Numerical Methods for Chemical Engineering: Solving PDEs and BVPs

Chemical engineering systems—from heat exchangers to reactor designs—rely heavily on transport phenomena described by partial differential equations (PDEs) and boundary value problems (BVPs). Understanding how to translate these physical systems into solvable numerical models is a core skill for any modern engineer. This text-based course guides you from the fundamental mathematical definitions of transport equations to writing and executing clean, efficient numerical solvers. You will gain the confidence to model real-world chemical processes by converting complex physical boundaries into structured code. What you'll learn: - Understand the core mathematical theory behind elliptic, parabolic, and hyperbolic PDEs in chemical processes - Formulate boundary value problems for steady-state diffusion, heat transfer, and chemical reactions - Implement finite difference methods and built-in numerical solvers like bvp4c and pdepe in MATLAB - Apply modern coding practices such as vectorization and structured functions to optimize solver performance - Analyze numerical stability, convergence, and error limits to ensure your simulation results are robust - Practice translating physical boundary conditions (Dirichlet, Neumann, and Robin) into precise code parameters You will start with foundational definitions of transport phenomena and numerical discretization. From there, the written lessons walk you through step-by-step code implementations for classic chemical engineering scenarios, including tubular reactors and transient heat conduction. This course is designed for engineering students, researchers, and practicing chemical engineers who are new to numerical modeling. No advanced programming background is required, though a basic familiarity with algebra and calculus is helpful. Start reading today to master the numerical tools essential for chemical engineering design and analysis.