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Our Innovative Similarity Transformation Models of Convection Velocity Field

  • De-Yi ShangEmail author
  • Liang-Cai Zhong
Chapter
Part of the Heat and Mass Transfer book series (HMT)

Abstract

Our innovative similarity transformation models for in-depth research of convection heat and mass transfer are presented in this Chapter. For demonstration of the theoretical rationality on these similarity transformation models, the related theoretical derivations are performed. For solving convection heat and mass transfer issues, the boundary layer analysis method is always used. There could be different similarity transformation models which are related to different study levels on convection heat transfer. For example, Falkner-Skan transformation is currently still popularly used to treat the similarity transformation of core similarity variables of velocity field. In fact this type of transformation is inconvenient to do this core work for similarity transformation of velocity field, because it is necessary to first induce flow function and group theory to derive an intermediate function for an indirect similarity transformation of the velocity field. This case also causes a difficult situation on consideration of variable physical properties. However, our innovative similarity transformation models are based on the laws of physics and the analysis of convection partial differential equations. Thus, the above difficult situation caused by derivation of the Falkner-Skan transformation model could be resolved. Furthermore, with our innovative similarity transformation models, the velocity components can be directly transformed to the related dimensionless similarity ones. Then, the similarity analysis and transformation of the convection governing partial differential equations can have obvious physical significance. Moreover, our innovative similarity transformation models can conveniently treat variable physical properties and their coupled effect on convection heat and mass transfer for enhancement of the theoretical and practical value of the related study.

Keywords

Free convection Forced convection Mixed convection Innovative similarity transformation models Laws of physics Analysis of convection partial differential equations Similarity variable Falkner-Skan transformation Flow function Group theory 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.OttawaCanada
  2. 2.Department of Ferrous MetallurgyNortheastern UniversityShenyangChina

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