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Methods used to track the free surface in numerical flow simulations, typically during the casting of metals into moulds are examined in this paper. The algorithm employed makes use of a mixed interpolation formulation to approximate the discretised governing equations for elimination on a Langrangian type moving mesh. Significant savings in CPU time are realised by virtue of the the air domain not being considered in the finite element analysis. The advantages and drawbacks of commonly used methods are discussed, and a method proposed for the numerical simulation of flow where the free surface boundary conditions are important. The effectiveness of the proposed algorithm in solving typical industrial flow problems is demonstrated using numerical examples. The results obtained are compared with analytical and numerical data with a view to validating the algorithm.

The purpose of this paper is to describe how a 3D/1D transient heat transfer model has been developed for getting accurate thermal boundary conditions when investigating the heat transfer in the TiAl castings and also for reducing the computational cost and simplifying the mesh generation.

Heat transfer in the mould is assumed to take place only in a direction perpendicular to the mould wall, called 1D heat transfer. The coordinates of cell centre and the temperature in the mould wall can be calculated by the model instead of meshing mould. Heat transfer in the mould is computed via the FD solution of a 1D heat transfer equation.

For some types of geometry, the model works very well. However, for some, which contain the geometric feature called “dead corner”, the model can't cover. There is some impact on the accuracy of the model.

In the casting industry, the geometry of the casting is usually very complex and contains different features. This leads to difficult meshing when using numerical model to predict the casting process. Furthermore, an accurate calculation is very important on the thermal boundary during filling and solidification, to support practice, to improve the process and minimise the casting defects.

In this paper, a novel method is developed to calculate the heat transfer through the casting‐mould interface to the mould wall in a casting.

The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients.

The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well.

Several test problems are provided to confirm the validity and efficiently of the proposed method.

For the first time, some famous examples are solved by using the proposed high-order technique.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

A new coupled model is developed to simulate the interaction between fluid droplet collisions on discrete particles (DPs) by using mathematic function.

In this model, the smoothed particle hydrodynamics (SPH) is used based on the kernel function and the time step which takes into consideration to the fluid domain in accordance with the discrete element method (DEM) with resistance function. The interaction between fluid and DPs consists of three parts, which are repulsive force, viscous shear force and attractive force caused by the capillary action. The numerical simulation of droplet collision on DPs presents the whole process of droplet motion. Otherwise, an experimental data were conducted to record the realistic process for verification.

The comparison result indicated that the numerical simulation is capable of capturing the entire process for droplet collision on DPs.

However, based on the difference of experimental environment, type of the DP and setups, the maximum spreading dimeters of could not fit the experimental data exactly.

In sum, the coupled SPH-DEM method simulation shows that the coupled model of SPH-DEM developed an entire effectiveness process for fluid–solid interaction problem.

The purpose of this paper is to describe the implementation of discrete singular convolution (DSC) method to steady seepage flow while presenting one of the possible uses of DSC method in geotechnical engineering. It also aims to present the implementation of DSC to the problems with mixed boundary conditions.

Second order spatial derivatives of potential and stream functions in Laplace's equation are discretized using the DSC method in which the regularized Shannon's delta kernel is used as an approximation to delta distribution. After implementation of boundary conditions, the system of equations is solved for the unknown terms.

The results are compared with those obtained from the finite element method and the finite difference method.

The method is applied to the flow problem through porous medium for the first time.

The purpose of this paper is to investigate the effects of Ha and the Nanoparticles (NP) volume fraction over the irreversibility and heat transport in Darcy–Forchheimer nanofluid saturated lid-driven porous medium.

The present paper highlights entropy generation because of mixed convection for a lid-driven porous enclosure filled through a nanoliquid and submitted to a uniform magnetic field. The analysis is achieved using Darcy–Brinkman–Forchheimer technique. The set of partial differential equations governing the considered system was numerically solved using the finite element method.

The main observations are as follows. The results indicate that the movement of horizontal wall is an important factor for the entropy generation inside the porous cavity filled through Cu–water nanoliquid. The variation of the thermal entropy generation is linear through NPs volume fraction. The total entropy generation reduces when the Darcy, Hartmann and the nanoparticle volume fraction increase. The porous media and magnetic field effects reduce the total entropy generation.

Interest in studying thermal interactions by convective flow within a saturating porous medium has many fundamental considerations and has received extensive consideration in the literature because of its usefulness in a large variety of engineering applications, such as the energy storage and solar collectors, crystal growth, food processing, nuclear reactors and cooling of electronic devices, etc.

