Numerical Methods for Chemical Engineering: Solving PDEs

Chemical engineering systems—from heat exchangers to chemical reactors—rely heavily on transport phenomena described by partial differential equations (PDEs). Understanding how to set up, discretize, and solve these equations numerically is essential for modern engineering analysis. This text-based course guides you from foundational mathematical concepts to implementing practical numerical solvers. You will transition from theoretical equations to running clean, structured simulations of real-world chemical processes. By focusing on modern engineering workflows, you will learn to translate transport phenomena into solvable numerical models. What you'll learn: - Understand the classification of PDEs (parabolic, elliptic, and hyperbolic) and their physical meaning in transport processes - Apply finite difference methods to discretize spatial and temporal derivatives - Implement numerical algorithms in Python using modern libraries like NumPy and SciPy - Solve transient heat conduction and mass diffusion problems numerically - Analyze numerical stability and convergence criteria for explicit and implicit schemes - Set up appropriate boundary conditions for realistic chemical engineering boundaries This course begins with fundamental definitions of PDEs and numerical approximation theory before introducing discretization techniques. You will then progress through structured text explanations and code implementations, applying your knowledge to classic engineering scenarios like heat transfer and mass transport. This course is designed for undergraduate chemical engineering students, practicing engineers, and researchers who want to build a solid foundation in numerical modeling. No advanced programming or numerical analysis experience is required.