The advection-diffusion equation is used to compute the distribution of concentration along the length of a rectangular chemical reactor (see Sec. 32.1). ∂ c /∂ t = D ∂ 2 c /∂ x 2 – U ∂ c /∂ x – kc where c = concentration (mg/m 3 ), t = time (min), D = a diffusion coefficient (m 2

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The advection-diffusion equation is used to compute the distribution of concentration along the length of a rectangular chemical reactor (see Sec. 32.1).

c/∂t = D2c/∂x2 – U ∂c/∂xkc

where c = concentration (mg/m3), t = time (min), D = a diffusion coefficient (m2/min), x = distance along the tank’s longitudinal axis (m) where x = 0 at the tank’s inlet, U = velocity in the x direction (m/min), and k = a reaction rate (min-1) whereby the chemical decays to another form. Develop an explicit scheme to solve this equation numerically. Test it for k = 0.15, D = 100, and U = 1 for a tank of length 10 m. Use a Δx = 1 m, and a step size Δt = 0.005. Assume that the inflow concentration is 100 and that the initial concentration in the tank is zero. Perform the simulation from t = 0 to 100 and plot the final resulting concentrations versus x.

Distribution
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Related Book For

Numerical Methods For Engineers

5th Edition

Authors: Steven C. Chapra, Raymond P. Canale

ISBN: 9780071244299