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∂²c/∂x² – U ∂c/∂x – kc

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.