Dimensional Analysis and Scaling of Boundary Value Problems
Norman W. Loney · 2016
In the practice of chemical engineering, dimensional analysis and scaling are techniques that can be employed to emphasize similarities between a prototype and its model. Dimensionless quantities are developed, which can serve as new variables. Usually, the number of new variables is much smaller than the original number of physical variables of the system under consideration. In studying transport phenomena one is guaranteed to encounter situations involving fluid-solid or gas-liquid interfaces. These problems usually become more complex when fluid motion is involved. Traditionally, such complex problems are analyzed with the aid of the concept of a boundary layer. Scaling is also helpful in assessing the error incurred in making the simplifying assumptions. Generally, one can observe that the error incurred in using the discussed scaling technique will be of the same order as the dimensionless group, which must be small enough to be neglected.