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Taylor dispersion coefficients for laminar, longitudinal flow past arrays of circular tubes

Authors
Journal
International Journal of Heat and Mass Transfer
0017-9310
Publisher
Elsevier
Publication Date
Volume
50
Identifiers
DOI: 10.1016/j.ijheatmasstransfer.2006.08.032
Keywords
  • Taylor Dispersion Coefficient
  • Shell-And-Tube Configuration
  • Effective-Medium Theory
  • Conditional Average
  • Cell Theory
  • Multipole Expansion Method

Abstract

Abstract The problem of determining shell-side Taylor dispersion coefficients for a shell-and-tube configuration is examined in detail for both ordered as well as disordered arrangement of tubes. The latter is modeled by randomly placing N tubes within a unit cell of a periodic array. It is shown that shell-side Taylor dispersion coefficient D T is expressed by D T = D M(1 + λPe 2) and the coefficient λ is divergent with N, where D M is the molecular diffusivity of solute on the shell side and Pe is the Peclet number given by aU/D M with a and U being the radius of tube and the mean fluid velocity on the shell side, respectively. The coefficient λ depends on the spatial average and the fluid velocity weighted average of the concentration of solute on the shell side. The behavior of the coefficient λ with N arises due to logarithmically divergent nature of concentration disturbances caused by each tube in the plane normal to the axes of the tubes. An effective-medium theory is developed for determining conditionally-averaged velocity and concentration fields and hence the shell-side Taylor dispersion coefficients. Its predictions are compared with the results of rigorous numerical computations. The present study also presents formulas for determining the shell-side Taylor dispersion coefficients for square and hexagonal arrays of tubes with cell theory approximations.

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