Numerical Simulation of Thermocapillary Convection in a Shallow Rectangular Cavity Under the Action of Combining Horizontal Temperature Gradient with Vertical Heat Flux

In order to understand the influence of the vertical heat flux on thermocapillary convection, we conducted a series of unsteady two-dimensional numerical simulations of thermocapillary convection in a differently heated shallow rectangular cavity with vertical heat flux on the bottom by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and aspect ratio is 30. It is found that a small vertical heat flux has slightly influence on the flow pattern of stable or unstable thermocapillary convection. However, the critical Marangoni number increases first, and then decreases with the increase of the heat flux. And the flow pattern of the oscillatory thermocapillary convection transits from a series of the rolls rotating clockwise and moving from the cold wall to the hot wall to the single roll near the hot wall and a series of rolls near the cold wall, further, two series of rolls moving from the hot wall and cold wall towards the hot spot with the maximum temperature. With the increase of the Marangoni number, the period and the wavelength of the oscillatory thermocapillary convection increase, but the wave speed decreases.     

Heat transfer enhancement by Marangoni convection in the NH3–H2O absorption process

The objectives of this paper are to quantify the effect of Marangini convection on the absorption performance for the ammonia–water absorption process, and to visualize Marangoni convection that is induced by adding a heat transfer additive, n-octanol. A real-time single-wavelength holographic interferometer is used for the visualization using a He–Ne gas laser. The interface temperature is always the highest due to the absorption heat release near the interface. It was found that the thermal boundary layer (TBL) increased faster than the diffusion boundary layer (DBL), and the DBL thickness increased by adding the heat transfer additive. At 5 s after absorption started, the DBL thickness for 5 mass% NH₃ without and with the heat transfer additive was 3.0 and 4.5 mm, respectively. Marangoni convection was observed near the interface only in the cases with heat transfer additive. The Marangoni convection was very strong just after the absorption started and it weakened as time elapsed. It was concluded that the absorption performance could be improved by increasing the absorption driving potential (x_vb−x_vi) and by increasing the heat transfer additive concentration. The absorption heat transfer was enhanced as high as 3.0–4.6 times by adding the heat transfer additive that generated Marangoni convection.     

Numerical Investigation of Bubble Induced Marangoni Convection: Some Aspects of Bubble Geometry

Thermocapillary or Marangoni convection is a surface tension driven flow that occurs when a gas–liquid or vapor–liquid interface is subjected to a temperature gradient. In the past, the contribution to local heat transfer arising from Marangoni convection has been overlooked as insignificant since under earth gravity it is overshadowed by buoyant convection. This study numerically investigates some aspects of bubble size and shape on local wall heat transfer resulting from Marangoni convection about individual bubbles on a heated wall immersed in a liquid silicone oil layer (Pr = 110) of depth 5 mm. It was found that increasing bubble volume causes an increase in the area over which Marangoni convection has affect. Heat transfer therefore increases with bubble size. Over the effective area, the surface averaged hot wall heat transfer is not affected greatly by bubble shape. The surface averaged heat transfer over the effective area on both the hot and cold walls is affected dramatically by bubble size, but the increase is more profound on the cold wall.     

The Influence of Gravity and Confinement on Marangoni Flow and Heat Transfer Around a Bubble in a Cavity: A Numerical Study

Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the open literature. Despite extensive research efforts there still remains insufficient quantitative information regarding the impact of thermocapillary flow on the heat transfer. As a result, this paper aims to present a numerical investigation of the heat transfer enhancement due to Marangoni thermocapillary convection under both earth gravity (1-g) and zero gravity (0-g) conditions. A hemispherical bubble of fixed shape is considered atop a heated top wall of a domain with variable height. The heat transfer enhancement is quantified for Marangoni numbers in the range of 100 ≤ Ma ≤ 3,000 for channel heights of 1.5 ≤ H/R_b?≤ 7.5 which, for the 1-g cases, correspond with a Raleigh number range of 51 ≤ Ra_H?≤ 6.5 × 10⁴. For the most confined cases the flow and heat transfer were found to be very similar for the 0-g and 1-g cases. Also, the 0-g test cases were found to be very sensitive to increasing domain height whereas the 1-g simulations were far less sensitive.     

