Effect of Marangoni number on thermocapillary convection and free-surface deformation in liquid bridges

Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.     

Coupled thermocapillary convection on Marangoni convection in liquid layers with curved free surface

This paper numerically studied the coupled Marangoni convection and thermocapillary convection in a finite liquid layer (Pr = 11.6) in the microgravity conditions. The multi-cellular flow structure and the marginal instability boundary of the coupled convection are predicted. Oscillatory coupled convection is also reported in concave liquid layers of volume ratio between 0.80 and 0.85.     

Contact angles and interface behavior during rapid evaporation of liquid on a heated surface

Photographic observations of the boiling phenomena have played an important role in gaining insight into the boiling mechanism. This paper presents a brief historical review of the available literature on the photographic studies in pool and flow boiling. This is followed by the results of the photographic studies conducted in the authors' laboratory on liquid droplets impinging on a heated surface. Liquid-vapor interface and contact line movements are observed through a high speed camera at high resolution. The effect of surface roughness and surface temperature on dynamic advancing and receding contact angles has been studied. In addition, the effects of rapid evaporation on advancing and receding contact angles, liquid-vapor interface motion, and the dryout front propagation have been investigated.     

Instability of the Marangoni convection in a liquid bridge with liquid encapsulation under microgravity condition

Linear stability theory is used to analyze the stability of the basic state solution of Marangoni convection in a liquid bridge with liquid encapsulation. By processing the linear disturbance equations numerically, stability analysis can be evolved to a complex general eigenvalue problem. Inverse iteration algorithm combined with LZ algorithm is employed to solve the complex generalized eigenvalue problem. The results show that the stability of the system can be enhanced greatly by choosing reasonable matching parameters of the two fluid layers. The preferred mode of instability is axial wave number α=2,3 and 4, which means that the system is more sensitive to the disturbance with larger wave lengths.     

On effect of non-uniform basic temperature gradient on Bénard–Marangoni convection in micropolar fluid

Linear stability analysis is performed to study the effect of non-uniform basic temperature gradients on the onset of Bénard–Marangoni convection in a micropolar fluid. The influence of various parameters on the onset of convection has been analysed. The possibility of delaying the onset of convection by the application of a cubic basic state temperature profile is demonstrated.     

Forced convection droplet evaporation with finite vaporization kinetics and liquid heat transfer

Stagnation point calculations, including the effects of liquid phase heat transfer and finite rate evaporation kinetics, are presented for the case of a high Reynolds number flow over a vaporizing droplet. A correlation is developed to compute the entire droplet vaporization rate from the stagnation point results. Numerical emphasis is placed on high temperature, rapid vaporization processes such as occur in flight vehicle engines, and sufficient calculations are presented to allow estimates for any given case to be made.     

Influence of thermal and solutal Marangoni effects on free surface deformation in an open rectangular cavity

Steady thermo-solutocapillary convection in a rectangular cavity with deformable free surface under microgravity condition is numerically studied, where level set method is employed to capture the free surface deformation. Both the temperature and solute concentration gradients are applied horizontally. The computational results show that, as the thermal to solutal Marangoni number ratio varies between-10 and-1(namely,-10 ≤ R_σ -1), the flow field exists one anti-clockwise rotating convective cell driven by thermocapillary convection, and the free surface bulges out near the left end wall and bulges in near the right end wall. As-1 R_σ 0, the flow field exists one clockwise rotating convective cell driven by solutocapillary convection, and the free surface bulges out near the right end wall and bulges in near the left end wall. As R_σ =-1, the flow field consists of one clockwise and one anti-clockwise rotating convective cells, and the free surface bulges in at the central point and bulges out near the left and right end walls.     

A study of the liquid evaporation with Darcian resistance effect on mixed convection in porous media

A problem of the evaporation of liquid with Darcian resistance effect on mixed convection flow over a vertical plate in an isotropic porous medium has been studied. Two flow models, aiding and opposing flows, are considered. The boundary layer equations are integrated numerically to obtain the non-similar solutions for the velocity, temperature and concentration distributions for several values of the Darcian resistance and buoyancy force parameters. The results show that the evaporation of liquid on the wall increases when the buoyancy force Ra_K / Pe_x is gradually increased and the overall heat transfer rate will be pronounced when the Darcian resistance ζ is very small.     

