chbe2120spring2011hw8

chbe2120spring2011hw8 - ChBE 2120 Homework 8 Due: Friday,...

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ChBE 2120 Homework 8 Due: Friday, March 18, 2011 at 8:05 am NOTE that even though the economics portion of this assignment does not require MATLAB, you must still turn in your assignment via T-Square. This means turning in the work via a scanned PDF of your handwritten work, or via a Word document. Part 1 . Adapted from Chapra & Canale problem 28.14: The following differential equation describes the steady-state concentration of a substance that reacts with first-order kinetics in an axially-dispersed plug-flow reactor: ܦ ݀ ܿ ݀ݔ െܷ ݀ܿ ݀ݔ െ݇ܿൌ0 ܿሺݔൌ0ሻൌܿ ௜௡ ݀ܿ ݀ݔ Where D = the dispersion coefficient [m 2 /hr], c = concentration [mol/L], U = velocity [m/hr], and k = the reaction rate [1/hr]. The boundary conditions can be approximated as: ሺݔൌܮሻൌ0 Where c in is the concentration in the inflow [mol/L], and L = the length of the reactor [m]. Use the following parameter values in the next tasks: D = 5000 m 2 /hr, U = 100 m/hr, k = 2 hr -1 , L = 100 m, c in = 100 mol/L. Use the shooting method to solve this boundary value problem. Include the code to perform these calculations in a script named hw8_myGtAccountId.m . Plot the concentration profile c as a function of x, save this plot as a .png file, and submit this as plugFlowPlot_myGtAccountId.png . While that prompt should be sufficient for you to solve the problem, here are some hints that will help you: - We said that the shooting method essentially reduces to a certain kind of root-finding method. We have not coded up that root-finding method yet, so you will want to put the appropriate equation(s) in a loop in your hw8 script. - We said that your shooting method BVP reduces to a series of IVPs.
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chbe2120spring2011hw8 - ChBE 2120 Homework 8 Due: Friday,...

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