By examining the literature, the authors found that little attention has been paid to entropy generation encountered during convection of nanofluids. Hence, this work aims to numerically study entropy generation and heat transport in a lid-driven porous enclosure filled with a nanoliquid.

This paper aims to investigate the effects of different volume fractions of Al₂O₃-water nanofluid on flow and heat transfer under chaotic convection conditions in an L-shaped channel, comparing the difference of numerical simulation results between single-phase and Eulerian–Lagrangian models.

The correctness and accuracy of the two calculation models were verified by comparing with the experimental values in literature. An experimental model of the L-shaped channel was processed, and the laser Doppler velocimeter was used to measure the velocities of special positions in the channel. The simulated values were compared with the experimental results, and the correctness and accuracy of the simulation method were verified.

The calculated results using the two models are basically consistent. Under the condition of Reynolds number is 500, when the volume fractions of nanofluid range from 1% to 4%, the heat transfer coefficients simulated by single-phase model are 1.49%–25.80% higher than that of pure water, and simulated by Eulerian–Lagrangian model are 3.19%–27.48% higher than that of pure water. Meanwhile, the friction coefficients are barely affected. Besides, there are obvious secondary flow caused by lateral oscillations on the cross sections, and the appearance of secondary flow makes the temperature distributions uniform on the cross section and takes more heat away, thus the heat transfer performance is enhanced.

The originality of this work is to reveal the differences between single-phase and two-phase numerical simulations under different flow states. The combination of chaotic convection and nanofluid indicates the direction for further improving the heat transfer threshold.

The purpose of this paper is to investigate the effect of pulsed magnetic field (PMF) with different duty cycles on the melt flow and heat transfer behaviors during direct-chill (DC) casting of large-size magnesium alloy billet and find the appropriate range of duty cycle.

A transient two-dimensional mathematical model coupled electromagnetic field, flow field and thermal field, is conducted to study the melt flow and temperature field under PMF and compared with that under the harmonic magnetic field.

The results reveal that melt vibration and fluctuation are generated due to the instantaneous impact of repeated thrust and pull effects of Lorentz force under PMF. The peak of Lorentz force decreases greatly with the increasing duty cycle, but the melt fluctuation region is expanded with higher duty cycle, which accelerates the interior melt velocity and reduces the temperature gradient at the liquid-solid interface. However, PMF with overly high duty cycle has adverse effect on the melt convection and limited influence on the interior melt. A duty cycle of 20% to 50% is a reasonable range.

This paper can provide guiding significance for the setting of duty cycle parameters on DC casting under PMF.

There are few reports on the effect of PMF parameters during DC casting with applying PMF, especially for duty cycle, a parameter unique to PMF. The findings will be helpful for applying the external field of PMF on DC casting.

The purpose of this paper is to evaluate the temperature, the Dirichlet conditions have been considered to the parallel horizontal plates. The model of generalized Brinkman-extended Darcy with the Boussinesq approximation is considered and the governing equations are computed by COMSOL multiphysics.

In the current study, the thermodynamic irreversible principle is applied to study the unsteady Poiseuille–Rayleigh–Bénard (PRB) mixed convection in a channel (aspect ratio A = 5), with the effect of a uniform transverse magnetic field.

The effects of various flow parameters on the fluid flow, Hartmann number (Ha), Darcy number (Da), Brinkman number (Br) and porosity (ε), are presented graphically and discussed. Numerical results for temperature and velocity profiles, entropy generation variations and contour maps of streamlines, are presented as functions of the governing parameter mentioned above. Basing on the generalized Brinkman-extended Darcy formulation, which allows the satisfaction of the no-slip boundary condition on a solid wall, it is found that the flow field and then entropy generation is notably influenced by the considering control parameters. The results demonstrate that the flow tends toward the steady-state with four various regimes, which strongly depends on the Hartman and Darcy numbers variations. Local thermodynamic irreversibilities are more confined near the active top and bottom horizontal walls of the channel when increasing the Da and decreasing the Hartmann number. Entropy generation is also found to be considerably affected by Brinkman number variation.

In the present work, we are presenting our investigations on the influence of a transverse applied external magnetohydrodynamic on entropy generation at the unsteady laminar PRB flow of an incompressible, Newtonian, viscous electrically conducting binary gas mixture fluid in porous channel of two horizontal heated plates. The numerical solutions for the liquid velocity, the temperature distribution and the rates of heat transport and entropy generation are obtained and are plotted graphically.