Flow transitions in vacuum arc remelting

Abstract

The metallurgical structure of an ingot produced by vacuum arc remelting (VAR) depends critically on the temperature distribution within the liquid portion of the partially solidified ingot. This, in turn, depends on the fluid motion in the pool, since the dominant mechanism for transporting heat is convection. There are three primary sources of motion: buoyancy; Lorentz forces arising from the passage of current through the pool; and Lorentz forces arising from the presence of external inductors. These forces are constantly in competition with each other, and each tends to induce a quite different distribution of velocity and temperature. We examine the transition between these different flow regimes and derive dimensionless criteria which determine which regime is dominant. We show that the structure of an ingot produced by VAR depends critically on the temperature distribution within the liquid portion of the partially solidified ingot. This, in turn, depends on the fluid motion in the pool, since the dominant mechanism for transporting heat is convection. There are three primary sources of motion: buoyancy; Lorentz forces arising from the passage of current through the pool; and Lorentz forces arising from the presence of external inductors. These forces are constantly in competition with each other, and each tends to induce a quite different distribution of velocity and temperature. We examine the transition between these different flow regimes and derive dimensionless criteria which determine which regime is dominant. We show that modest changes in ingot current can produce radical changes in temperature distribution, and that weak, steady magnetic fields, of only ～1 Gs, can induce a powerful swirling motion which suppresses the normal flow.     

Hydromagnetic stagnation point flow by a perturbation technique

An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generating/absorbing fluid at the stagnation point of an isothermal two-dimensional porous body immersed in a fluid saturated porous medium. The results are obtained by solving the coupled non-linear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique [A. Aziz, T.Y. Na, Perturbation Methods in Heat Transfer, Springer-Verlag, Berlin, 1984 (pp. 1–184), R. Kenneth Cramer, Shih-I Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill Book Company, New York, 1973 (pp. 164–171).]. These results are presented to illustrate the influence of the Hartmann number, Prandtl number, and dimensionless heat generation/absorption coefficient and suction injection parameter. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These effects of the different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are presented graphically.     

Effect of thermal conductivity ratio on flow features and convective heat transfer

In this paper, we numerically investigate the steady laminar natural convection in a water-filled 2D enclosure containing a rectangular conducting body. Computations are performed for a wide range of dimensionless parameters including the Rayleigh number Ra, the thermal conductivity ratio k, and the location of the inner body δ, while the value of the Prandtl number is maintained constant at 6.8. This simulation spans four decades of Rayleigh number, Ra, from 103 to 106. The influence of these various dimensionless parameters on the flow behavior is investigated. Correlations of the averaged Nusselt numbers are obtained as a function of two parameters (Ra and δ) for each working thermal conductivity ratio. The results indicate that the heat transfer rate through the enclosure can be controlled by the position of the rectangular body. A comparative study was also carried out between a horizontal and a vertical conducting shape inside the enclosure. It is proved that a vertical position leads to a better heat transfer compared to the horizontal case.     

Combined heat and mass transfer in natural convection between vertical parallel plates

Abstract

This study is to examine the effects of latent heat transfer associated with liquid film vaporization on heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air‐water system under various conditions. The influences of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy‐aiding and opposing flows is clearly demonstrated.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption

The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that is mixed convection parameter λ_t, modified mixed convection parameter λ_c, Prandtl number Pr, heat generation/absorption parameter δ, Schmidt number Sc, thermophoresis parameter N_t, and thermophoretic coefficient k are sketched in graphical form. Numerical results for skin friction, heat transfer rate and the mass transfer rate are tabulated for various emerging physical parameters. It is reported that in enhancement in heat, generation boosts up the fluid temperature at some positions of the surface of the sphere. As heat absorption parameter is decreased temperature field increases at position X = π/4 on the other hand, no alteration at other considered circumferential positions is noticed.     

40Cr轴面激光熔覆Ni60数值模拟

目的 针对激光熔覆过程中熔池内部复杂的传热和对流现象,分析激光功率和扫描速度对熔池内部温度场、流场演变和分布的影响.方法 采用双椭球热源模型,建立了40Cr轴面基体激光熔覆Ni60粉末过程的三维温度场流场数值模型,并进行试验验证.结果 熔覆过程形成了近似椭球体的熔池,最高温度位于移动光斑中心偏后方,达到了2080.4 ...     

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.     

Natural convection flow of a non-Newtonian fluid between two concentric vertical cylinders

Summary The natural convection of a homogeneous incompressible fluid of grade three between two infinite concentric vertical cylinders is studied. We consider the effect of the non-Newtonian nature of the fluid on the skin friction and heat transfer. Some numerical experimentation is presented to show the effect on the velocity and temperature profiles as the dimensionless parameters are varied.     

