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.     

Transient Free Convection and Thermal Stratification in Uniformly—Heated Partially—Filled Horizontal Cylindrical and Spherical Vessels

An integral approach has been used to analyze the development of the free convection boundary layer on heatedconcave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar andturbulent velocity and temperature profiles closed form expressions for the boundary layer thickness,velocityscale as well as the boundary layer commencement after the point of instability are obtained.In addition,themass flowrate to the thermal stratified region is given.     

Simulation of Thermocapillary Convection in a Two—Layer Immiscible Fluid System using a Boundary Element Method

A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid systemwith flat and free interface has been developed.The divergence theorem is applied to the non-linear convectivevolume integral of the boundary element formulation with the pressure penalty function.Consequently,velocitygradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficultyof convective discretizations and provides considerable reductions in storage and computational requirementswhile improving accuracy.In this paper,we give the influence of different parameters(Marangoni number,Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by thenumerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately,the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface onthermocapillary convection is also shown.     

Challenges of Tomorrowm——Fire Hazards of Systems Using Renewable Sources of Energy

Dramatic climate change, caused by over consumption of coal, oil and other traditional energy sources, as well as exhaustion of their reserves, imposed technological need to look for their substitution with new, renewable energy sources. The exploitation of these new forms of energy, solar, wind, earth and bio-fuels, initiated the development and application of new technologies, so far unused in practice. Rapid development and wide application of installations for use of renewable energy in many households and companies opened a whole new risk and danger in the fire protection field. With the purpose of introducing this problem to engineers in the area of fire protection, health and safety at work, this paper systematically presents various types of facilities for exploitation of renewable energy sources as well as potential dangers, risks and issues related to their safe operation.     

Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.     

Marangoni Convection in the LiCaAIF_6 Crystal Growth by the Czochralski Technique

Numerical simulation of the mixed convection induced by buoyancy, crystal rotation, and also unbalanced surface tension at the melt-gas interface is conducted by means of the finite volume method in the model of the Czochralski crystal growth. The role of Marangoni convection in the heat and mass transfer is investigated by the comparison of the models with and without surface tension included, and our results indicate that Marangoni convection plays an important role in the heat and mass transfer near the interface of melt and crystal, and also the convection structure.     

Application of program generation technology in solving heat and flow problems

Based on a new DIY concept for software development,an automatic program-generating technology attached ona software system called as Finite Element Program Generator(FEPG)provides a platform of developing pro-grams,through which a scientific researcher can submit his special physico-mathematical problem to the systemin a more direct and convenient way for solution.For solving flow and heat problems by using finite elementmethod,the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficul-ties caused mainly due to the dominated convection.A couple of benchmark problems are given in this paper asexamples to illustrate the usage and the superiority of the automatic program generation technique,including theflow in a lid-driven cavity,the starting flow in a circular pipe,the natural convection in a square cavity,and theflow past a circular cylinder,etc.They are also shown as the verification of the algorithms.     

Effect of Complex Parameters of Porous Media on Desalination Performance in Air-Gap Diffusion Distillation Based on Multiple Regression Analysis

Air-Gap Diffusion Distillation(AGDD) is a new technology aiming at solving the problem of the safety of drinking water for residents in remote areas that uses a super hydrophilic porous medium as the hot channel and evaporation surface. In the experiment, it was found that the parameters of porous media have a significant influence on the desalination(evaporation) efficiency of AGDD. Although porous media are widely used as evaporation components, the factors affecting their evaporation efficien...     

Numerical Study of Forced Convection Lid-Driven Cavity Flows Using LES （Large Eddy Simulation）

This study presents the LES （large eddy simulation） of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state. The main purpose is the evaluation of a developed numerical methodology for the simulation of forced convection flows at various Reynolds numbers （100 _〈 Rex 〈_ 10,000） and for a fixed Prandtl number （Pr = 1.0）. The hexahedral eight-node FEM （finite element method） with an explicit Taylor-Galerkin scheme is used to obtain the numerical solutions of the conservation equations of mass, momentum and energy. The Smagorinsky model is employed for the sub-grid treatment. The time-averaged velocity and temperature profiles are compared with results of literature and a CFD （computational fluid dynamics） package based on finite volume method, leading to a highest deviation of nearly 6%. Moreover, characteristics of the forced convection flows are properly obtained, e.g., the effect of the Reynolds number over the multiplicity of scales.     

Nonlinear parity space applied to an electric autonomous vehicle

The autonomous navigation of an electric vehicle requires the implementation of a number of sensors and actuators intended to inform it about his environment or his position and velocity and deliver necessary inputs. That＇s why it is important to detect and locate sensor and actuator faults as soon as possible to enable the operator to run the vehicle in degraded mode or use the fault tolerant control system if it exists. The main purpose of this paper deals with sensors or actuators faults diagnosis of autonomous vehicle. A diagnosis method using a nonlinear model of the vehicle is developed. Nonlinear state space model of the autonomous electric vehicle is used with the method of nonlinear analytical redundancy to detect and to isolate faults occurred on sensors or actuators. Computer simulations are carried out to verify the effectiveness of the method.     

Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated Porous Medium

Steady state solutions are obtained for non-Darcy free convection flow along a horizontal cylinder in a non-Newtonian fluid saturated porous medium. The boundary-layer equations governing the flow are solved numerically by using an implicit finite-difference method developed by Keller. Numerical results are obtained for the velocity and heat transfer at the wall for various values of the parameters namely, the Ergun number, Rayleigh number, power-law index and transpiration parameter.     

