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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.

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.

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.

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.

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.

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 model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique.

The problem is solved numerically by using the ISPH method.

The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties.

The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.

This paper aims to adopt incompressible smoothed particle hydrodynamics (ISPH) method to simulate MHD double-diffusive natural convection in a cavity containing an oscillating pipe and filled with nanofluid.

The Lagrangian description of the governing partial differential equations are solved numerically using improved ISPH method. The inner oscillating pipe is divided into two different pipes as an open and a closed pipe. The sidewalls of the cavity are cooled with a lower concentration C_c and the horizontal walls are adiabatic. The inner pipe is heated with higher concentration C_h. The analysis has been conducted for the two different cases of inner oscillating pipes under the effects of wide range of governing parameters.

It is found that a suitable oscillating pipe makes a well convective transport inside a cavity. Presence of the oscillating pipe has effects on the heat and mass transfer and fluid intensity inside a cavity. Hartman parameter suppresses the velocity and weakens the maximum values of the stream function. An increase on Hartman, Lewis and solid volume fraction parameters leads to an increase on average Nusselt number on an oscillating pipe and left cavity wall. Average Sherwood number on an oscillating pipe and left cavity wall decreases as Hartman parameter increases.

The main objective of this work is to study the MHD double-diffusive natural convection of a nanofluid in a square cavity containing an oscillating pipe using improved ISPH method.

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.

The purpose of this study is to apply the incompressible smoothed particle hydrodynamics method for simulating the natural convection flow inside a cavity including cross blades or circular cylinder cylinder.

The base fluid is water and copper-water nanofluid is treated as a working fluid. The left and rights walls are maintained at a cool temperature, the horizontal cavity walls are isolated and the inner shape was heated. The physical parameters are the length of the blades L_Blade, the number of cross blades, circular cylinder radius L_R, Rayleigh number Ra and the nanoparticles volume fraction.

The results reveal that the lengths of the cross blade, number of the blades and radius of the circular cylinder is working as an enhancement factor for heat transfer and fluid flows inside a cavity. Adding nanoparticles augments heat transfer and reduces the fluid flow intensity inside a cavity. The best case for buoyancy-driven flow was obtained when the inner shape is the circular cylinder at a higher Rayleigh number.

This work uses a distinctive numerical method to study the natural convection heat from cross blades inside a cavity filled with nanofluid. It provides a new analysis of this issue and presented good results.