Evaporation heat and mass transfer in natural convection pipe flow

Abstract

A numerical analysis has been performed to examine film evaporation on natural convection heat and mass transfer in a vertical pipe. Coupled governing equations for liquid film and induced gas flow were simultaneously solved by the implicit finite difference method. Results for interfacial heat and mass transfer coefficients are specifically presented for ethanol film and water film vaporization. The predicted results indicate that the heat transfer from gas‐liquid interface to the gas flow is predominated by the transport of latent heat in association with film evaporation. The results are also contrasted with those of zero film thickness and show that the assumption of extremely thin film thickness made by Chang et al. [5] and Yan and Lin [19] is only valid for a system with a low liquid Reynolds number Re _l1. But as the liquid Reynolds number is high, the assumption becomes inappropriate.     

Maximum density effects on natural convection in a porous cavity under thermal non-equilibrium conditions

Summary The problem of natural convection flow in a cavity filled with a water near its maximum density saturated porous medium and subjected to thermal non-equilibrium condition is investigated numerically in the present article. The natural convection flow in the horizontally heated rectangular cavity is assumed to be two-dimensional. A parabolic relationship of the density-temperature is used in Darcy's model. The dimensionless governing equations were solved using the finite volume method, and the results are presented to show the effect of the governing parameters. The numerical results are presented in the form of variations of the average Nusselt number with the Rayleigh number with different values of the heat transfer coefficient parameter H, and the thermal conductivity parameter K _r . It is found that by increasing H and K _r the shape of the isotherms of the solid phase appear to be similar to those of the water due to the enhancement of the thermal communications between the two phases. The results for the average Nusselt number of the thermal equilibrium model, which is the maximum possible value, can be achieved for high values of H×K _r . The numerical results reveal the dependence of the total (solid + fluid) average Nusselt number on the aspect ratio, and the maximum values of the average Nusselt number are found for the cavities of aspect ratio A≈0.5.     

Buoyancy effects on the laminar boundary layer heat transfer along vertically moving cylinders

Abstract

The effects of buoyancy forces on the laminar boundary layer flow and heat transfer along vertically moving cylinders are analyzed for the cases of prescribed surface temperature and prescribed wall heat flux in power of streamwise distance. Local similarity solutions are obtained to show the effects of buoyancy parameters and the transverse curvature of the cylinder on the surface friction and heat transfer rate.     

Prediction of solidification behaviour of weld pool through modelling of heat transfer and fluid flow during gas tungsten arc welding of commercial pure aluminium

Abstract

A mathematical model is developed to assess the solidification behaviour of the weld pools. To do so, during gas tungsten arc welding of commercial pure aluminium, equations of conversation of mass, energy and momentum are numerically solved considering three-dimensional steady state heat transfer and fluid flow conditions. The weld pool geometry, weld thermal cycles and various solidification parameters are calculated using temperature and velocity fields acquiring from the utilised model. The solidification behaviour of the weld pool at the weld centreline and the fusion line is then studied using the solidification parameters including temperature gradient G, solidification rate R and the combined forms G/R and GR. In order to verify the predictions, welding experiments are performed and geometry of the weld fusion zone is measured. The calculated geometry of the weld fusion zone is found to be in good agreement with the corresponding experimental result. The predictions show that the cooling rate GR increases toward the centreline while the other solidification parameter G/R shows a different behaviour. In addition, it is found that under the employed welding conditions, as the welding speed increases temperature gradients both at the weld centreline and at the fusion line are reduced.     

Mixed convection of non-Newtonian nanofluid in an H-shaped cavity with cooler and heater cylinders filled by a porous material: Two phase approach

In the present problem, two-phase mixed convection of a non-Newtonian nanofluid in a porous H-shaped cavity is studied. Inside the enclosure there are four rotating cylinders, using the Boussinesq approximation, mixed convection is created. Nanofluid includes H₂O + 0.5% CMC and copper oxide nanoparticles. The mixture model was used to model physical phenomena. Different aspect ratios were used in order to achieve the best heat transfer rate. The Darcy and Richardson numbers ranges are 10⁻⁴ ≤ Da ≤ 10⁻² and 1 ≤ Ri ≤ 100 respectively. Also, the aspect ratio and dimensionless angular velocities of cylinders ranges are 1.4 ≤ AR ≤ 1.6 and −10 ≤ Ω ≤ 10 respectively. Streamlines and isotherm-lines contours have been obtained for the variation of Darcy and Richardson numbers, aspect ratio and angular velocity. The heat transfer rates have been obtained for various aspect ratios, Darcy and Richardson numbers, and the direction of the cylinder's rotation, and are compared with each other. The results show that the direction of cylinders rotation influences the strength and extent of the generation vortices. Also, the use of porous material in high permeability can be a good alternative to lowering the angular velocity of the cylinders and ultimately reducing the need for less energy.     

Finite element solutions for laminar flow and heat transfer around a square prism

Abstract

The finite element solutions of Navier‐Stokes and energy equations for steady laminar flow and heat transfer around square prisms, with attack angles of 0° and 45° have been obtained for a gas of Pr=0.7. The variations of surface shear stress, local pressure and Nusselt number are obtained over the entire prism surface including the zone beyond the point of separation. The predicted values of drag coefficients, the location of. separation, the average Nusselt number and the plots of velocity flow fields and isotherms are also presented. The trend of the present numerical results seems reasonable.     

