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Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) technique. In this technique, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is applied. The paper aims to discuss these issues.

The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions. The solutions represented in temperature, vertical velocity and horizontal velocity have been studied with different values of Rayleigh number Ra parameter (103=Ra=105). In addition, characteristic based scheme in Finite Element Method is introduced for modeling the natural convection in a square cavity.

The results for Rayleigh-Taylor instability and natural convection flow had been compared with the previous researches.

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an ISPH technique. In ISPH method, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is introduced. The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions.

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method.

In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique.

The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow.

The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.

A study on heat and mass transfer behavior for an anisotropic porous medium embedded in square cavity/annulus is conducted using incompressible smoothed particle hydrodynamics (ISPH) method. In the case of square cavity, the left wall has hot temperature T_h and mass C_h and the right wall have cool temperature T_c and mass C_c and both of the top and bottom walls are adiabatic. While in the case of square annulus, the inner surface wall is considered to have a cool temperature T_c and mass C_c while the outer surface is exposed to a hot temperature T_h and mass C_h. The paper aims to discuss these issues.

The governing partial differential equations are transformed to non-dimensional governing equations and are solved using ISPH method. The results present the influences of the Dufour and Soret effects on the fluid flow and heat and mass transfer.

The effects of various physical parameters such as Darcy parameter, permeability ratio, inclination angle of permeability and Rayleigh numbers on the temperature and concentration profiles together with the local Nusselt and Sherwood numbers are presented graphically. The results from the current ISPH method are well-validated and have favorable comparisons with previously published results and solutions by the finite volume method.

A study on heat and mass transfer behavior on an anisotropic porous medium embedded in square cavity/annulus is conducted using Incompressible Smoothed Particle Hydrodynamics (ISPH) method. In the ISPH algorithm, a semi-implicit velocity correction procedure is utilized, and the pressure is implicitly evaluated by solving pressure Poisson equation (PPE). The evaluated pressure has been improved by relaxing the density invariance condition to formulate a modified PPE.

The purpose of this paper is to perform numerical simulations based on the incompressible smoothed particle hydrodynamics (ISPH) method for thermo-diffusion convection in a hexagonal-shaped cavity saturated by a porous medium and suspended by a nano-encapsulated phase change material (NEPCM). Here, the solid particles are inserted into a phase change material to enhance its thermal performance.

Superellipse rotated shapes with variable lengths are embedded inside a hexagonal-shaped cavity. These inner shapes are rotated around their center by a uniform circular velocity and their conditions are positioned at high temperature and concentration. The controlling equations in a non-dimensional form were analyzed by using the ISPH method. At first, the validation of the ISPH results is performed. Afterward, the implications of a fusion temperature, lengths/types of the superellipse shapes, nanoparticles parameter and time parameter on the phase change heat transfer, isotherms, isoconcentration and streamlines were addressed.

The achieved simulations indicated that the excess in the length of an inner superellipse shape augments the temperature, concentration and maximum of the streamlines in a hexagonal-shaped cavity. The largest values of mean Nusselt number are attained at the inner rhombus shape with convex (n = 1.5) and the largest values of mean Sherwood number are attained at the inner rectangle shape with rounded corners (n = 4).

The ISPH method is developed to emulate the influences of the uniform rotation of the novel geometry shapes on heat/mass transport inside a hexagonal-shaped cavity suspended by NEPCM and saturated by porous media.

The purpose of this paper is to improve the 2D incompressible smoothed particle hydrodynamics (ISPH) method by working on the wall boundary conditions in ISPH method. Here, two different wall boundary conditions in ISPH method including dummy wall particles and analytical kernel renormalization wall boundary conditions have been discussed in details.

The ISPH algorithm based on the projection method with a divergence velocity condition with improved boundary conditions has been adapted.

The authors tested the current ISPH method with the improved boundary conditions by a lid-driven cavity for different Reynolds number 100 ≤ Re ≤ 1,000. The results are well validated with the benchmark problems.

In the case of dummy wall boundary particles, the homogeneous Newman boundary condition was applied in solving the linear systems of pressure Poisson equation. In the case of renormalization wall boundary conditions, the authors analytically computed the renormalization factor and its gradient based on a quintic kernel function.

This study aims to illustrate the impacts of the motion of circular cylinders on the natural convection flow from variable heated partitions inside the X-shaped cavity filled with Al₂O₃-water nanofluid. A partial layer of a homogeneous/heterogeneous porous medium is located in the top area of the X-shaped cavity.

Three different cases of the porous media including homogeneous, horizontal heterogeneous and vertical heterogeneous porous media were considered. Three different thermal conditions of the embedded circular cylinders including hot, cold and adiabatic conditions are investigated. An incompressible scheme of smoothed particle hydrodynamics (ISPH) method is modified to compute the non-linear partial differential equations of the current problem. Two variable lengths of the left and right sides of the X-shaped cavity have a high-temperature T_h and a low-temperature T_c, respectively. The other wall parts are adiabatic. The numerical simulations are elucidating the dependence of the heat transfer and fluid flow characteristics on lengths of hot/cold source L_h, porous cases, Darcy parameter, thermal conditions of the embedded circular cylinders and solid volume fraction.