The drying of liquid films on cylindrical and spherical substrates

The drying of liquid films from binary solid–solvent mixtures on cylindrical and spherical substrates is investigated by solving the diffusion equation on the cylindrical or spherical domains with account for the shrinkage of the systems due to the solvent evaporation. As a main result of the gas phase analysis, d²-laws for both the cylindrical and the spherical cases are found. The spatio-temporal evolution of the component mass fractions in the liquid are obtained for varying initial film thickness and drying conditions. Large mass fraction gradients, formed at high drying rates, lead to a skin-core morphology with low product quality. Initially very thin films dry very uniformly, which is analogous to the flat temperature profiles in unsteady heat conduction at small Biot numbers. The maximum initial film thickness allowable to ensure flat solute mass fraction profiles in the films, and thus high quality of the dry films, is computed for varying drying rates. From these results a guideline for the drying of liquid films on cylindrical and spherical substrates is deduced.     

Soret,viscous dissipation,and thermal radiation effects on MHD free convective flow of Williamson liquid with variable viscosity and thermal conductivity

The flow model of heat and mass transport of a Williamson liquid through a porous stretching sheet with radiation, viscous dissipation, Soret effect, and chemical reaction has been explored. The motion starts from the slot to the free stream. The present study is unique, because it examines the flow of a Williamson fluid under the influence of variable viscosity and thermal conductivity. The Williamson fluid term as added to the momentum and energy equation is considered in a nonlinear form as compared with other studies in literature. The flow model is a set of coupled highly nonlinear partial differential equations that are simplified and lead to coupled nonlinear total differential equations by employing sufficient similarity variables. The simplified equations are later solved by utilizing the spectral homotopy analysis method. Our experiment shows that the injected variable viscosity, together with thermal conductivity, has a great impact on the fluid profiles. An increase in the Williamson parameter (β) leads to a decrease in the thickness of the hydrodynamic thermal layer. Our numerical calculations were compared with earlier published work, and they were discovered to be correct.     

Numerical study of natural convection in asymmetrically heated channel considering thermal stratification and surface radiation

This article consists in a numerical study of the influence of thermal stratification and surface radiation on laminar airflow induced by natural convection in vertical, asymmetrically heated channels. Several cases are investigated to spotlight their influence on fluid dynamics and thermal quantities. Thermal stratification is obtained by a weak gradient of temperature outside of the channel, and then the temperature at the bottom end of the channel is considered as a function of time. Significant effects on vertical velocities, mass flow, and flow structure are shown. Surface radiation is also considered but appears less predominant than thermal stratification for the selected conditions of this article. The impact on heat transfer is also evaluated for each studied configuration. It is observed that local and mean Nusselt numbers weakly increase for the investigated cases.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

Effects of thermal nonequilibrium and non-uniform temperature gradients on the onset of convection in a heterogeneous porous medium

The simultaneous effect of local thermal nonequilibrium (LTNE), vertical heterogeneity of permeability, and non-uniform basic temperature gradient on the criterion for the onset of Darcy-Benard convection is studied. The eigenvalue problem is solved numerically using the Galerkin method. The interaction of various types of permeability heterogeneity and non-uniform basic temperature gradient functions on the stability characteristics of the system is analyzed. It is observed that the linear variation (about the mean) of the permeability and the basic temperature gradient with depth has no added effect on the criterion for the onset of convection. However, the concurrent variation in heterogeneous permeability and non-uniform basic temperature gradient functions has more stabilizing effect on the system, while opposite is the trend when the effect of non-uniform basic temperature gradient alone is present.     

Rotation,electromagnetic field,and variable thermal conductivity effects on free convection flow past an eternity vertical porous plate

The present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo-elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase.     

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.     

