Download Scaling Analysis in Modeling Transport and Reaction by William B. Krantz PDF
By William B. Krantz
This publication is exclusive because the first attempt to expound with reference to systematic scaling research. no longer written for a particular self-discipline, the booklet goals any reader attracted to shipping phenomena and response methods. The publication is logically divided into chapters at the use of systematic scaling research in fluid dynamics, warmth move, mass move, and response strategies. An integrating bankruptcy is integrated that considers extra advanced difficulties related to mixed delivery phenomena. every one bankruptcy comprises a number of difficulties which are defined in huge element. those are by way of numerous labored examples for which the final define for the scaling is given. each one bankruptcy additionally contains many perform problems.This publication is predicated on spotting the worth of systematic scaling research as a pedagogical technique for instructing shipping and response strategies and as a examine software for constructing and fixing types and in designing experiments. hence, the e-book can function either a textbook and a reference publication.
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Extra info for Scaling Analysis in Modeling Transport and Reaction Processes: A Systematic Approach to Model Building and the Art of Approximation
Example text
Determine the scale and reference factors by setting dimensionless groups equal to 1 (for scale factors) or zero (for reference factors); this yields the minimum parametric representation in the form f( 1, 2, . . 4-1) where i denotes a dimensionless group. These i ’s include dimensionless groups formed from combinations of the physical and geometric quantities and any dimensionless independent variables. 8. The dimensionless groups in step 7 are not unique; it might be advantageous to isolate two or more dimensional quantities into one group (if possible) to determine their interdependence; this is done by forming a new group from the k dimensionless groups via the operation p =φ· a 1, b 2, .
1, the error in determining the average velocity when the upper plate velocity is ignored is 38%. 7%. This demonstrates clearly that proper scaling analysis provides results within an order of magnitude. If one wants to be certain that some assumption can be invoked with confidence, two orders of magnitude should be demanded for any “much less than” or “much greater than” condition. Note, however, that the error encountered in making an approximation, such 1, depends not only on the magnitude of 1 but also on as assuming that 1 the quantity that is being determined from the solution.
Scaling Analysis in Modeling Transport and Reaction Processes: A Systematic Approach to Model Building and the Art of Approximation, By William B. Krantz Copyright © 2007 John Wiley & Sons, Inc. 19 20 APPLICATIONS IN FLUID DYNAMICS dynamics, specifically creeping, lubrication, boundary-layer, and quasi-steady-state flows. We then apply ◦(1) scaling to show how it can be used to justify ignoring end and sidewall effects. We also consider the application of ◦(1) scaling in simplifying more complex flows, such as those involving free surfaces, porous media, and compressible fluids.