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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear convection in a rotating layer with finite conducting boundaries (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 353-358 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Small-amplitude steady thermal convection is a horizontal layer of fluid with finite conducting boundaries and rotating about a vertical axis is investigated. Both analytical and numerical techniques are used to solve the nonlinear and stability problems. Conditions on the parameters γb, γt, and τ are determined under which either square cells or two-dimensional rolls can be the preferred form of convection (γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and τ is the rotation parameter). Transition from steady rolls to time-dependent flow occurs for τ beyond some value, which decreases with decreasing γb or γt. Square cell convection is not subject to such transition, but there is a transition from steady squares to steady rolls for τ beyond a critical value. The dependence on γb, γt, and τ of the time-dependent transition and of the heat transported by convection are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857785
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  • 2
    Electronic Resource
    Electronic Resource
    On the stability of a cellular flow under a solidifying surface (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2816-2818 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation k and for cases where the amplitude of motion is not restricted to be small. In contrast to the small-amplitude case, it is found that there is no subcritical instability and that squares can be the only stable flow pattern for a significant range of amplitudes that widens as k decreases or as Péclet number z∞ increases. All the other flow structures are unstable with the exception of down-hexagons, which can be stable only in a narrow range of small amplitudes. This later range of amplitudes is independent of k, but it reduces in size as z∞ increases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858170
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  • 3
    Electronic Resource
    Electronic Resource
    Solutal convection in the melt during solidification of a binary alloy (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 27-32 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation. Stationary solutions of the nonlinear problem are obtained and the preferred mode of convection is determined by a stability analysis. It is found that down-hexagons (where motion is downward at the cells' centers) are stable for sufficiently small amplitude Ε, while both down-hexagons and squares are stable in a range of larger Ε. The dependence of various flow features on the segregation coefficient and the effective depth of the melt is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866573
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  • 4
    Electronic Resource
    Electronic Resource
    Pattern generation by convection in spherical shells (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 699-712 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Das Problem der Strukturselektion für thermische Konvektion in dünnen Kugelschalen mit nahezu thermisch isolierenden Rändern wird untersucht im nicht-singulären und im singulären Fall, wobei die Rayleighzahl im ersteren Fall ihr Minimum für einen einzigen Wert für den Gradl der spherischen Harmonischen erreicht, während dies im zweiten Fall für zwei benachbarte Werte vonl geschieht. Die Zahl der zu verschiedenen Strukturen gehörenden Lösungen ist im letzteren Fall wesentlich größer als im ersten Fall. Im nicht-singulären Fall existiert stets eine stabile Lösung, während im singulären Fall zusätzlich eine stabile gemischte Lösung existiert, wie im Falll=1,l *=2 gezeigt wird.
    Notes: Summary The problem of pattern selection by thermal convection in thin spherical shells with nearly insulating boundaries is investigated for both non-singular and singular cases where the Rayleigh number attains its minimum value for a single and double values of the degreel of spherical harmonics, respectively. The number of distinct solutions for the singular case is found to be substantially larger than the number of distinct solutions for the non-singular case. While there is at least one stable solution for the non-singular case, there is an additional stable mixed mode solution in the singular case as is shown in the casel=1 andl *=2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948731
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  • 5
    Electronic Resource
    Electronic Resource
    On the structure of an unsteady convecting mushy layer (1998)
    Springer
    Acta mechanica 127 (1998), S. 83-96 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Nonlinear time dependent natural convection in a mushy layer during solidification of a binary alloy is investigated. Asymptotic and scaling analyses are applied to convective flow within the mushy layer and in cylindrical chimneys with small radiusa. Various results in four distinctly identified regimes, corresponding to high or low Prandtl number melt and strongly or weakly time dependent flow, are determined. In particular, it is found that strongly time dependent flow can provide non-vertical chimneys, and for weakly time dependent flow of a low Prandtl number melt vertical chimneys are possible only for sufficiently smalla.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170365
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  • 6
    Electronic Resource
    Electronic Resource
    Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint (1997)
    Springer
    Acta mechanica 121 (1997), S. 143-152 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Linear flow instabilities due to oscillatory disturbances of the liquid and mushy regions during solidification of binary alloys are investigated under a rotational constraint where the rotation axis is inclined to gravity vector. Results of stability analyses and numerical computations for a preferred centrifugal mode of general oscillatory disturbances at zero and non-zero rotation rates are determined which provide information about the preference of oscillatory flow and its role on the solidification system as modified by the rotational effects. The main results are due to a preferred oscillatory mode of convection which is more significant for non-zero rotation case and is restricted mostly to the mushy region. The preferred oscillatory mode of convection is a traveling wave in the presence of rotation, but it is a standing wave in the absence of rotation. The results for different Prandtl numbers indicate that the freckles formation tendency for metallic alloys is less than that for aqueous solutions. Freckles are imperfections that reduce the quality of the solidified materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01262528
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  • 7
    Electronic Resource
    Electronic Resource
    Direct resonance analysis and modeling for a turbulent boundary layer over a corrugated surface (1998)
    Springer
    Acta mechanica 131 (1998), S. 225-233 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Effects of surface corrugation on turbulent flow in a boundary layer are studied using a model based on the direct resonance theory. The induced mean flow due to weakly nonlinear waves, superimposed on the mean and fluctuating components of turbulence, is determined. The mean turbulent flow is affected by the surface corrugation throughout the boundary layer. The corrugated surface generates higher harmonics and affects the streamwise vortices generated by the waves superimposed on turbulence whose mean flow includes secondary induced mean flow components due to the corrugation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177226
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  • 8
    Electronic Resource
    Electronic Resource
    Effect of rotation on the structure of a convecting mushy layer (1996)
    Springer
    Acta mechanica 118 (1996), S. 109-119 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Nonlinear natural convection in a mushy layer during solidification of a binary alloy is investigated under a high gravity environment where the rotation axis is inclined to the high gravity vector. Asymptotic and scaling analyses are applied to convective flow within the mushy layer and in vertical chimneys. The main result is that, for some particular moderate rotation range, vertical velocity in the chimneys decreases rapidly with increasing rotation rate and appears to have opposite signs across some rotation dependent vertical level.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410511
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  • 9
    Electronic Resource
    Electronic Resource
    Thermocapillary instability of a low Prandtl number fluid with negligible gravitational effects (1988)
    Springer
    Acta mechanica 71 (1988), S. 249-252 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Finite amplitude fluid motion is investigated in a horizontal layer of a low Prandtl number fluid for the case where thermocapillary effects are significant and gravitational effects are negligible. The main result is that down-hexagons (where motion is downward at the cells' centers) are preferred for sufficiently small amplitude in contrast to uphexagons (where motion is upward at the cells' centers) that represent the preferred pattern for large Prandtl number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01173952
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  • 10
    Electronic Resource
    Electronic Resource
    Effect of rotation on the stability of the melt during the solidification of a binary alloy (1993)
    Springer
    Acta mechanica 99 (1993), S. 95-101 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Nonlinear solutal convective flow in the melt under a planar solidifying surface and rotating about the vertical axis is investigated in the limit of small segregation. An evolution equation governing the cellular structure of the flow of a binary alloy is derived. This equation incorporates convective instabilities and rotational effects. The presence of rotation can inhibit the onset of the cellular structure by effectively magnifying the segregation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177237
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