The effect of gravity modulation on solutal convection during directional
                        solidification

Murray, B T; Coriell, S R; McFadden, G B

doi:10.6028/nist.ir.4389

Cited by 3 publications

(3 citation statements)

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“…Alexander et al (1991) also analyze low-gravity-tolerance (or Bridgman-Stockbarger) crystal growth. The e ect of gravity modulation on the onset of convection for unidirectional solidiÿcation was considered by Murray et al (1991) while Wheeler et al (1991) analyzed the high-frequency limit of this problem. In this limit the method of averaging may be used to determine the e ect of large-amplitude gravity modulation on both the primary instability and its subsequent evolution.…”

Section: Introductionmentioning

confidence: 99%

Natural doubly diffusive convection with vibration

et al. 2001

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We present a numerical and analytical study of doubly di usive convection driven by horizontal thermal and solutal gradients in square and rectangular enclosures with no-slip walls subjected to high-frequency vibration. The two vertical walls of the enclosure are maintained at di erent but uniform temperatures and concentrations while the horizontal walls are assumed to be impermeable and insulating. The resulting system is described by time-averaged Boussinesq equations. These equations possess a doubly di usive quasi-equilibrium solution provided the thermal and solutal buoyancy forces are equal and opposite. This solution is linearly stable up to a critical value of the stability parameter independently of the strength and orientation of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength and orientation of the vibration, and the larger amplitude states are computed numerically using a spectral collocation method. For vertical oscillation increasing the vibration amplitude decreases the subcriticality of the solutions and may even reverse it; the opposite occurs with horizontal vibration.

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Section: Introductionmentioning

confidence: 99%

Natural doubly diffusive convection with vibration

et al. 2001

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“…The effect of GM on the stability of a heated fluid layer was first examined by Gresho and Sani [16] and Gershuni and colleagues [17]. Murray and colleagues [18] considered the effect of GM on the onset of convection for the unidirectional solidification problem. Saunders and colleagues [19] studied the effect of GM on the stability of a horizontal double-diffusive layer.…”

Section: Introductionmentioning

confidence: 99%

g-Jitter-Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

Swamy

2014

Heat Trans. Asian Res.

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This paper presents linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated sparsely packed porous layer subject to the combined effect of time-periodic gravity modulation (GM) and an AC electric field. In the domain of linear theory, the critical stability parameters are computed by the regular perturbation method in the form of a perturbation series in powers of frequency of modulation. The local nonlinear theory based on the truncated Fourier series method gives information on convection amplitudes and heat transfer. The principle of the exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system, several qualitative results on stability are discussed. The sensitive dependence of the solution of a Lorenz system of electrothermal convection subject to the choice of initial conditions points to the possibility of chaos. Low-frequency g-jitter is found to have a significant stabilizing influence, which is in turn diminished by an imposed AC electric field. The role of sparseness of the porous layer, viscosity ratio, and normalized porosity on the stability criterion and on heat transport is determined. C⃝

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“…In the case of a porous medium saturated by a fluid, the effect of vertical vibrations on thermal stability of a conductive solution is studied in [26]; for other directions of vibration, depending on the vibrational parameter and the angle of vibration, stabilizing and destabilizing effects are possible [27]. Mechanical and thermal vibrations have also been studied in connection with the Rayleigh-Bénard convection [10,11], directional solidification [12,21], and doubly diffusive convection [9]. In spite of numerous results on the influence of vibrations on convective instability, some questions still remain open.…”

Section: Introductionmentioning

confidence: 99%