Lecture
This lecture focuses on solving diffusion equations in steady state conditions, specifically in the context of concentric spheres with fixed concentration and flux. The instructor explains the process of simplifying the diffusion equation in spherical coordinates, leading to a second-order ordinary differential equation. By applying boundary conditions, the solution space is determined, and the general solution is constructed. The lecture then delves into the concept of steady state solutions and the role of diffusion coefficients in boundary conditions. Additionally, the method of separation of variables is introduced for solving time-dependent diffusion problems in finite and infinite domains, emphasizing the importance of linearity and homogeneity in the equations and boundary conditions.