Natural and Marangoni convections in a two-dimensional rectangular open boat.

Okano, Yasunori; Itoh, Masayasu; Hirata, Akira

doi:10.1252/jcej.22.275

“…The similarity results agree well with the measured velocities for indium. Okano and colleagues [6] showed that the Reynolds number should vary as the two-thirds root of the Marangoni number for large Reynolds numbers. The similarity and experimental results agree with their analysis that the surface velocity should vary as the two-thirds root of the temperature difference.…”

Section: Similarity Resultsmentioning

confidence: 99%

“…Some of the papers most relevant to this work include the order-of-magnitude analysis of Marangoni flow given by Okano and colleagues [6] that presented the general trends for the variation of the Reynolds number with the Grashof number, Marangoni number, and Prandtl number. Hirata and his co-workers experimentally and numerically investigated Marangoni flow for various substances in geometries with flat surfaces relevant to this work [4,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…Some of the papers most relevant to this work include the order-of-magnitude analysis of Marangoni flow given by Okano and colleagues [6] that presented the general trends for the variation of the Reynolds number with the Grashof number, Marangoni number, and Prandtl number. Hirata and his co-workers experimentally and numerically investigated Marangoni flow for various substances in geometries with flat surfaces relevant to this work [4,6,7]. Arafune and Hirata [8] presented a similarity analysis for just the velocity profile for Marangoni flow that is very similar to this derivation but the results are effectively limited to surface tension variations that are linearly related to the surface position.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Heat transfer for Marangoni‐driven boundary layer flow

Christopher

¹

,

Wang

²

2002

Heat Trans. Asian Res.

1

0

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Marangoni convection induced by variation of the surface tension with temperature along a surface influences crystal growth melts and other processes with liquidvapor interfaces, such as boiling in both microgravity and normal gravity in some cases. This paper presents the Nusselt number for Marangoni flow over a flat surface calculated using a similarity solution for both the momentum equations and the energy equation assuming developing boundary layer flow along a surface. Solutions are presented for the surface velocity, the total flow rate, and the Nusselt number for various temperature profiles, Marangoni numbers, and Prandtl numbers. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble.

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“…Some of the papers most relevant to this work include the order-of-magnitude analysis of Marangoni flow given by Okano et al [15] that gave the general trends for the variation of the Reynolds number with the Grashof number, Marangoni number, and Prandtl number. Hirata and his co-workers experimentally and numerically investigated Marangoni flow for various substances in geometries with flat surfaces relevant to this work [13,15,16].…”

Section: Introductionmentioning

confidence: 99%

“…Some of the papers most relevant to this work include the order-of-magnitude analysis of Marangoni flow given by Okano et al [15] that gave the general trends for the variation of the Reynolds number with the Grashof number, Marangoni number, and Prandtl number. Hirata and his co-workers experimentally and numerically investigated Marangoni flow for various substances in geometries with flat surfaces relevant to this work [13,15,16]. Arafune and Hirata [17] presented a similarity analysis for just the velocity profile for Marangoni flow that is very similar to this derivation but the results are effectively limited to surface tension variations that are linearly related to the surface position.…”

Section: Introductionmentioning

confidence: 99%

Exact analytical solutions for thermosolutal Marangoni convection in the presence of heat and mass generation or consumption

Magyari

¹

,

Chamkha

²

2006

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The steady laminar thermosolutal Marangoni convection in the presence of temperature-dependent volumetric heat sources/sinks as well as of a firstorder chemical reaction is considered in this paper. Assuming that the surface tension varies linearly with temperature and concentration and that the interface temperature and concentration are quadratic functions of the interface arc length x, exact analytical similarity solutions are obtained for the velocity, temperature and concentration fields. The features of these exact solutions as functions of the physical parameters of the problem are discussed in detail. Greek symbols a thermal diffusivity, Eq. 3 D discriminant, Eq. 25 c coefficients, Eq. 5 g similarity independent variable, Eq. 8 / dimensionless heat generation/absorption coefficient, Eq. 13 l dynamic viscosity t kinematic viscosity, m = l/q h temperature similarity variable, Eq. 8 q density r surface tension, Eq. 5 w stream function, Eq. 8 Subscripts T thermal quantity c solutal quantity 0 at g = 0 ¥ for g fi ¥ List of symbols

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