1. Multiphysics Modeling in F EMLAB 2.2 Fall 2001 COMSOL

2. Contents Introduction Modeling in F EMLAB –A first simple model of direct current conduction Influence of wave guide geometry on wave propagation –3D Electromagnetics Reaction distribution in a monolithic reactor –Chemical engineering and transport phenomena Study of the stresses in a guyed mast –Preview of the upcoming structural mechanics module Support and courses

3. Why modeling ? Education –Accelerates understanding Saves time and money –Rapid prototyping Safety –Spares equipment Fun?

4. Our company Founded in 1986 by two Ph.D. Students at the Royal Institute of Technology Developed several products within the Matlab family 95 employees in offices in Sweden, Finland, Norway, Denmark, USA, Germany, UK and France We want to provide user- friendly and powerful software for modeling in education, research, design, and development

5. Our first F EMLAB model Shows the main steps of the modeling process in F EMLAB Highlights –Single physics –2D and 3D drawing tools –Several subdomains with different properties –Post processing including boundary integration –M-file features

6. Problem definition V = 1 V = 0  V     Outflow 2 Outflow 1 How is the current distributed between outflows 1 and 2 ?

7. Results Integrate current density Integrate current density

8. Summary of the modeling process Draw Mode Boundary Mode Subdomain Mode Mesh Mode Post Mode

9. Study of waveguide geometry in 3D How does the geometry influence the reflection of the wave? How is the mode of the traveling wave changed in the waveguide ? Exemplifies the use of F EMLAB in prototyping Shows the new 3D Electromagnetics Module

10. Problem definition Incoming wave Transmitted wave  x (  xE ) - k 2 E = 0 nx(  xE) + ikE t = 2 ikE inc Is there a change in mode ? What is the dependency between the frequency and the reflection coefficient?

11. Results InOut propagating wavestanding wave A frequency of 8.1 GHz gives minimal reflection, 7 % The incoming TE11-mode is transformed to a TE10-wave

12. Results: S-parameters Frequency (Hz) minimal reflection |S 21 | 2

13. Results: S-parameters The S-parameter S 21 (for open-ends) is: This can be computed as boundary integrals in the FEMLAB GUI

14. Reaction distribution in a monolithic reactor To which extent is the catalyst utilized ? How will the catalyst degrade due to temperature effects ? Exemplifies the use of F EMLAB in chemical reaction engineering design Shows the new version of the chemical engineering module

15. Problem definition  (- D  c + cv ) = 0  (- D  c ) + kc = 0 Inlet Outlet Porous catlyst Free fluid

16. Results Substantial depletion within the catalyst at a given z-position Utilization of the catalyst is not optimal Depletion along the z-axis gives a fairly good reactor performance

17. Socket for a guyed mast Minimize transport and material costs Minimize weight and maximize mechanical strength Study the distribution of stresses in a suggested design Decide if we should pursue the work based upon the suggested design, which implies a displacement below 0.1 mm at the thinnest part

18. Socket in a guyed mast Guyed mast for telecom

19. Problem definition z no displacement in z-direction P symmetry ¼ is modeled due to symmetry  2u2u t2t2  c  u = K Navier’s equations

20. Results Von Misses stresses and displacement Maximum stress and displacement max stress

21. Support & courses Experienced engineering staff Searchable FAQ database Extensive technical: support@femlab.com Download minicourse, apply for on-site minicourse or attend to our courses Developer Zone

22. Next step Download white papers, articles product sheets etc. Try F EMLAB yourself at hands-on seminars or trials Apply for on-site seminars and hands-on seminars Run tutorials and models at www.femlab.com