Pseudo-Similarity Transformation of Governing Partial Differential Equations

Abstract

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.