By R. Kh. Zeytounian (auth.)
In the current monograph, fullyyt dedicated to “Convection in Fluids”, the aim is to provide a unified rational technique of varied convective phenomena in fluids (mainly regarded as a thermally excellent gasoline or an expansible liquid), the place the most riding mechanism is the buoyancy strength (Archimedean thrust) or temperature-dependent floor stress in homogeneities (Marangoni effect). additionally, the final mathematical formula (for example, within the Bénard challenge - heated from below)and the influence of the loose floor deformation are taken into consideration. in relation to the atmospheric thermal convection, the Coriolis strength and stratification results also are considered.
The major motivation is to offer a rational, analytical, research of major above pointed out actual results in every one case, at the foundation of the complete unsteady Navier-Stokes and Fourier (NS-F) equations - for a Newtonian compressible viscous and heat-conducting fluid - coupled with the linked initiales (at preliminary time), boundary (lower-at the cast airplane) and unfastened floor (upper-in touch with ambiant air) stipulations. This, evidently, isn't really a simple yet an important job if we've got in brain a rational modelling technique with a view of a numerical coherent simulation on a excessive pace computer.
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Additional resources for Convection in Fluids
Yakubenko, Spatio-temporal instability in free ultra-thin films. Eur. J. Mech. B/Fluids 17(3), 371–384, 1998. 38. S. Turner, Annu. Rev. Fluid Mech. 17, 11–44, 1985. 39. A. Oberbeck, Ann. Phys. , Neue Folge 7, 271–292, 1879. 40. Kh. Zeytounian, Meteorological Fluid Mechanics, Lecture Notes in Physics, Vol. m5. Springer-Verlag, Heidelberg, 1991. 41. S. Turner, Buoyancy Effects in Fluids. Cambridge, Cambridge University Press, 1973. 42. K. Jöhnk and B. Svendsen, A thermodynamic formulation of the equations of motion and buoyancy frequency for Earth’s fluid outer core.
Sci. 30, 739–745, 1992. 28 Short Preliminary Comments and Summary of Chapters 2 to 10 33. B. Straughan, Mathematical Aspects of Penetrative Convection. Longman, 1993. 34. R. Hills and P. Roberts, Stab. Appl. Anal. Continuous Media, 1, 205–212, 1991. 35. Kh. Zeytounian, The Bénard–Marangoni thermocapillary-instability problem, Phys. Uspekhi, 41(3), pp. 241-267, March 1998 [English edition]. 36. G. J. Lawrence and S. K. Wilson (guest-editors), The Dynamics of Thin Liquid Film, Journal of Engineering Mathematics Special Issue, 50(2–3), 2004.
As a consequence: it is not consistent (from an asymptotic point of view, at least in the leading-order, limiting, case) to take into account fully the above three effects – thermocapillarity, buoyancy and free surface deformation – simultaneously, for a weakly expansible viscous liquid. The buoyancy is operative only in the RB thermal convection rigid-free problem. Conversely, the effects linked with the deformable upper, free surface are operative only in the Bénard–Marangoni (BM) thermocapillary thin film problem.