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lec06_09182006

lec06_09182006 - 10.34 Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #6: Modern Methods for Solving Nonlinear Equations. 1D-Problem unknown: T of reactor f(x) = 0 Q rxn exp( -Ea / RT ) + h(T – T a ) + c(T 4 – T a 4 ) = 0 heat of reaction convection radiation (+) (-) (-) Gain heat Lose heat Lose heat f( T ) 0 T 2 steady state temperatures Make a plot with MATLAB *netheat.m* function qdot = netheat(T) % computes the net heating rate of a reactor % qdot = 0 at the steady state qdot = Q.*exp(-Ea/(R.*T)) + h.*(T-Ta) + c.*(T.^4-Ta.^4); Figure 2. Professor Green modified variables Q and c until the plot looked like the one above. Increased Q and decreased c. To solve for steady state zeros f( T ) = 0 a Æ Å b Figure 1. 1D problem Q = -2e-5; Ea = 5000; R = 1.987; h = 3; Ta = 300; c = 1e-8; Tvec = linspace(300,3000) qdot = netheat(Tvec) plot(Tvec,qdot) Figure 3. Have computer bracket in and find small range where plot goes from negative to positive. 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].

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