the excellent customer support. The developer has a knowledgeable staff willing to help with a wide variety of modeling problems.

Another prepackaged FE program might be a better choice for users doing only, say, linear-stress analysis on machine parts. However, 3.3 makes an excellent choice for users dealing with a wide variety of problems or ones involving multiple physical interactions.

The software comes from **Comsol Inc., **1 New England Executive Park, Suite 350, Burlington, MA 01803, (781) 273-3322, *comsol.com*.

*Krishan Kumar Bhatia is an Assistant Professor of Mechanical Engineering at Rowan Univ., 201 Mullica Hill Rd., Glassboro, NJ 08028, (856) 256-5346, bhatia@rowan.edu.*