An experimental study of bubble behavior in a temperature gradient near a heated wall under low-gravity and microgravity conditions aboard NASA DC9 airplane

The behavior of a single bubble and a pair of bubbles under microgravity conditions has been investigated using the NASA-DC9 aircraft in order to understand the effects of various parameters and to control the bubble behavior in space. Silicone oil was used as the test liquid, and a nitrogen gas bubble was injected from the top wall under different experimental conditions. In an isothermal case, two different microgravity conditions were achieved by either fixing the experimental apparatus to the aircraft floor or freely floating the apparatus in the aircraft cabin. The bubble behavior was found to be clearly influenced by the quality of the microgravity environment, and variations of the bubble aspect ratio with the Bond number were presented. The results indicate that there is a critical Bond number of the order of 10⁻¹ which determines the bubble shape deformation. In the free-floating experiments, a temperature gradient was imposed on the liquid around the bubble near the heated top wall. Marangoni convection was expected to occur around the bubble and the bubble behavior was studied under various temperature gradients. The bubble aspect ratio was found to decrease with an increase in the Marangoni number. A theoretical model for the relation between the Marangoni flow around the bubble and the aspect ratio is proposed based on simple assumptions. Visualization of Marangoni convection around the bubbles using the photochromic dye activation method was successfully performed. The aspect ratios predicted by the model agreed with the experimental results reasonably well. Direct measurements of surface velocity are, however, necessary to further evaluate the validity of the model.     

Thermal interaction between laminar film condensation and forced convection along a conducting wall

Summary A theoretical analysis is presented to investigate the thermal interaction between laminar film condensation of a saturated vapor and a forced convection system separated by a heat conducting wall. In this work, the effect of the wall thermal resistance is considered. It is assumed that the countercurrent boundary layer flow is formed on the two sides. Governing boundary layer equations together with their corresponding boundary conditions for film condensation and forced convection are all cast into dimensionless forms by using the non-similarity transformation. The resulting system of equations is solved by using the local non-similarity method in conjunction with the fourth order Runge-Kutta method in conjunction with the Nachtsheim-Swigert iteration scheme. The total heat flux through the wall and the wall temperature distribution are determined. The present results show that the effect of the forced convection Prandtl number Pr _c is not negligible for large values of the thermal resistance ratioA ^*, and the effect ofA ^* and Pr _c on the overall heat transfer through the wall is more pronounced than that of the Jakob number and film Prandtl number.     

Experiments on the transition from the steady to the oscillatory marangoni convection of a floating-zone under various cold wall temperatures and various ambient air temperature effects

The transition from the steady to the oscillatory Marangoni convection of a floating-zone under various cold wall temperatures and various ambient air temperature effects have been investigated experimentally by heating the sample from above (opposite direction of Marangoni convection and buoyant forces). The heat transfer takes place mainly through conduction as well as the natural convection of the air around the cylindrical liquid bridge. The ambient airflow in the present work is varied by varying the cold wall temperature and ambient air temperature. In this study, the transition from the steady to the oscillatory Marangoni convection flow of a high Prandtl number fluid in a floating half-zone is visualized by means of the already proven method of the “light-cut-technique”. The test fluid zone is held in ambient air at +4 °C, +10 °C, +16 °C, +23 °C, and +28 °C. The onset of oscillations, the oscillation level, and oscillation pattern are investigated under various conditions. It is found that the critical temperature difference (ΔT_Cr) varies substantially when the cold wall temperature and the ambient air temperature are varied.     

Marangoni convection in a rectangular container

If the free liquid-gas interface of a liquid in a rectangular Container is subjected to a temperature gra-dient the shear stress on the free liquid surface being temperature dependent transmits by viscous traction a thermo-capillary convection into the bulk of the liquid. For constant temperature T ₁ at one wall and T ₂ at the other a steady Marangoni convection takes place while for time-oscillatory temperatures of the walls a time-dependent thermo-capillary convection appears, which will create wave patterns on the free liquid surface. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution, the response magnitude inside the Container, the forced free surface displacement and the influence of the Prandtl number have been investigated.

     

Marangoni Convection Instabilities Induced by Evaporation of Liquid Layer in an Open Rectangular Pool

In order to investigate the Marangoni convection instability of 0.65cSt silicone oil induced by evaporation in liquid layer, a series of experiments are carried out in an open rectangular pool. The effects of side wall temperature as well as ambient temperature on competitions between BM convection and thermocapillary convection are analyzed thoroughly. Increasing of the side wall temperature would inevitably enhance thermocapillary convection and suppress the formation of BM cells by transferring hot fluid from border to surface. As long as the side wall temperature is high enough, BM cells would disappear completely and multicellular rolls as well as hydrothermal waves would occur in the whole layer. Increasing ambient temperature would enhance both BM convection and thermocapillary convection, but the later one benefits more from it because hydrothermal waves can occur at a lower Ma number. Critical Marangoni numbers for the incipience of hydrothermal waves and that disappearance of BM convection cells are obtained under different ambient temperatures.     

