Heat transfer — a review of 1997 literature

Eckert, E. R. G.; Goldstein, R. J.; Ibele, W.E.; Patankar, S. V.; Simon, Terrence W.; Kuehn, Thomas H.; Strykowski, Paul J; Tamma, Kumar K.; Bar‐Cohen, Avram; Heberlein, J.; Davidson, Jane H.; Bischof, John C.; Kulacki, F. A.; Kortshagen, Uwe R.; Garrick, Sean C.

doi:10.1016/s0017-9310(99)00196-9

Cited by 8 publications

(3 citation statements)

References 1,636 publications

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“…In [10], the authors investigated the existence of codimension-three bifurcations that are the points where the codimensions two curves intersect on the Prandtl-Biot plane and an also new kind of instability was found, hydrothermal waves of second kind (HWII). The interest in understanding the influence of gravitational effects in thermoconvective phenomena has been rapidly growing [15][16][17]. However, less attention has been paid to the effect of the domain geometry on the onset of the flow motion and the dynamics of the different bifurcations appearing.…”

Section: Introductionmentioning

confidence: 99%

Influence of geometrical parameters on the linear stability of a Bénard-Marangoni problem

2016

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A linear stability analysis of a thin liquid film flowing over a plate is performed. The analysis is performed in an annular domain when momentum diffusivity and thermal diffusivity are comparable (relatively low Prandtl number, Pr=1.2). The influence of the aspect ratio (Γ) and gravity, through the Bond number (Bo), in the linear stability of the flow are analyzed together. Two different regions in the Γ-Bo plane have been identified. In the first one the basic state presents a linear regime (in which the temperature gradient does not change sign with r). In the second one, the flow presents a nonlinear regime, also called return flow. A great diversity of bifurcations have been found just by changing the domain depth d. The results obtained in this work are in agreement with some reported experiments, and give a deeper insight into the effect of physical parameters on bifurcations.

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Section: Introductionmentioning

confidence: 99%

Influence of geometrical parameters on the linear stability of a Bénard-Marangoni problem

2016

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“…Those latter works dealt with the influence of Biot number in the flow solutions. The interest in understanding the influence of gravitational effects in thermo-convective phenomena has been rapidly growing [7,23]. However, less attention has been paid to the effect of the capillarity forces of the onset of the flow motion and the behavior of the bifurcations that can appear.…”

Section: Introductionmentioning

confidence: 99%

Analysis of bifurcations in a Bénard–Marangoni problem: Gravitational effects

Hoyas

Fajardo

Gil

et al. 2014

International Journal of Heat and Mass Transfer

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Abstract:This article studies the linear stability of a thermoconvective problem in an annular domain for different Bond (capillarity or buoyancy effects) and Biot (heat transfer) numbers for two set of Prandtl numbers (viscosity effects). The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. Different kind of competing solutions appear on localized zones of the Bond-Biot plane. The boundaries of these zones are made up of codimension two points. A co-dimension four point has been found for the first time. The main result found in this work is that in the range of low Prandtl number studied and in low-gravity conditions, capillarity forces control the instabilities of the flow, independently of the Prandtl number.

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“…Zhu et al [27] discussed the relationship between oscillatory frequency and Marangoni number. The effects of gravitation in thermoconvective instabilities has been studied by several authors [28,29,30].…”

Section: Introductionmentioning

confidence: 99%