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Ind. Eng. Chem. Res. 199433,2331-2335
Thermal and Diffusion Boundary Layers in Viscoelastic Flows Eli Ruckenstein Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260
Scaling arguments are employed to obtain an expression for the thickness of the hydrodynamic boundary layer for a viscoelastic fluid flowing along a plate. This expression, which is valid a t relatively large Reynolds numbers, is used to derive equations for the heat or mass transfer coefficient along a plate and a cylinder which involve, in addition to the usual dimensionless groups, the Deborah number. The present equations show that viscoelasticity moderates the dependence of the transfer coefficient on velocity. An explanation is also suggested for the experimental observation of James and Acosta that for a viscoelastic fluid a t low Reynolds numbers the heat transfer coefficient across a cylinder becomes independent of velocity a t large values of the latter. The ratio between the relaxation time of the polymer chains of aviscoelastic fluid and the duration of the process was called by Reiner (1964) the Deborah number, and its implications for short-time processes have been examined by Metzner, White, and Denn (1966) in a most significant contribution to the chemical engineering literature. In addition to the above paper, the following papers are relevant to the present one: James and Acosta (1970) and James and Gupta (1970) observed that, during the flow a t relatively low Reynolds numbers (