Non-Darcy natural convection of a non-Newtonian fluid in a porous cavity

A numerical study of non-Darcy natural convection in a porous enclosure saturated with a power-law fluid is presented. Hydrodynamic and heat transfer results are reported for the configuration in which the enclosure is heated from a side-wall while the horizontal walls are insulated. The flow in the porous medium is modeled using the modified Brinkman–Forchheimer-extended Darcy model for power-law fluids, which accounts for both inertia and boundary effects. The results indicate that when the power law index is decreased, the circulation within the enclosure increases leading to a higher Nusselt number and these effects are enhanced as the Darcy number is increased. Consequently as the power law index decreases, the onset of the transitions from Darcy regime to Darcy–Forchheimer–Brinkman regime to asymptotic convection (boundary layer) regime shift to higher corresponding values of the Darcy number. An increase in Rayleigh number produces similar effects as a decrease in power law index.     

Modelling of Non-Darcy Flows through Porous Media Using Extended Incompressible Smoothed Particle Hydrodynamics

In this article, a novel numerical method is presented for the simulation of non-Darcy flows through porous media by the incompressible smooth particle hydrodynamics (ISPH) method with a predictor-corrector scheme. In the ISPH algorithm, a semi-implicit velocity-correction procedure is used and the pressure is obtained by solving the pressure Poisson equation. The key point for the application to non-Darcy flows is to include porosity and drag forces of the medium (the Darcy term and the Forcheimer term) in the ISPH method. Unsteady lid-driven flow, natural convection in non-Darcy porous cavities, and natural convection at a porous medium–fluid interface are examined separately by our extended ISPH method. The results are presented with flow configurations, isotherms, and average Nusselt numbers for different Darcy numbers from 10^?4 to 10^?2, porosity values from 0.4 to 0.9, and Reynolds/Rayleigh numbers. The flow pattern and rate of heat transfer inside the cavity are affected by these parameters. The results demonstrate the important effect of the Darcy number on both the heat transfer rate and the flow regime. The results from this investigation are well validated and compare favorably with previously published results.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Natural Convection in a Non-Darcy Porous Cavity Filled with Cu–Water Nanofluid Using the Characteristic-Based Split Procedure in Finite-Element Method

Natural convection of Cu–water nanofluid in a differentially heated non-Darcy porous cavity was numerically investigated by using the characteristic-based split algorithm in finite element method. Effects of the various thermophysical parameters and the solid volume fraction of nanoparticle on heat transfer and fluid flow in different flow regimes were demonstrated. Although the addition of nanoparticles in the porous medium generally resulted in the higher average Nusselt number in most flow regimes, the average Nusselt number appears to decrease or stay nearly the same with increased solid volume fraction in Darcy flow regime at a high Rayleigh number and low Darcy number.     

Double diffusive natural convection in an enclosure filled with a step type porous layer: Non-Darcy flow

The double diffusive natural convection between a saturated porous layer and an overlying fluid layer in an enclosure has been investigated using the non-Darcy flow model. The problem has been investigated for two cases; namely case I where the interface between fluid and porous layer is horizontal, and case II where the interface contains a step that has a height a. The fluid flow and heat and mass transfer has been investigated for different values of the step height and the Rayleigh and Darcy numbers. The results show that the height of the step at the interface has a significant effect on the flow field and heat and mass transfer from the left-hand to the right-hand walls in the composite enclosure. This is very important for insulation problems and for heat and mass blockage in enclosure systems.     

Analysis of Laminar Mixed Convective Heat Transfer in Horizontal Triangular Ducts

Numerical simulations for fluid flow and heat transfer in triangular ducts are carried out. Flow is considered to be laminar, hydrodynamically, and thermally developing. Heat transfer by both forced and natural convection is taken into account. Simulations are carried out for constant wall temperature cases which are at a higher temperature than the inlet temperature of the fluid. The effect of Rayleigh number on bulk mean temperature and Nusselt number is studied. Isotherm and secondary velocity profile formed because of natural convection is shown at different locations with varying Rayleigh number. The effect of the apex angle of the triangular duct on Nusselt number and bulk mean temperature is studied. Results are compared with the cases of mixed convective heat transfer in a square duct.     

Buoyancy-induced flow and heat transfer in a porous annulus between concentric horizontal circular and square cylinders

ABSTRACT

This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature T_h, whereas the cooled outer square duct is held at the uniform cold temperature T_c. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (?), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ?. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.     

Non-Darcy Mixed Convection in a Porous Square Enclosure Under Suction/Injection Effects with a Non-Isothermal Vertical Wall

The influence of suction/injection at bottom/top or top/bottom walls on non-Darcy mixed convection flow with a sinusoidally varying temperature on the left vertical wall in a two-dimensional square porous enclosure is analyzed. The Forchheimer extended Darcy model is considered for flow equations. The fully developed equations are nondimensionalized, and then solved numerically by the Galerkin finite element method. A parametric study is carried out and the results are obtained for various values of the parameters such as the Grashof number (Gr*), Rayleigh number (Ra), suction/injection velocity (a), suction/injection window width (D/H), and amplitude (λ) of the sinusoidally varying temperature profile. The computed flow and temperature fields are visualized through streamlines, isotherms, and loal/global cumulative heat flux plots.