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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 paper is to implement the numerical analysis based on finite volume method to compare the effects of stress-jump (SJ) and stress-continuity (SC) conditions on flow structure around and through a porous circular cylinder.

In this study, a steady flow of a viscous, incompressible fluid around and through a porous circular cylinder of diameter “D,” using Darcy-Brinkman-Forchheimer’s equation in the porous region, is discussed. The SJ condition proposed by Ochoa-Tapia and Whitaker is applied at the porous-fluid interface and compared with the traditional interfacial condition based on the SC condition in fluid and porous media. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of 1 < Re < 40 and 10-7 < Da < 10-2, respectively, and the porosities are e=0.45, 0.7 and 0.95.

Results show that the SJ condition leads to a much smaller boundary layer within porous medium near the interface as compared to the SC condition. Two interfacial conditions yield similar results with decrease in porosity.

There is no published research in the literature about the effects of important parameters, such as Porosity and Darcy numbers on different fluid-porous interface conditions for a porous cylinder and comparison the effects of SJ and SC conditions on flow structure around and through a porous circular cylinder.

This study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10⁻⁴ ≤ Da ≤ 10⁻²) are studied.

To perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.

The results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.

The LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method.

The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method.

The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity.

The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method.

This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces.

The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10⁻⁵ ≤ Da ≤ 5 × 10⁻¹) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces.

No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.

The paper aims to report on the flow past a porous trapezoidal‐cylinder, in which the porous‐fluid interface was treated by implementing the stress jump boundary conditions.

The numerical method was based on the finite‐volume method with body‐fitted and multi‐block grids. The Brinkman‐Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress.

The present model was validated by comparing with those for the flow around a solid circular cylinder. Results for flow around porous expanded trapezoidal cylinder are presented with flow configurations for different Darcy number, 10⁻² to 10⁻⁷, porosity from 0.4 to 0.8, and Reynolds number 20 to 200. The flow develops from steady to unsteady periodic vortex shedding state. The first coefficient β has a more noticeable effect, whereas the second coefficient β₁ has very small effect, even for Re   =   200.

The effects of the porosity, Darcy number and Reynolds number on lift and drag coefficients, and the length of circulation zone or shedding period are studied.

This paper aims to investigate magnetic impacts on bioconvection flow within a porous annulus between an outer cylinder and five inner cylinders. The annulus is filled by oxytactic microorganisms and nano-encapsulated phase change materials.

The modified ISPH method based on the time-fractional derivative is applied to solve the regulating equations in Lagrangian dimensionless forms. The pertinent factors are bioconvection Rayleigh number Ra_b (1–100), circular cylinder’s radius R_c (0.1–0.3), fractional time derivative α (0.95–1), Darcy parameter Da (10⁻⁵–10⁻²), nanoparticle parameter ϕ (0–0.1), Hartmann number Ha (0–50), Lewis number Le (1–20), Peclet number Pe (0.1–0.75), s (0.1–0.9), number of cylinders N_Cylinders (1–4), Rayleigh number Ra (10³–10⁶) and fusion temperature θ_f (0.005–0.9).

The simulations revealed that there is a strong enhancement in the velocity field according to an increase in Ra_b. The intensity and location of the phase zone change in response to changes in θ_f. The time-fractional derivative a acting on a nanofluid velocity and flow characteristics in an annulus. The number of embedded cylinders N_Cylinders is playing a significant role in the cooling processes and as N_Cylinders increases from 1 to 4, the velocity field’s maximum reduces by almost 33.3%.

The novelty of this study is examining the impacts of the magnetic field and the presence of several numbers of embedded cylinders on bioconvection flow within a porous annulus between an outer cylinder and five inner cylinders.

The purpose of this paper is to investigate the unsteady flow past through a permeable diamond-shaped cylinder and to study the effects of the aspect ratios and Darcy numbers of the cylinder.

The lattice Boltzmann method with D2Q9 lattice model was used to simulate the unsteady flow through permeable diamond-shaped cylinders. The present numerical method is validated against the available data.

The key findings are that increasing the permeability enhances the suppression of vortex shedding, and that the Strouhal number is directly proportion to the Darcy number, Reynolds number and the aspect ratio of the porous cylinder.

The present study considers unsteady laminar flow past through single permeable diamond-shaped cylinder. According to the authors’ knowledge, very few studies have been found in this field. The present findings are novel and original, which in turn can attract wide attention and citations.

The purpose of this paper is to study steady, laminar, and two-dimensional flow around and through a porous diamond cylinder.

The governing equations are written for two zones: the clear fluid zone and the porous zone. For the porous zone, the modified Navier-Stokes equations, including Darcy, Brinkman, and Forcheimer terms are used. The governing equations are solved numerically using a finite volume approach.

It was found that as the apex angle and Reynolds number decreases the wake length decreases and the separation is delayed.

There is no published research in the literature about flow around and into porous diamond cylinders to study the effect of important parameters, such as apex angle, Darcy number, and Reynolds number.

This paper aims to predict the effects of uniform injection or suction through a porous square cylinder on the flow field and on some aerodynamic parameters.

The finite volume method has been used for solving the ensemble averaged Navier–Stokes equations for incompressible flow in conjunction with the k‐ ε turbulence model equations including the Kato and Launder modification.

The parameters taken into account are injection or suction velocity, position of injection and suction surface, drag and lift coefficients and Strouhal number. The numerical results show that increasing suction velocity decreases the drag coefficient for all the suction configurations considered in the present study, except that of suction through rear surface. The vortex‐shedding motion gets weak by the suction application through top and bottom surfaces.

The problem is restricted with a 2‐D simple geometry such as square cylinder due to the limited computer capability. Further extensions of the present study could include the more complex configurations and some other aspects such as heat transfer between porous cylinder and main flow.

The injection or suction application through a porous bluff body can be used as an efficient drag and vortex control method in aerodynamics.

This paper describes an attempt to simulate numerically the flow around square cylinder with uniform injection and suction in a manner different from what is given in the literature.