New Descriptions of Dispersion in Flow Through Tubes: Convolution and Collocation Methods.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The convective dispersion of a solute in steady flow through a tube is analyzed, and the concentration profile for any Peclet number is obtained as a convolution of the profile for infinite Paclet number. Close approximations are obtained for the concentration profile and its axial moments, by use of orthogonal collocation in the radial direction. The moments thus obtained converge rapidly, and the concentration profile less rapidly, toward exactness as the number of collocation points is increased. A two-point radial grid gives results of practical accuracy analytical solutions are obtained at this level of approximation. Convective dispersion plays an important role in many processes of chemical reaction and separation. Such systems are commonly analyzed by use of a radially-averaged diffusion equation. The foregoing approach is not easy to apply to reaction or separation processes if the fluid properties vary, nor if the kinetics or equilibria are non-linear. Therefore, in this paper we consider an alternate method we solve the full diffusion equation by orthogonal collocation in the radial direction. Non-reactive systems are emphasized here reactive ones will be studied more fully in the sequel to this paper.
- Fluid Mechanics