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A two‐dimensional laser surface remelting problem is numerically simulated. The mathematical formulation of this multiphase problem is obtained using a continuum model, constructed from classical mixture theory. This formulation permits the construction of a set of continuum conservation equations for pure or binary, solid‐liquid phase change systems. The numerical resolution of this set of coupled partial differential equations is performed using a finite volume method associated with a PISO algorithm. The numerical results show the modifications caused by an increase of the free surface shear stress (represented by the Reynolds number R_e) upon the stability of the thermocapillary flow in the melting pool. The solutions exhibit a symmetry‐breaking flow transition, oscillatory behaviour at higher values of R_e. Spectral analysis of temperature and velocity signals for particular points situated in the melted pool, show that these oscillations are at first mono‐periodic them new frequencies appear generating a quasi‐periodic behaviour. These oscillations of the flow in the melted pool could induce the deformation of the free surface which in turn could explain the formation of surface ripples observed during laser surface treatments (surface remelting, cladding) or laser welding.

To conduct a numerical study on two‐dimensional, transient, buoyant flow inside an air‐filled 45°‐inclined enclosure, heated and cooled on adjacent walls.

The governing equations obtained through the stream function‐vorticity formulation are solved using finite differences. Flow characteristics have been investigated for an aspect ratio of 1. Calculations are carried out for the Rayleigh numbers in the range of 10³≤Ra≤5×10⁷.

With the increasing Rayleigh number, four distinct flow regimes were identified based on the time variations of the mid‐point stream function and the mean Nusselt number at the heated wall as well as those of flow and temperature fields: steady flow with symmetric two cells at low Ra; steady flow with asymmetric two cells at lower moderate Ra; oscillatory flow with the periodic nature at upper moderate Ra; and oscillatory flow in chaotic nature at higher Ra range.

The distinct flow regimes are observed only at ϕ=45°; a small deviation of the tilting angle from ϕ=45° results in the disappearance of the distinction.

This paper aims to numerically study the laminar natural convection in a thermosyphon filled with liquid gallium exposed to a constant magnetic field. The left wall of the thermosyphon is at an uniformed hot temperature, whereas the right wall is at a uniform cold temperature. The top and bottom walls are considered to be adiabatic. All walls are electrically insulated. The effects of Hartmann number, in a wide range of Rayleigh number and aspect ratio combinations, on the natural convection throughout the thermosyphon, are investigated and discussed. Furthermore, different forces that influence the natural flow structure are studied.

A Fortran code is developed based on the finite volume method to solve the two-dimensional unsteady governing equations.

Imposing a magnetic field improves the stability of the fluid flow and thus reduces the Nusselt number. For a given Hartmann and Rayleigh number, there is an optimum aspect ratio for which the average velocity becomes maximum.

This paper is a two-dimensional investigation.

To the best of the authors’ knowledge, the effect of the magnetic field on natural convection of liquid gallium in the considered thermosyphon has not been studied numerically in detail. The results of this paper would be helpful in considering the application of the low Prandtl number’s liquid metals in thermosyphon MHD generators and certain cooling devices.

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high‐order difference method. Numerical stability is improved by using fourth‐order accurate upwind‐biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth‐order central difference. To demonstrate the versatility of the boundary‐fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline‐driven flows in a two‐dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those by Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.

The purpose of this paper is to conduct a numerical study of the effect of magnetic field on thermocapillary convection of a two layered system of Newtonian fluids, confined in a rectangular cavity. The flow within the cavity is subject to the horizontal temperature gradient. Attention is focused on how the heat transfer and flow properties are affected subject to the applied magnetic field, particularly in the lower layer. For this purpose, the fluid combinations of di‐Boron Trioxide (B₂O₃) over Gallium Arsenide GaAs (III‐V), and Silicon oil 10 cSt over Fluorinert FC 70 are considered in the present study.

The non‐linear two‐dimensional vorticity transport equations along with the energy equations are solved for the two liquid layers using the Alternate Direct Implicit method, whereas the elliptic partial differential equations of the stream function are solved using the Successive Over Relaxation method.

It was found that despite the significant reduction of flow in the two layers, the number of cells in the lower layer increases with the increase in Hartmann number Ha. However, the flow intensity decreases with the increase in Hartmann number. This decrease is more pronounced in the lower layer, as compared to the upper layer. The numerical scheme employed for the solution is found to be in good agreement with the previous work.

The analysis is made for two layer liquid system with undeformable interface and free surface. The detailed study of the effect of magnetic field on oscillatory Marangoni convection in two layer system with deformable interface is left for future work.

The approach is useful in optimizing the flow properties of the fluids in a two layer system, particularly the lower layer, to yield the results of potential practical interest.

The results of the study may be of some interest to researchers in the field of semiconductor technology, as the melt control is intensively investigated for the development in the manufacture of defect‐free semiconductors and crystals.