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

In order to understand the stability characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr = 0.011) fluid, a linear stability analysis had been performed. The annular pool was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surface were adiabatic. The results show that the critical Marangoni number and the critical wave number decrease with the increase of the aspect ratio, which is defined as the ratio of the depth to the gap width of the annular pool. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. As the radius ratio increases, the critical Marangoni number decreases slightly, while the critical wave number increases. In the gravity condition, the effect of the buoyancy on the critical Marangoni number and wave number increases gradually with the increase of the aspect ratio.     

Visualization and model development of Marangoni convection in NH3–H2O systemVisualization et développement d'un modèle de convection de Marangoni dans un système à NH3–H2O

The objectives of this paper are to obtain experimental data of surface tension and interfacial tension, and to develop a new model of Marangoni convection for the best selection of heat transfer additive in ammonia–water absorption systems. The basic mechanism of Marangoni convection in absorption systems was reviewed from the viewpoints of the surface tension and the interfacial tension gradients. Marangoni convection was successfully visualized using a shadow graphic method. The solubility limits of the additives in ammonia–water solution ranged from 500 to 3000 ppm depending on the heat transfer additives. These values are much higher than those in LiBr–H₂O solution in which the solubility ranged from 70 to 400 ppm. The temperature gradient of the surface tension should not be a criterion for Marangoni convection inducement in NH₃–H₂O system. The concentration and temperature gradients of the interfacial tension should not be a criterion for Marangoni convection inducement in NH₃–H₂O system. The magnitude of the interfacial tension did not affect the occurrence of Marangoni convection either. It was found that addition of the heat transfer additive beyond the solubility limit assisted Marangoni convection occurrence, but should not be a criterion for Marangoni convection inducement. It was proposed that the radical-out model should be a criterion for Marangoni convection inducement within the solubility limit in NH₃–H₂O system.     

Time-dependent nodal integral methods in natural convection near a fluid density maximum

Time-dependent nodal integral methods were extended to natural convection near a fluid density maximum (inversion layer). An investigation of convection in a rectangular cavity as a function of tilt angle, aspect ratio, and other parameters was performed at low Rayleigh Number (Ra) using the low-order nodal integral methodologies. Bifurcation of the solution into flow and no-flow regimes was examined as a function of Ra and the dimensionless position (R) of the wall temperatures with respect to the extremum temperature. The first critical bifurcation point, Ra ^*, was shown to be a function of R as well as of angle of tilt and aspect ratio.     

Shear cell development for diffusion experiments in FOTON-Satellite missions and on the ground with consideration of shear-induced convection

A shear cell technique was developed to obtain exact diffusion data. The shear cell in this study was designed for the utilization under μg-conditions, especially in the FOTON-M2 mission, but also under 1g-conditions. To minimize the influence of the shear convection, the cell size, the rotation system and the speed of the discs were optimized. To minimize free surfaces, which can cause Marangoni convection, a reservoir system providing pressure on the liquid was introduced. Using this FOTON shear cell we performed short-time diffusion experiments in the In-Sn system in a parabolic flight and under 1g conditions to investigate the influence of the shear convection quantitatively. As a result, the influence of the shear convection was so small that the mean square diffusion depth caused by the shear convection was in the order of10^{? 7}m², which is smaller than 1% of the typical value X _diff ² ≈ 10^{? 4}m² in a standard diffusion experiment using the FOTON shear cell. By using this result a correction method for the evaluation of the diffusion coefficient was established. In several ground experiments, the FOTON shear cell showed the same diffusion coefficients as from μg reference experiments within the range of errors and no obvious indication of Marangoni convection was detected. From these results we confirmed that the FOTON shear cell can be applied to μg-experiments and ground-based experiments as well.     

Marangoni convection in a rectangular container

If the free liquid-gas interface of a liquid in a rectangular Container is subjected to a temperature gra-dient the shear stress on the free liquid surface being temperature dependent transmits by viscous traction a thermo-capillary convection into the bulk of the liquid. For constant temperature T ₁ at one wall and T ₂ at the other a steady Marangoni convection takes place while for time-oscillatory temperatures of the walls a time-dependent thermo-capillary convection appears, which will create wave patterns on the free liquid surface. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution, the response magnitude inside the Container, the forced free surface displacement and the influence of the Prandtl number have been investigated.     

