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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.

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 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 use an incompressible smoothed particle hydrodynamics (ISPH) method for simulating buoyancy ratio and magnetic field effects on double diffusive natural convection of a cooper-water nanofluid in a cavity. An open pipe is embedded inside the center of a cavity, and it is occupied by solid particles.

The dimensionless governing equations in Lagrangian form were solved by ISPH method. Two different thermal conditions were considered for the solid particles. The actions of the solid particles were tracked inside a cavity. The effects of Hartman parameter, Rayleigh number, nanoparticles volume fraction and Lewis number on features of heat and mass transfer and flow field were tested.

The results showed that the buoyancy ratio changes the directions of the solid particles diffusion in a cavity. The hot solid particles were raised upwards at aiding mode (N > 0) and downwards at an opposing mode (N < 0). A comparison is made with experimental and numerical simulation results, and it showed a well agreement.

Novel studies for the impacts of buoyancy ratio on the diffusion of solid particles embedded in an open pipe during double-diffusive flow were conducted.

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

This paper aims to investigate the conformable fractal approaches of unsteady natural convection in a partial layer porous H-shaped cavity suspended by nano-encapsulated phase change material (NEPCM) by the incompressible smoothed particle hydrodynamics method.

The partial hot sources with variable height L_Hot are in the H-cavity’s sides and center. The performed numerical simulations are obtained at the variations of the following parameters: source of hot length L_Hot = (0.4–1.6), conformable fractal parameter α (0.97–1), fusion temperature θ_f (0.05–0.9), thermal radiation parameter Rd (0–7), Rayleigh number Ra (10³–10⁶), Darcy parameter Da (10⁻² to 10⁻⁵) and Hartmann number Ha (0–80).

The main outcomes showed the implication of hot source length L_Hot, Rayleigh number and fusion temperature in controlling the contours of a heat capacity within H-shaped cavity. The presence of a porous layer in the right zone of H-shaped cavity prevents the nanofluid flow within this area at lower Darcy parameter. An increment in the thermal radiation parameter declines the heat transfer and changes the heat capacity contours within H-shaped cavity. The velocity field is strongly enhanced by an augmentation on Rayleigh number. Increasing the Hartmann number shrinks the velocity field within H-shaped cavity.

The novelty of this work is solving the conformable fractal approaches of unsteady natural convection in a partial layer porous H-shaped cavity suspended by NEPCM.

The purpose of this study is to use the incompressible smoothed particle hydrodynamics method to examine the influences of a magnetic field on the double-diffusive convection caused by a rotating circular cylinder with paddles within a square cavity filled by a nanofluid.

The cavity is saturated by two wavy layers of non-Darcy porous media with a variable amplitude parameter. The embedded circular cylinder with paddles carrying T_h and C_h is rotating around the cavity center by a uniform circular velocity.

The lineaments of nanofluid velocity and convective flow, as well as the mean of Nusselt and Sherwood numbers, are represented below the variations on the frequency parameter, amplitude parameter of the wavy porous layers, Darcy parameter, nanoparticles parameter, Hartmann number and Ryleigh number. The performed simulations showed the role of paddles mounted on circular cylinders for enhancing the transmission of heat and mass within a cavity. The wavy porous layers at the lower Darcy parameter are playing as a blockage for the nanofluid flow within the porous area. Increasing the concentration of the nanoparticles to 6% reduces the maximum flow speed by 8.97% and maximum streamlines |ψ|_max by 10.76%. Increasing Hartmann number to 100 reduces the maximum flow speed by 65.83% and |ψ|_max by 75.54%.

The novelty of this work is to examine the effects of an inclined magnetic field and rotating novel shape of a circular cylinder with paddles on the transmission of heat/mass in the interior of a nanofluid-filled cavity saturated by undulating porous medium layers.