We develop a numerical analysis of the buoyancy driven natural convection of a fluid in a three dimensional shallow cavity (4 ⋅ 1 ⋅ 1) with a horizontal gradient of temperature along the larger dimension. The fluid is a liquid metal (Prandtl number equal to 0. 015) while the Grashof number (Gr) varies in the range 100,000‐300,000. The Navier‐Stokes equations in vorticity‐velocity formulation have been integrated by means of a linearized fully implicit scheme. The evaluation of fractal dimension of the attractors in the phase space has allowed the detection of the chaotic regime. The Ruelle‐Takens bifurcation sequence has been observed as mechanism for the transition to chaos: the quasi periodic regime with three incommensurate frequencies is the instability mechanism responsible for the transition to chaos. Physical experiments confirm the existence of this scenario.

The aim of this study is to present numerical analyses for combined effects of the inlet temperature (ΔT⁺) and the wall‐to‐fluid thermal capacitance ratio (a*) on the laminar mixed convection unsteady flows in a vertical pipe.

The full Navier‐Stokes and energy, coupled, unsteady state, two‐dimensional governing equations for ascending laminar mixed convection in a vertical pipe are solved numerically using a finite‐difference scheme.

The results show that the thermohydraulic flow behaviour is highly dependent on both parameters (ΔT⁺, a*). Moreover, the unsteady characteristics of the flow can involve oscillatory and reversed flow phenomena yielding the unstable flows. For the heating case, the reversed flow appears below the wave instability and the unsteady vortex is always significant in the vicinity of the wall, whatever ΔT⁺ and a*<100. For the cooling case, the reversed flow appears in the central region of the pipe; it develops on top of the wave instability.

This study should be very useful to improve heat transfer equipment.

The paper shows clearly the combined effects of both parameters (ΔT⁺, a*) on the laminar mixed convection flow.

The purpose of this paper is to numerically study transient natural convective flow in a square cavity with partially heated and cooled vertical walls, thermally insulated top wall and linearly heated bottom wall.

The governing equations of motion are non‐dimensionalized and reformulated using stream function‐vorticity approach. Alternating direction implicit finite difference scheme is used to solve the coupled equations.

The transient results obtained for different values of Grashof number (Gr) and fixed Prandtl number Pr = 0.733 are presented in the form of isotherms, streamlines, bifurcation diagram and time series. The transition from steady to oscillatory motions is analyzed in detail with respect to Gr. The flow is observed to be steady up to Gr ≈ 2 × 10⁴. A time‐periodic unsteady solution first appears at Gr = 20,900 and the amplitude of the fluctuation grows as Gr is increased.

The study is limited to laminar flow in a square cavity. Further extension of this work could include the influence of various choices of Prandtl number and the effect of aspect ratio. Buoyancy‐driven convection in a sealed cavity with differentially heated walls is a prototype of many industrial applications such as energy‐efficient design of buildings and rooms, convective heat transfer associated with boilers, etc.

The paper presents an original computer program written in FORTRAN to solve the partial differential equations.

The purpose of this paper is to study numerically and experimentally incompressible Newtonian flow in a three‐dimensional cylindrical branching channel.

The flow configuration studied in the present investigation is such that a fully developed laminar flow enters an abruptly expanded cylinder and the flow leaves this cylinder by two identical cylindrical outlet branch pipes. A numerical analysis was performed by developing a three‐dimensional numerical code using the highly simplified marker and cell method. Representative velocities in the flow field are recorded by Laser Doppler Velocimeter measurements and volume flow rate from each outlet branch pipe is measured. Flow visualization in representative symmetrical planes is also carried out. Comparisons of numerical predictions and experimental data are presented and the reasonable agreement between the numerical and experimental results is encouraging.

The flow field in the three‐dimensional cylindrical branching channel is clarified within the range of laminar flow. The characteristics of the branch flow rate are obtained and show that there exist two distinct domains of strong asymmetric flow distribution from the outlet branch pipes, depending on the Reynolds numbers. It is further observed that the flow became time periodic as the Reynolds number is increased. It becomes apparent that the swirl flow component plays a key role in the flow phenomena.

The present investigation sheds light on the three‐dimensionality in the prevailing flow field for various inlet Reynolds numbers in the laminar flow range. Flow rate deflection characteristics in a three‐dimensional cylindrical branching channel are also obtained.

The purpose of this paper is to describe the flow structure and the time-resolved and time-mean heat transfer characteristics in the interaction between a synthetic jet and a cross flow, when an obstruction reduces the cross-section of the orifice where the jet is formed.

The microchannel flow interacted by the pulsed jet is modeled using a two-dimensional finite volume simulation with unsteady Reynolds-averaged Navier-Stokes equations while using the Shear-Stress-Transport (SST) k-ω turbulence model to account for fluid turbulence.

The computational results show a good and rapid increase of the synthetic jet influence on heat transfer enhancement when the obstruction of the orifice is superior to 30 per cent and the synthetic jet oscillating amplitudes are below 50 µm. It is found that when the obstruction is close to the exit orifice, the heat transfer enhancement is significant. The obstruction has proved to accelerate the jet and change the formation of large vortical structures. Additional windward vortices appear, which influence the flow field and enhance the heat transfer.

The work proposes the use of a compound enhancement technique for electronics cooling. A limited range of operating conditions and geometrical configurations is presented. A further analysis of the performance evaluation, based on the increased energy consumption of the device, would complement the study.

The authors provide a compound technique to enhance heat transfer in synthetic-jet electronic cooling devices.