A study about the solution of convection-diffusion-reaction equation with Danckwerts boundary conditions by analytical, method of lines and Crank-Nicholson techniques

We compare different solutions of the convection-diffusion-reaction problem with Danckwerts boundary conditions. Analytical solution is found, and method of lines and Crank-Nicholson method are described, applied, and compared for different values of Peclet and Damkohler numbers. The eigenvalues and eigenfunctions have been obtained for all the possible values of the dimensionless parameters. And the analytical expression of the concentration has been calculated with the optimum number of terms in the Fourier expansion.

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This paper compares different solutions for the convection-diffusion-reaction problem with Danckwerts boundary conditions. The analytical solution is obtained, and the method of lines and Crank-Nicholson method are described, applied, and compared for various Peclet and Damkohler numbers. The eigenvalues, eigenfunctions, and the analytical expression of concentration are calculated for all possible dimensionless parameters.