Effects of wetted wall on laminar natural convection in vertical annular ducts

Abstract

A detailed numerical analysis is performed to investigate the effects of latent heat exchange, in connection with evaporation of the liquid film on the wall, on the natural convection heat transfer in vertical concentric annuli. Major governing parameters identified are Gr_T, Gr_M, Pr, Sc, and N. Results are specifically presented for an air‐water system under various heating conditions to illustrate the latent heat transport during the evaporation process. The effects of the channel length, ratio of radii N and wetted wall temperature on the momentum, heat and mass transfer are examined in detail. Tremendous enhancement in heat transfer due to the exchange of latent heat was clearly demonstrated.     

Surfactants with NH3H2O

To avoid rivulet flow in compact absorbers, which consist of compact heat exchanger plates, the surface tension of the ammonia-water solution has to be reduced by surfactants. The influence of these additives on the absorption of ammonia into water is investigated for two anionic tensides, two non-ionic tensides and the alcohol 1-octanol in a stagnant pool measuring cell. All four tensides had no influence on the absorption in the concentration range investigated (0.25–0.91 wt%), although they were able to reduce the surface tension of water down to 30mN m⁻¹. In order to increase the mass transfer, 1-octanol was used in three concentrations, which probably lead to a convection in the liquid layer, called Marangoni convection. The experiments have shown that the presence of surfactant islands is not necessary to induce Marangoni turbulence. The best result was achieved with 50 ppm 1-octanol dissolved in water.     

Bi12SiO20熔体表面张力对流研究

利用高温熔体实时观察装置观察和研究了Ｂi12SiO2０熔体表面张力对流从稳态向振荡态的转变过程;稳态过程中的对流图样变化;可能与对流转变有关的两个对流区域的交叉;振荡态对流的分叉现象。     

Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge

With a comprehensive and rigorous method, this paper has successfully examined the transient heat transfer in a steady and two-dimensional (2D) laminar boundary layer flow on a wedge with sudden change of thermal boundary conditions of uniform wall temperature (UWT) and heat flux (UHF). Additionally, a correlation of unsteady forced convection was also formulated through an exact solution of transient heat conduction (ξ=0) and the similarity solutions of a steady forced convection on a wedge (ξ=1) in this study. Particularly, for the wedge with −0.198838?ξ?1, the deviation of the wall temperatures estimated by correlation is less than 7.5% within full time of 0?ξ?1 comparing with numerical results in the case of UHF ranging from Pr=10⁻⁴ to 10⁴.     

Experimental study on time evolution of Marangoni flow instability in molten silicon bridge

Temperature oscillations due to Marangoni flow instability in molten silicon half zone bridges with various aspect ratios of As = 0.5–2.0 were measured using six thermocouples set azimuthally 60^° apart in the liquid bridge close to the cold rod. The Marangoni number was estimated to range from 3000 to 14000, based on the measured axial temperature difference. Fourier spectra of the temperature oscillations were broad and continuous; each peak was not clearly distinguished but rather appeared as a frequency band. Thus, the convection was estimated to be turbulent-like. The time evolution of the azimuthal wave number was observed by analyzing the time-dependence of the phase relationship of the temperature oscillation detected by the six thermocouples. Analyzing the mode appearance coefficient MAC as a function of the aspect ratio, the relationship between the azimuthal mode number m and the aspect ratio As was observed to be m ? As ≈ 2.4; the basic structure of flow instability is sustained even under high Marangoni number. The temperature oscillation data was decomposed into that for each frequency band by using wavelet analysis. The frequencies for the m = 1 and m = 3 modes were estimated to be 0.08 to 0.2 Hz and 0.01 to 0.2 Hz, respectively.     

Effects of CO2 shielding gas additions and welding speed on GTA weld shape

Gas tungsten arc (GTA) welding with deep penetration for high efficiency has long been of concern in industry. Experimental results showed that the small addition of carbon dioxide to the argon shielding gas produces an increase in the weld metal oxygen content, which is one of the compositional variables that strongly influence the Marangoni convection on the pool surface and ultimately change the weld pool shape. An inward Marangoni convection on the weld pool occurs, and hence a narrow and deep weld pool forms when the weld metal oxygen content is over the critical value of 100 ppm. When lower than this value, the weld shape becomes wide and shallow. A heavy oxide layer forms in the periphery area on the pool surface when the CO₂ concentration in the shielding gas is over 0.6%. This continuous heavy oxide layer becomes a barrier for oxygen absorption into the molten pool, and also changes the convection mode on the pool surface. A higher welding speed decreases the heat input and temperature gradient on the pool surface, which weakens the Marangoni convection on the liquid surface.