{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lec36_12152006 - 10.34 Numerical Methods Applied to...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #36: TA-Led Final Review. BVP: Finite Differences or Method of Lines x C = Forward/Upwind/Central difference formulas 2 2 x C = Central difference-like Understand when to use the different formulas. Boundary Condition (Flux) D boundary x C =Reaction per surface area [moles/m 2 ·s] [m 2 /s] Internal Flux [(mol/m 3 )/m] A B The flux is the same for these two arrows can solve even if A and B are not known Partition function coefficient Figure 1. The flux is the same for arrows at A and B. Method of Lines Solve a differential equation along line i = 2, …, N-1 x C C x C 2 1 3 2 = Sparse Discretize y 1 2 3 x Boundary Condition may need to use shooting method Initial Condition gradient stiff in y-directon Figure 2. Example problem good for method of lines. If this is the B.C.: x C C x C Δ = 1 2 1 Use this additional equation with rest to solve for C 1 D.A.E. Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Models vs. Data y = f(x , θ ) y 1 = f(x 1 , θ ) y 2 = f(x 2 , θ ) | y n = f(x n , θ ) Assumption: 1) y distributed normally around y ˆ 2) x are known exactly P(y) σ y ˆ y 10.34, Numerical Methods Applied to Chemical Engineering Lecture 36 Prof. William Green Page 2 of 6 Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern