Numerical Investigation of Marangoni Convection Around a Vapor Bubble in Aqueous Surfactant Solutions

2000 ◽  
Author(s):  
Vivek M. Wasekar ◽  
Raj M. Manglik ◽  
Milind A. Jog
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Marangoni Convection ◽  
Bubble Surface ◽  
Heated Wall ◽  
Rate Equations ◽  
Bulk Liquid ◽  
Initial Time ◽  
Self Diffusion ◽  
Bubble Sizes

Abstract The effect of surfactant concentration on the Marangoni convection around vapor bubbles has been numerically investigated. The model consists of an adiabatic, hemispherical bubble on a downward facing constant temperature heated wall, in a fluid pool with an initial uniform temperature gradient. The time-dependent liquid mass, momentum, energy, surfactant bulk and surface transport, and adsorption kinetic rate equations are solved simultaneously. Conditions for bubble sizes varying from boiling nuclei to growing bubbles, and different surfactant bulk concentrations and wall heat flux levels are represented by a range of Marangoni and Rayleigh numbers: 100 ≤ MaT ≤ 6000, 0 ≤ MaS ≤ 2.2×106, 0 ≤ Ra ≤ 2.2. In the early transients, liquid motion is found to be induced by the temperature non-uniformity over the bubble surface, which along with self-diffusion, transports surfactant molecules from the bulk liquid towards the bubble surface. Consequently, the surface excess concentration is higher at the bubble base and decreases along the interface towards the bubble crown. The resulting concentration gradients promote diffusocapillary flows, which act in the same direction as the temperature-gradient induced thermocapillary flows, thereby enhancing the convection significantly. Also, for conditions representing boiling nuclei (in both partially and fully developed boiling regimes), the initial time transients appear to be heat flux independent.

Experimental Analysis of the Heat Transfer Induced by Thermocapillary Convection Around a Bubble

1999 ◽  
Vol 122 (1) ◽  
pp. 66-73 ◽  
Author(s):  
P. Arlabosse ◽  
L. Tadrist ◽  
H. Tadrist ◽  
J. Pantaloni
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Marangoni Convection ◽  
Heated Wall ◽  
Meridian Plane ◽  
Oil Viscosity ◽  
Dimensionless Numbers ◽  
Wide Range

The surface tension driven flow in the liquid vicinity of gas bubbles on a heated wall and its contribution to the heat transfer are investigated experimentally in a configuration where surface tension force and buoyancy forces oppose one another. This liquid flow caused by the temperature gradient along the interface is called thermocapillary or thermal Marangoni convection. The studies were made with silicone oils of different viscosities so that a wide range of dimensionless numbers were encountered. The velocity fields are determined from the motion of carbon particles in the meridian plane of the bubble. The influence of the temperature gradient, the oil viscosity, and the bubble shape on the profiles along the interface and in the direction normal to the interface is analyzed. The temperature field is determined by holographic interferometry. For the axisymmetric problem, the interferograms are evaluated by solving the Abel-integral equation. From the isotherms, the temperature distribution along the bubble surface and in the liquid beneath the bubble is measured. To quantify the contribution of thermocapillarity to the heat transfer, the heat flux transferred by thermocapillarity is measured. A heat exchange law giving the increase in heat flux due to Marangoni convection in comparison to the conductive regime is proposed. [S0022-1481(00)70501-9]

Influence of Thermal Loading on the Thermal Conductivity of Single-Wall Carbon Nanotube

2008 ◽  
Author(s):  
Bin-Hao Chen ◽  
Ming-Shan Jeng ◽  
Fang-Hei Tsau
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Carbon Nanotube ◽  
Temperature Gradient ◽  
Thermal Loading ◽  
Dynamics Simulation ◽  
Initial Time ◽  
Single Wall Carbon Nanotube ◽  
Single Wall Carbon

This investigation determines carbon nanotube thermal conductivity at heat flux ranging from 0.01 to 0.3 subject to different thermal loading of 5 ∼ 50 K/nm, using a non-equilibrium molecular dynamics simulation with true carbon potentials. The numerical model adopts Morse bending, a harmonic cosine and a torsion potential. The applied Nose´-Hoover thermostate describes atomic interactions taking place between the atoms. Hot and cold temperature reservoirs are respectively imposed on both computational domain sides to establish the temperature gradient along the carbon nanotube. Atoms at the interface exhibit transient behavior and undergo an exponential type decay with exerted temperature gradient. The thermal impact causes system fluctuation in the initial 3 ps leading to a transport region temperature as high as 600K. The thermal relaxation process reduces impact energy influence after 30 ps and leads to Maxwell’s distribution. Steady-state constant heat flux is observed after thermal equilibrium. Furthermore, the temperature curves show distinct high disturbance at initial time and linear distribution along the tube axial direction after steady-state. Results suggest that thermal conductivity value increases with increasing CNT subjected to thermal loading up to a temperature gradient of at least ∼ 41.3 K/Å representing thermal gradient convergence at heat conduction value 1258. Simulation results yield precise understanding of nano-scale transient heat transfer characteristics in a single-wall carbon nanotube.

scholarly journals Computational fluid dynamics and population balance modelling of nucleate boiling of cryogenic liquids: Theoretical developments

2016 ◽  
Vol 8 (4) ◽  
pp. 178-200 ◽  
Author(s):  
Guan Heng Yeoh ◽  
Xiaobin Zhang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nucleate Boiling ◽  
Nucleation Site ◽  
Heat Transfer Process ◽  
Wall Heat Flux ◽  
Heated Wall ◽  
Balance Model ◽  
Bulk Liquid ◽  
Two Phase

The main focus in the analysis of pool or flow boiling in saturated or subcooled conditions is the basic understanding of the phase change process through the heat transfer and wall heat flux partitioning at the heated wall and the two-phase bubble behaviours in the bulk liquid as they migrate away from the heated wall. This paper reviews the work in this rapid developing area with special reference to modelling nucleate boiling of cryogenic liquids in the context of computational fluid dynamics and associated theoretical developments. The partitioning of the wall heat flux at the heated wall into three components – single-phase convection, transient conduction and evaporation – remains the most popular mechanistic approach in predicting the heat transfer process during boiling. Nevertheless, the respective wall heat flux components generally require the determination of the active nucleation site density, bubble departure diameter and nucleation frequency, which are crucial to the proper prediction of the heat transfer process. Numerous empirical correlations presented in this paper have been developed to ascertain these three important parameters with some degree of success. Albeit the simplicity of empirical correlations, they remain applicable to only a narrow range of flow conditions. In order to extend the wall heat flux partitioning approach to a wider range of flow conditions, the fractal model proposed for the active nucleation site density, force balance model for bubble departing from the cavity and bubble lifting off from the heated wall and evaluation of nucleation frequency based on fundamental theory depict the many enhancements that can improve the mechanistic model predictions. The macroscopic consideration of the two-phase boiling in the bulk liquid via the two-fluid model represents the most effective continuum approach in predicting the volume fraction and velocity distributions of each phase. Nevertheless, the interfacial mass, momentum and energy exchange terms that appear in the transport equations generally require the determination of the Sauter mean diameter or interfacial area concentration, which strongly governs the fluid flow and heat transfer in the bulk liquid. In order to accommodate the dynamically changing bubble sizes that are prevalent in the bulk liquid, the mechanistic approach based on the population balance model allows the appropriate prediction of local distributions of Sauter mean diameter or interfacial area concentration, which in turn can improve the predictions of the interfacial mass, momentum and energy exchanges that occur across the interface between the phases. Need for further developments are discussed.

Short-Time-Transient Surfactant Dynamics and Marangoni Convection Around Boiling Nuclei

2003 ◽  
Vol 125 (5) ◽  
pp. 858-866 ◽  
Author(s):  
Vivek M. Wasekar ◽  
Raj M. Manglik
Keyword(s):  
Temperature Gradient ◽  
Marangoni Convection ◽  
Bubble Radius ◽  
Surface Concentration ◽  
Heated Wall ◽  
Short Time Scale ◽  
Surfactant Adsorption ◽  
Dependent Transport ◽  
Interfacial Surfactant ◽  
Short Time

The effects of surfactant concentration on the initial short-time-scale Marangoni convection around boiling nuclei in aqueous solutions have been computationally investigated. The model consists of a hemispherical bubble (1–100 μm radius) on a downward-facing constant-temperature heated wall in a fluid pool with an initial uniform temperature gradient. Time-dependent transport of liquid mass, momentum, energy, and surfactant bulk and surface convection along with the adsorption kinetics are considered. Conditions for bubble sizes, surfactant bulk concentrations, and wall heat flux levels are represented by a range of thermocapillary and diffusocapillary Marangoni numbers (6⩽MaT⩽103,0⩽MaS⩽8.6×105) over a micro-scale time period (1 μs–1 ms). With a surfactant in solution, a surface concentration gradient develops at the bubble interface that tends to oppose the temperature gradient and reduce the overall Marangoni convection. The maximum circulation strength, which is dependent on the bubble size, corresponds to a characteristic surfactant adsorption time. This, when scaled by a ratio of bubble radius, is found to depend solely on the surfactant bulk concentration. Moreover, the interfacial surfactant adsorption does not display a stagnant cap behavior for the range of parameters and time scales covered in this study.

Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep

1971 ◽  
Vol 45 (4) ◽  
pp. 759-768 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Kinetic Theory ◽  
Effective Thermal Conductivity ◽  
Half Space ◽  
Thermal Creep ◽  
Kinetic Theory Of Gases ◽  
Boundary Wall ◽  
Creep Velocity

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.

PROPERTIES OF HEAT FLUX FUNCTIONS AND A LINEAR THEORY OF HEAT FLUX

1995 ◽  
Vol 09 (09) ◽  
pp. 1113-1122 ◽  
Author(s):  
LIQIU WANG
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Linear Function ◽  
Linear Theory ◽  
Strain Tensor ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Flux Vector ◽  
Heat Flux Vector

The symmetry and positive definiteness of thermal conductivity tensor K are used to derive some properties of heat flux functions ɸi (i=0, 1, 2). All ɸi are shown to be real-valued. Both ɸ0 and ɸ2 are found to be positive definite, and ɸ1 is constrained between −(ɸ0 + ɸ2) and (ɸ0 + ɸ2). By assuming heat flux vector q to be a linear function of temperature gradient ∇θ and velocity strain tensor D, ɸi reduce to three coefficients which are independent of D and ∇θ.

scholarly journals Experimental Heat Transfer Investigation of Stationary and Orthogonally Rotating Asymmetric and Symmetric Heated Smooth and Turbulated Channels

1992 ◽  
Author(s):  
H. A. El-Husayni ◽  
M. E. Taslim ◽  
D. M. Kercher
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Rotation Number ◽  
Symmetric Case ◽  
Wall Heat Flux ◽  
Heated Wall ◽  
Wall Heat Transfer ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Smooth Channel

An experimental investigation was conducted to determine the effects of variations in wall thermal boundary conditions on local heat transfer coefficients in stationary and orthogonally rotating smooth wall and two opposite-wall turbulated square channels. Results were obtained for three distributions of uniform wall heat flux: asymmetric, applied to the primary wall only; symmetric, applied to two opposite walls only; and fully-symmetric, applied to all four channel walls. Measured stationary and rotating smooth channel average heat transfer coefficients at channel location L/Dh = 9.53 were not significantly sensitive to wall heat flux distributions. Trailing side heat transfer generally increased with Rotation number whereas the leading wall results showed a decreasing trend at low Rotation numbers to a minimum and then an increasing trend with further increase in Rotation number. The stationary turbulated wall heat transfer coefficients did not vary markedly with the variations in wall heat flux distributions. Rotating leading wall heat transfer decreased with Rotation number and showed little sensitivity to heat flux distributions except for the fully-symmetric heated wall case at the highest Reynolds number tested. Trailing wall heat transfer coefficients were sensitive to the thermal wall distributions generally at all Reynolds numbers tested and particularly with increasing Rotation number. While the asymmetric case showed a slight deficit in trailing wall heat transfer coefficients due to rotation, the symmetric case indicated little change whereas the fully-symmetric case exhibited an enhancement.

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