Abstract
This work examines the diffusion equation in curvilinear coordinates by using the method of characteristics. The method is commonly applied to solve first order partial differential equations. Applying the method to the diffusion equation, the main difficulty is when the general case is considered i.e., produces variable coefficients. The method utilizes the separation of order in order to solve the problem. The resulted ODEs in the main equation and characteristic variables are performed by the implementation of the general Riccati equation. The procedure is then repeated sequentially to reach the final solutions for concentration distributions.
Original language | English |
---|---|
Title of host publication | Lithium-Ion Batteries |
Subtitle of host publication | Properties, Advantages and Limitations |
Publisher | Nova Science Publishers, Inc. |
Pages | 127-146 |
Number of pages | 20 |
ISBN (Electronic) | 9781536168464 |
ISBN (Print) | 9781536168457 |
Publication status | Published - 1 Jan 2020 |
Keywords
- Analytical solutions
- Curvilinear coordinates
- Diffusion equation
- Method of characteristics
- Reduction of PDEs