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 forced convection and two–phase film flows. First, the derivation of the Reynolds number together with the Nusselt number and Prandtl number is reviewed by means of Buckingham Π-theorem and dimension analysis, where the Reynolds number is taken as the one of the new set of dimensionless analysis variables. Then 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 forced convection. On this basis, the new similarity analysis method is produced for complete similarity transformation of the conservation partial differential equations of laminar forced convection and its film flows. Owing to dimensionless velocity components devoted in this chapter, the new similarity analysis method has obvious advantages compared with the Falkner–Skan transformation. These advantages are the following: (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.
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References
D.Y. Shang, B.X. Wang, Effect of variable thermophysical properties on laminar free convection of gas. Int. J. Heat Mass Transfer 33(7), 1387–1395 (1990)
D.Y. Shang, Free Convection Film Flows and Heat Transfer (Springer Berlin, Heidelberg, New York, NY, 2006)
D.Y. Shang, B.X. Wang, Effect of variable thermophysical properties on laminar free convection of polyatomic gas. Int. J. Heat Mass Transfer 34(3), 749–755 (1991)
Shang, B.X. Wang, Y. Wang, Y. Quan, Study on liquid laminar free convection with consideration of variable thermophysical properties. Int. J. Heat Mass Transfer 36(14), 3411–3419 (1993)
D.Y. Shang , B.X. Wang, L.C. Zhong, A study on laminar film boiling of Liquid along an isothermal vertical plate in a pool with consideration of variable thermophysical properties. Int. J. Heat Mass Transfer 37(5), 819–828 (1994)
D.Y. Shang, T. Adamek, Study on laminar film condensation of saturated steam on a vertical flat plate for consideration of various physical factors including variable thermophysical properties. Wärme- und Stoffübertragung 30, 89–100 (1994)
D.Y. Shang, B.X. Wang, An extended study on steady-state laminar film condensation of a superheated vapor on an isothermal vertical plate. Int. J. Heat Mass Transfer 40(4), 931–941 (1997)
H.I. Andersson, D.Y. Shang, An extended study of hydrodynamics of gravity- driven film flow of power-law fluids. Fluid Dyn Res 22, 345–357 (1998)
D.Y. Shang, H. Andersson, Heat transfer in gravity-driven film flow of power-law fluids. Int. J. Heat Mass Transfer 42(11), 2085–2099 (1999)
D.Y. Shang, J. Gu, Analyses of pseudo-similarity and boundary layer thickness for non-Newtonian falling film flow. Heat Mass Transfer 41(1), 44–50, (2004)
E. Buckingham, On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345–376 (1914)
E. Buckingham, The principle of similitude. Nature 96, 396–397 (1915)
E. Buckingham, Model experiments and the forms of empirical equations. Trans. A.S.M.E 37, 263–296 (1915)
S.G. Taylor, The formation of a blast wave by a very intense explosion I. theoretical discussion. Proc. Roy. Soc. A 201, 159–174 (1950)
S.G. Taylor, The formation of a blast wave by a very intense explosion II. the atomic explosion of 1945. Proc. Roy. Soc. A 201, 175–186 (1950)
H. Hanche-Olsen Buckingham’s pi-theorem, NTNU. Retrieved April 9, 2007 (2004).
S J. Kline Similitude and Approximation Theory (Springer, New York, NY, 1986).
F. Y.M. Wan, Mathematical Models and their Analysis (Harper & Row Publishers, New York, NY, 1989)
G.W. Hart Multidimensional Analysis: Algebras and Systems for Science and Engineering (Springer, Heidelberg, 1995)
Vignaux, G.A., Dimensional analysis in data modelling, Victoria University of Wellington, 1991. Retrieved December 15 (2005)
Mike Sheppard, Systematic Search for Expressions of Dimensionless Constants using the NIST database of Physical Constants (2007)
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Shang, D. (2010). A New Similarity Analysis Method for Laminar Forced Convection Boundary Layer. In: Theory of Heat Transfer with Forced Convection Film Flows. Heat and Mass Transfer. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12581-2_4
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DOI: https://doi.org/10.1007/978-3-642-12581-2_4
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