# The advection-diffusion equation is used to compute the distribution of concentration along the length of a rectangular

## Question:

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}/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 Δ*x* = 1 m, and a step size Δ*t* = 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*.

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**Related Book For**

## Numerical Methods For Engineers

**ISBN:** 9780071244299

5th Edition

**Authors:** Steven C. Chapra, Raymond P. Canale