10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #6: Modern Methods for Solving Nonlinear Equations.1D-Problemunknown: T of reactor f(x) = 0 Qrxnexp(-Ea/RT) + h(T – Ta) + c(T4– Ta4) = 0 heat of reaction convection radiation (+) (-) (-) Gain heat Lose heat Lose heat f(T) 0 T2 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 ÆÅbFigure 1. 1D problemQ = -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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