====== Modeling Project: Lithium ion batteries ======


==== General information ====
. 

  * The modeling project is **optional** and to take it you must **register**. Register by sending me an email to [[dag.wessel-berg@ntnu.no | Dag]]. Either register a full (or partially full) group, or individually, and I will put you in a group. 
  * The project part of the course will count 25% of the final grade. If the project grade makes your final grade worse than the exam grade, the final exam counts 100% for your final grade. 
  * In the project you will work on a modeling problem in a group of 4-5 students over a period of 3 weeks.
  * The project description will published here in week 43. This year's topic is modelling Lithium ion batteries.  

====Tentative time line ====

^ Registration deadline:       ^ October 28.                                                                             ^
| Problems published:          | October 29.                                                                       |
| Preparations:                | (1)  **Read** carefully the information on this page.                                  |
|                              | (2)  **Read** the proposals and start thinking about the project.                      |
|                              | (3)  Arrange a meeting in the **project group** to discuss and possibly divide tasks.  |
|                                                                    ^
| Extended deadline for execution of project: | **November 23** |

====Help sessions ====

^  Help sessions                                                     |||||                                |
^ Day              ^ Date   ^ Time         ^ Room               ^ Persons                ^        
| Friday              | 05.11  | 10:15-11:00  | S6                 | Xavier, Louis, Dag             |
| Friday              | 05.11  | 14:15-16:00  | S6                 | Xavier, Louis, Dag             |
| Monday              | 08.11  | 14:15-16:00  | R8                 | Louis, Dag                     |
| Friday              | 12.11  | 10:15-11:00  | S6                 | Louis, Dag                     |
| Friday              | 12.11  | 14:15-16:00  | S6                 | Louis, Dag                     |


==== Project Groups 2021====
You will find the project groups[[http://www.math.ntnu.no/emner/TMA4195/2021h/public/Project groups.pdf | here]]. Please notify me if something is wrong. If you enter the Blackboard site for this course, you will find e-mail addresses for all students there.    



==== Project description for 2021====
[[http://www.math.ntnu.no/emner/TMA4195/2021h/public/project/project.pdf|Mathematical modeling of Lithium battery]]


 

  


==== Errata  ====
  * ** 29/10 ** : projet description is posted
  * ** 30/10 ** : fixes in terminology (positive versus negative electrode in first part) 
  * ** 2/11 ** : 
    * new question in section 1 (Chemical equilibrium and Gibbs free energy)
    * Fixed governing equation for concentration evolution in section 2 (Kinetics of chemical reactions in solutions)
    * more details and precise expressions in the questions in section 3 (Effect of the electrical state of the reaction kinetics)
    * fixed asymptotic expansion in section 7 (Modeling equations for the whole battery)
  * ** 3/11 ** : fix notation for total number of reactants and products in the general form of a chemical reaction (section 1 and 2)  
  * ** 4/11 ** : 
    * Fix in equation (7)-(8) in section 2.
    * Fixed definition of $\eta$ in question 6 in section 3 (it should be the same as given previously)
    * Added definition of current in question 6 in section 3
  * ** 8/11 ** :
    * Fixed typo in equation for $r$ at the end of section 2 (Kinetics of chemical reactions in solutions)
    * Fixed typo in the definition of $i_0$ and of the current $i$ at the end of section 3 (Effect of the electrical state of the reaction kinetics)
    * Fixed expression for the value of the resistance at the end of section 4 (charge conservation equation)
    * Clarified question in section 5 (activation phase) and added choice of $\beta = \frac12$ in question in section 
    * Added unit for mobility in section 6 (Ion transport in the electrolyte)
  * ** 22/11 ** :
    * Fixed typo in equation (15b) for the conservation equation of $PF_6^-$

==== Each group delivers====
  - A **written report** 5-10 pages long.
     * The report can be either English or Norwegian.
  

====How to work====
  * **Manage your time:** 
    * Expected total time per person: About 3x12=36 hours.
    * Try to plan, focus, and limit the work so that you get some results in the expected time without using many extra hours.
    * Imagine you work in a company and the group is given 3 weeks and 36 hours per member to finish the project (some results, report, presentation). Do your best with these constraints.
  * **Focus** - at least to begin with. You are **not** expected to work on all the questions/projects.
  * You can present **partial results**.
  * **Try and fail** is ok as long as you do not cover up.
  * You may discuss across the groups, but reports and presentations must be made independently.
  * You may use any literature you find, but you must give references to the source!
  * Do not copy from any source without understanding the material first!


====Presentations====

  * Do not use too much time during your presentation.
  * **Language:** Norwegian or English
  * ** Vote ** for best presentation: Anonymous, one vote per group, can not vote for your own group.