Pseudo-Similarity Transformation of Governing Partial Differential Equations

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


The governing partial differential equations of laminar mixed convection with consideration of variable physical properties are equivalently transformed into the similarity governing partial differential equations by our innovative similarity transformation model. Due to our previous study, the pseudo-similarity transformation will be very coincident to the related partial-similarity transformation for the calculation results of convection heat transfer. Therefore, a pseudo-similarity transformation can be performed for the similarity transformation of mixed convection. The similarity transformation model for forced convection is taken as main model for coincidence of forced boundary conditions. Meanwhile, Grashof number is induced for treatment of free convection characteristics. In this similarity transformation, the velocity similarity variables are taken as the core similarity variables. They have definite physical meanings, and can lead to a better advantage for treating the physical properties factors compared with those of Falkner-Skan transformation. In addition, by taking water mixed convection as an example, a polynomial model is induced for treatment of the coupled effect of liquid variable physical properties, so that the transformed governing similarity mathematical models have their theoretical and practical value.


Pseudo-similarity transformation Innovative similarity transformation Similarity variables Polynomial model Treatment of variable physical properties Theoretical equation of physical property factor Mixed convection 


  1. 1.
    Shang, D.Y., Gu, J.: Analyses of pseudo-similarity and boundary layer thickness for non-Newtonian falling film flow. Heat Mass Transf. 41(1), 44–50 (2004)Google Scholar
  2. 2.
    Shang, D.Y.: Free Convection Film Flows and Heat Transfer—Models of Laminar Free Convection with Phase Change for Heat and Mass Transfer Analysis. Springer, Berlin (2013)Google Scholar
  3. 3.
    Shang, D.Y.: Theory of Heat Transfer with Forced Convection Film Flows. Springer, Berlin (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

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

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