Overall, an increment in length of hot/cold source leads to augmentation on the temperature distributions and flow intensity inside the X-shaped cavity. The hot thermal condition of the circular cylinder augments the temperature distributions. The homogeneous porous medium slows down the flow speed in the top porous layer of the X-shaped cavity. The average Nusselt number decreases as L_h increases.

ISPH method simulated the motion of circular cylinders in the X-shaped cavity. The X-shaped cavity is saturated with a partial layer porous medium. It is found that an increase in hot source length augments the temperature and fluid flow. ISPH method can easily handle the motion of cylinders in the X-shaped cavity. Different thermal conditions of cylinders can change the temperature distributions in X-cavity.

The purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.

The ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.

The resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.

A novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

This study aims to focus on the numerical simulation of natural convection from heated novel fin shapes in a cavity filled with nanofluid and saturated with a partial layer of porous medium using improved incompressible smoothed particle hydrodynamics (ISPH) method.

The dimensionless of Lagrangian description for the governing equations were numerically solved using improved ISPH method. The current ISPH method was improved in term of wall boundary treatment by using renormalization kernel function. The effects of different novel heated (Tree, T, H, V, and Z) fin shapes, Rayleigh number Ra(10³ – 10⁶ ), porous height H_p (0.2-0.6), Darcy parameter Da(10⁻⁵ − 10⁻¹ ) and solid volume fraction ϕ(0.0-0.05) on the heat transfer of nanofluid have been investigated.

The results showed that the variation on the heated novel fin shapes gives a suitable choice for enhancement heat transfer inside multi-layer porous cavity. Among all fin shapes, the H-fin shape causes the maximum stream function and Z-fin shape causes the highest value of average Nusselt number. The concentrations of the fluid flows in the nanofluid region depend on the Rayleigh and Darcy parameters. In addition, the penetrations of the fluid flows through porous layers are affected by porous heights and Darcy parameter.

Natural convection from novel heated fins in a cavity filled with nanofluid and saturated with a partial layer of porous medium have been investigated numerically using improved ISPH method.

This paper aims to adopt incompressible smoothed particle hydrodynamics (ISPH) method for studying magnetohydrodynamic (MHD) double-diffusive natural convection from an inner open pipe in a cavity filled with a nanofluid.

The Lagrangian description of the governing equations was solved using the current ISPH method. The effects of two pipe shapes as a straight pipe and V-pipe, length of the pipe LPipe (0.2-0.8), length of V-pipe LV (0.04-0.32), Hartmann parameter Ha (40-120), solid volume fraction ϕ (0-0.1) and Lewis number Le (1-50) on the heat and mass transfer of nanofluid have been investigated.

The results demonstrate that the average Nusselt and Sherwood numbers are increased by increment on the straight-pipe length, V-pipe length, Hartmann parameter, solid volume fraction and Lewis number. In addition, the variation on the open pipe shapes gives a suitable choice for enhancement heat and mass transfer inside the cavity. The control parameters of the open pipes can enhance the heat and mass transfer inside a cavity. In addition, the variation on the open pipe shapes gives a suitable choice for enhancement heat and mass transfer inside the cavity.

ISPH method is developed to study the MHD double-diffusive natural convection from the novel shapes of the inner heated open pipes inside a cavity including straight-pipe and V-pipe shapes.

The purpose of this paper is to show how a surface tension model and an eddy viscosity based on the Smagorinsky sub‐grid scale model, which belongs to the Large‐Eddy Simulation (LES) theory for turbulent flow, have been introduced into ISPH (Incompressible smoothed particle hydrodynamics) method. In addition, a small modification in the source term of pressure Poisson equation has been introduced as a stabilizer for robust simulations. This stabilization generates a smoothed pressure distribution and keeps the total volume of fluid, and it is analogous to the recent modification in MPS.

The surface tension force in free surface flow is evaluated without a direct modeling of surrounding air for decreasing computational costs. The proposed model was validated by calculating the surface tension force in the free surface interface for a cubic‐droplet under null‐gravity and the milk crown problem with different resolution models. Finally, effects of the eddy viscosity have been discussed with a fluid‐fluid interaction simulation.

From the numerical tests, the surface tension model can handle free surface tension problems including high curvature without special treatments. The eddy viscosity has clear effects in adjusting the splashes and reduces the deformation of free surface in the interaction. Finally, the proposed stabilization appeared in the source term of pressure Poisson equation has an important role in the simulation to keep the total volume of fluid.

An incompressible smoothed particle hydrodynamics is developed to simulate milk crown problem using a surface tension model and the eddy viscosity.