On the use of transfer coefficients in dynamic process models

✍ Scribed by John C. Friedly

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 682 KB
• Volume: 25
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(70)85027-8

✦ Synopsis

The question of what conditions are necessary in order for lumped transfer coefficients to be useful in dynamic process models is considered. The unsteady state analog of the Graetz problem is used as an example. An expression is derived for a characteristic time required for transport to approach the steady state rate in the radial direction of a tube with constant wall temperature or concentration. Disturbances in the bulk properties occurring on a longer time scale can be considered in quasi-steady state in the radial direction although there may be significant dynamic effects in the axial direction. In this regime the dynamics can be described by a one-dimensional model with appropriate lumped transport coefficients.

The characteristic time for radial dynamics is found to be maximum far from the tube inlet. It is directly proportional to the fluid P&let number. The time constant is a function of the fluid velocity profile, decreasing to zero as the velocity approaches plug flow. Numerical results are presented for a parabolic velocity profile.