关键词: chemical engineering mathematics, similarity solution, dimensional analysis, variable transformation, mass transfer

Abstract: Similarity solution is a classical topic in chemical engineering, frequently encountered in analysis of flow and transport phenomena in semi-infinite domains. In this article, dimensional analysis is applied to resolve systematically the conditions for the existence of similarity solutions and formulate a basic procedure to get such solutions. With several classic examples, the method for finding the suitable combination of independent variables from original ones is demonstrated, so that the original partial differential equation can be transformed into a simpler ordinary differential equation, through which the desired similarity solution is finally achieved. In-depth analysis of one-dimensional diffusion/reaction problems by dimensional analysis results in some new insights. The elaboration is significant for deep insight of similarity solution and its application in chemical engineering.

Key words: chemical engineering mathematics, similarity solution, dimensional analysis, variable transformation, mass transfer