A study about the solution of convection–diffusion–reaction equation with Danckwerts boundary conditions by analytical,method of lines and Crank–Nicholson techniques |
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Authors: | Lucía Agud Albesa Macarena Boix García M. Leonor Pla Ferrando Salvador Cayetano Cardona Navarrete |
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Affiliation: | 1. Applied Mathematics Department, Universitat Politècnica de València, Valencia, Spain;2. Chemical and Nuclear Engineering Department, Universitat Politècnica de València, Valencia, Spain |
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Abstract: | 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 Péclet and Damköhler 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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Keywords: | convection-diffusion-reaction equation Crank–Nicholson Danckwerts conditions heat equation MOL Péclet and Damköhler numbers |
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