chbe2120fall2010hw6

chbe2120fall2010hw6 - ChBE 2120 Fall 2010, Homework 6 Due:...

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ChBE 2120 Fall 2010, Homework 6 Due: October 11, 2010, by 8:05 am We will consider two CSTR problems. The first problem deals with a unimolecular reaction A Æ B, while the second deals with a bimolecular reaction 2A + B Æ C. Part 1 We will derive the steady-state mass and energy balances for this CSTR in class. For the unimolecular reaction, they are: 0 = FC A0 – FC A – k 0 *exp(-E a /RT)*V*C A ( 1 ) 0 = -FC B + k 0 *exp(-E a /RT)*V*C A ( 2 ) 0 = F ρ c p (T 0 -T) - Δ H rxn *k 0 *exp(-E a /RT)*V*C A (3) As we pointed out in class, equation (2) can express C B in terms of C A and T, so we will ignore it for now (it is not a free variable). In this case, however, we can also rearrange equation (1) to express C A in terms of T, as follows: V RT E k F FC C a A A ⎛ − + = exp 0 0 Assume: C A0 = 1 mol/m 3 Initial concentration F = 0.1 m 3 /s Flow in V = 1 m 3 Reactor volume E a = 50,000 J/mol Activation energy for reaction Δ H rxn = -5420000 J/mol Heat of reaction R = 8.314 J/(K mol) Universal gas constant k 0 = 1 s -1 Prefactor for reaction ρ = 1000 kg/m3 Density (water) c p = 4184 J/(kg K) Heat capacity (water) T 0 = 298 K Inlet temperature The unknowns are temperature T and concentration C A . Plug your new equation for C A , derived from equation (1), into equation (3) to get an equation in T only. Do the following steps: (1) Define the function f(x) = 0 for this problem. Write a function called hw6CstrFo_myGtAccountId.m that takes a value of the unknown and returns the value of the function f . (2) You will be implementing and performing the secant method in order to solve this problem. To do so, you will need to identify two T values that are reasonable initial guesses for the solution. You should plot your function and choose two reasonably close values that look like they may converge to the right solution. You do not need to turn in your plot or code to make the plot for this step.
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(3) Write a Matlab function called secant_myGtAccountId.m that performs the secant method for this problem. The code should run until the distance between your previous guess and your current guess is less than ε tol = 10 -5 . Make sure to comment your code and include your name in a comment line. This function should take as input a function handle, and to initial guesses, representing your x
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chbe2120fall2010hw6 - ChBE 2120 Fall 2010, Homework 6 Due:...

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