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.
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References
Prandtl, L.: Über Die Flussigkeitsbewegung bei Sehr Kleiner Reibung. In: Proc. 3d Intern. Math. Koug. Heidelberg (1904)
Falkner, V.M., Skan, S.W.: Some approximate solutions of the boundary layer equations. Phil. Mag. 12, pp. 865 (1931)
Shang, D.Y., Zhong, L.C.: A similarity transformation of velocity field and its application for an in-depth study on laminar free convection heat transfer of gases, Int. J. Therm. Sci. 101, 106–115 (2016)
Shang, D.Y.: Theory of heat transfer with forced convection film flows. In: Series (Book) of Heat and Mass Transfer, 1st edn, p. 346. Springer, Berlin (2011)
Shang, D.Y.: Free convection film flows and heat transfer-models of laminar free convection with phase change for heat and mass transfer. In: Series (Book) of Heat and Mass Transfer, 2nd edn., p. 535. Springer, Berlin (2013)
Shang, D.Y., Wang, B.X.: Effect of variable thermophysical properties on laminar free convection of gas. Int. J. Heat Mass Transfer 33(7), 1387–1395 (1990)
Shang, D.Y., Wang, B.X.: Effect of variable thermophysical properties on laminar free convection of polyatomic gas. Int. J. Heat Mass Transfer 34(3), 749–755 (1991)
Shang, D.Y., Wang, B.X., Wang, Y., Quan, Y.: Study on liquid laminar free convection with consideration of variable thermophysical properties. Int. J. Heat Mass Transfer 36(14), 3411–3419 (1993)
Shang, D.Y., Wang, B.X., Zhong, L.C.: A study on laminar film boiling of liquid along an sothermal vertical plate in a pool with consideration of variable thermophysical properties. Int. J. Heat Mass Transfer 37(5), 819–828 (1994)
Shang, D.Y., Adamek, T.: Study on laminar film condensation of saturated steam on a vertical flat plate for consideration of various physical factors including variable thermophysical properties. Warme-und Stoffübertragung 30, 89–100 (1994)
Shang, D.Y., Wang, B.X.: 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)
Shang, D.Y., Zhong, L.C.: Extensive study on laminar free film condensation from vapor gas mixture. Int. J. Heat Mass Transfer 51, 4300–4314 (2008)
Andersson, H., Shang, D.Y.: An extended study of hydrodynamics of gravity-driven film flow of power-law fluids. Fluid Dyn. Res. pp. 345–357 (1998)
Shang, D.Y., Andersson, H.I.: Heat transfer in gravity driven film flow of power-law fluids. Int. J. Heat Mass Transfer 42(11), 2085–2099 (1999)
Shang, D.Y., Gu, J.: Analyses of pseudo-similarity and boundary layer thickness for non- Newtonian falling film flow. Heat Mass Transfer 41(1), 44–50 (2004)
Taton, G., Rok, T., Rokita, E.: Temperature distribution assessment during radiofrequency ablation. IFMBE Proc. 22, 2672–2676 (2008)
Taton, G., Rok, T., Rokita, E.: Estimation of temperature distribution with the use of a thermo-camera. Pol. J. Med. Phys. Eng. 14(1), 47–61 (2008)
Turkin, A.A., Dutka, M., Vainchtein, D., Gersen, S., et al.: Deposition of SiO2 nanoparticles in heat exchanger during combustion of biogas. Appl. Energy 113, 1141–1148 (2014)
Gao, Y., Liu, Q.K., Chow, W.K., Wu, M.: Analytical and experimental study on multiple fire sources in a kitchen. Fire Saf. J. 63, 101–112 (2014)
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Shang, DY., Zhong, LC. (2016). Our Innovative Similarity Transformation Models of Convection Velocity Field. In: Heat Transfer of Laminar Mixed Convection of Liquid . Heat and Mass Transfer. Springer, Cham. https://doi.org/10.1007/978-3-319-27959-6_3
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DOI: https://doi.org/10.1007/978-3-319-27959-6_3
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