Non-uniform porosity and thermal dispersion effects on natural convection about a heated horizontal cylinder in an enclosed porous medium

A numerical solution has been obtained for transient two-dimensional natural convection from a heated horizontal cylinder embedded in an enclosed porous medium. Non-Darcian effects are taken into consideration in the momentum equation, while the thermal dispersion effect is taken into consideration in the energy equation. The wall effect on porosity is approximated by an exponential function and its effect on thermal dispersion is modeled by a dispersive length. The governing equations in terms of the stream function, vorticity, and temperature are expressed in a body-fitted coordinate system, which were solved numerically by the finite difference method. Results are presented for the streamlines and isotherms, tangential velocity and temperature distributions, as well as the average Nusselt numbers at different values of Rayleigh number, dimensionless particle diameter, and Prandtl number. The non-uniform porosity effect tends to increase the temperature gradient near the wall while the thermal dispersion effect increases the effective thermal conductivity, both resulting in an increase in surface heat flux. The effect of thermal dispersion on natural convection in porous media at low to moderate Rayleigh number is small. With nonuniform porosity and thermal dispersion effects taken into consideration, the predicted average Nusselt numbers are found to be in better agreement with experimental data.     

Natural convection in partially divided square enclosures: Effects of thermal boundary conditions and thermal conductivity of the partitions

Natural convection in partitioned square enclosures filled with air is numerically studied, trying to characterize these enclosures mainly in what concerns its overall heat transfer performance. Two partitions of finite thickness are considered, placed in the enclosure following an ordered arrangement, which position, length and thermal conductivity are varied for some values of Rayleigh number and for different thermal boundary conditions. Study starts considering the simplest enclosures with two adiabatic partitions, after the more realistic enclosures of heat conductive walls and partitions are considered, and finally the even more realistic situation of enclosures with heat conductive partitions and walls subjected to cyclic thermal boundary conditions in the vertical direction is also considered. Position and length of the enclosures’ effects depend on the thermal boundary conditions prescribed for the enclosure, and different thermal boundary conditions (corresponding to the heating or cooling operations or seasons) are considered to capture this effect. Fluid flow field, thermal field and heat transfer are analyzed for some particular situations through the streamlines, isotherms, and heatlines. The overall thermal performance of the enclosure is analyzed through the overall Nusselt number, and many data are compactly presented for different placements and lengths of the partitions, for different thermal conductivity of the walls and partitions of the enclosure, for different Rayleigh numbers and for different thermal boundary conditions imposed to the enclosure. Considered boundary conditions and the enclosure walls and partitions of finite thickness and finite thermal conductivity are much more realistic conditions than simply the single cavity without walls and with perfectly adiabatic partitions usually considered in many studies of this kind.     

Fabrication and opto-electric properties of ITO/ZnO bilayer films on polyethersulfone substrates by ion beam-assisted evaporation

Transparent conducting oxides bilayer films stacked by one 130-nm-thick indium tin oxide (ITO) top layer and one 75-nm-thick zinc oxide (ZnO) buffer layer were grown onto polyethersulfone (PES) substrates by ion beam-assisted evaporation. The effects of ion energy and ZnO buffer layers on the structural and opto-electric properties of ITO films were initially investigated. The as-deposited ZnO buffer layers show wurtzite (0 0 2) preferred orientation on the PES substrates with ion beam assistance. The results of X-ray diffraction reveal a marked increase in the crystallinity of the ITO films which use ZnO as a buffer layer material. A drop of ∼60% in electrical resistivity of the ITO film on the PES can be achieved by using ZnO buffer layer. The transmittance of the ITO/ZnO bilayer was not deteriorated due to the insertion of ZnO layer. The lowest electrical resistivity of 6.552×10⁻⁴ Ω-cm associated with the transmittance of ∼80% at the wavelength of 550 nm can be obtained for the ITO film on the ZnO-coated PES at ion energy of 60 eV. The ITO films on the ZnO-buffered PES with moderate control of ion energy have a promising future for the application of the contact layers for flexible solar cells.