Study of dimensionless quantities to analyse front and rear wall of keyhole formed during laser beam welding

Fluid flow mechanisms present in Keyhole (KH) during Laser Beam Welding (LBW) process influence the associated heat and mass transfer. In an attempt to describe these complexities for eventual optimization of LBW parameters, a dimensionless analysis using Mach (Ma), Raleigh (Ra), Reynolds (Re) and Marangoni (Mg) numbers have been carried out. This analysis describes hydrodynamics of melt and vapour phase appearing in the front and rear wall of KH. The non-dimensional hydrodynamic quantities describe the mechanism behind flow pattern present in melt-vapour in terms of ratio of convection–conduction heat transfer occurring within KH. The analysis shows that the higher Marangoni number indicates stronger Marangoni convection in the KH causing relatively higher capillary flow in the melt pool. The laminar-turbulent flow of melt-vapour in KH medium is described in terms of ratio of Reynolds and Mach numbers (Re/Ma). The pressure distribution in the KH accounts for the melt-vapour ejection rate. A relationship between depth and radius of KH has been obtained as a function of delivered laser power.     

Forced convection heat transfer from concentrated and distributed thermal sources

Abstract

This paper proposes a novel formulation for the analysis of forced convection heat transfer from both a concentrated thermal source and a uniformly distributed thermal source. The illustrative examples are the wedges of various configurations with dual thermal sources; namely, each of the wedges is imposed with uniform‐flux on the surface and embedded with a line source at the leading edge. By introducing a parameter of relative source strength ξ and a dimensionless temperature based on the two characteristic temperature of the sources, a nonsimilar boundary‐layer energy equation is obtained. The nonsimilar energy equation is readily reducible to the self‐similar equations of adiabatic wedge plumes for ξ=0, and to those of uniform‐flux wedges for ξ=1. Numerical solutions are obtained by employing an effective numerical scheme which has been developed for nonsimilar plumes subject to an integral equation of flux conservation condition. Results are presented for the cases of flat plate, right angle wedge, stagnation point and separating wedge flow for Pr=0.7, 1, 7, 10, and 100. Dimensionless wall temperature for all the cases are proportional linearly to ξ over the entire range of ξ from 0 to 1. Solutions for the limiting cases of ξ=0 and 1 are in excellent agreement with the reported data.     

A mathematical model of the edge-defined film-fed growth process

A model is presented to simulate the steady-state growth of a fiber produced by the edge-defined film-fed growth (EFG) process. Equations describing the axisymmetric transport of heat in the melt and fiber are discussed. Heat transfer between the system and the surrounding environment is assumed to take place via convection and radiation. Given the fiber translation velocity, the external temperature profile, the die temperature, and the input flow rate or the pressure, asymptotic solutions for the temperature profiles in the melt and fiber, and the melt/gas and solidifying interfacial shapes are developed in the limit of a small melt slenderness ratio (fiber radius/approximate melt height). The effect of process parameters on the shape of the fiber system is investigated.     

Forced-convection heat transfer over a circular cylinder with Newtonian heating

A mathematical model for the forced convection boundary-layer flow over a circular cylinder is considered when there is Newtonian heating on the surface of the cylinder through which the heat transfer is proportional to the local surface temperature. The dimensionless version of the boundary-layer equations involve two parameters, the Prandtl number σ and γ measuring the strength of the surface heating. The solution near the stagnation point is considered first and this reveals that, to get a physically acceptable solution, γ must be less than some critical value γ _c , dependent on σ. Numerical solutions to the full boundary-layer problem are obtained which show that the surface temperature increases as the flow develops from the stagnation point.     

Modelling of dendritic solidification using finite element method

Abstract

Computer based numerical modelling of solidification is being increasingly used in an effort to develop and improve casting processes, a long term goal of this work being the prediction of microstructural features such as grain shape, size, and dendrite arm spacings throughout a casting. In a numerical heat flow model this can be achieved only through the inclusion of the kinetics of nucleation and dendrite growth. In the present paper strategies for including columnar and equiaxed solidification kinetics into a finite element model are reviewed. A detailed model for columnar solidification is then presented together with results obtained from calculations on an Al–5 wt-%Cu alloy and a multicomponent nickel based superalloy. It is shown that the inclusion of a dendrite tip undercooling is important, particularly in systems having a low Stefan number. Furthermore, the thermal histories in the superalloy can only be accurately calculated if an experimentally determined solid fraction versus temperature relationship is employed. A model for equiaxed solidification is also discussed and results obtained for an Al–5 wt-%Cu alloy outlined. In particular, the effects of heat transfer coefficient, heterogeneous nucleation site density, and nucleation undercooling on the grain size variation along a one dimensional casting have been examined. Finally, it is shown that grain sizes predicted by the present finite element model agree reasonably well with those of a previous numerical model for an Al–7 wt-%Si alloy.

MST/1468