New Similarity Analysis Method for Laminar Free Convection Boundary Layer and Film Flows

Abstract

A new similarity analysis method with a new set of dimensionless similarity variables is provided for complete similarity transformation of the governing partial differential equations of laminar free convection and two multi-phase film flows. The derivation of the Reynolds number together with the Nusselt number and Prandtl number is reviewed by means of Buckingham \(\pi \)-theorem and dimension analysis, where the Reynolds number is taken as the one of the new set of dimensionless analysis variables. The essential work focuses on derivation of equations for the dimensionless velocity components and the dimensionless coordinate variable, by means of a detailed analysis of quantity grade of the governing conservation partial differential equations of laminar free convection. On this basis, the new similarity analysis method is produced for complete similarity transformation of the conservation partial differential equations of laminar free convection and its film flows. With the novel dimensionless velocity components devoted in this chapter, the new similarity analysis method has obvious advantages compared with the Falkner–Skan transformation. These advantages are (i) more convenient for consideration and treatment of the variable physical properties, (ii) more convenient for analysis and investigation of the two-dimensional velocity field, and (iii) more convenient for satisfaction of the interfacial mass transfer matching conditions in the numerical calculation and for rigorous investigation of mass transfer for two-phase film flows with three-point boundary problem. These advantages will be found from the successive chapters.KeywordsNusselt NumberFree ConvectionSimilarity TransformationLocal Nusselt NumberBoussinesq ApproximationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.