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The purpose of this study is to simulate the thermo-solutal convection resulting from a circular cylinder hanging in a rod inside a ∧-shaped cavity.

The two dimensional ∧-shaped cavity is filled by Al₂O₃-water nanofluid and saturated by three different levels of heterogeneous porous media. An incompressible smoothed particle hydrodynamics (ISPH) method is adopted to solve the governing equations of the present problem. The present simulations have been performed for the alteration of buoyancy ratio (−2≤N≤2), radius of a circular cylinder (0.05≤Rc≤0.3), a height of a rod (0.1≤Lh≤0.4), Darcy parameter (10−3≤Da≤10−5), Lewis number (1≤Le≤40), solid volume fraction (0≤ϕ≤0.06), porous levels (0≤η1=η2≤1.5)and various boundary-wall conditions.

The performed numerical simulations indicated the importance of embedded shapes on the distributions of temperature, concentration and velocity fields inside ∧-shaped cavity. Increasing buoyancy ratio parameter enhances thermo-solutal convection and nanofluid velocity. Adiabatic conditions of the vertical-walls of ∧-shaped cavity augment the distributions of the temperature and concentration. Regardless the Darcy parameter, a homogeneous porous medium gives the lowest values of a nanofluid velocity.

ISPH method is used to simulate thermo-solutal convection of a nanofluid inside a novel ∧-shaped cavity containing a novel embedded shape and heterogeneous porous media.

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.

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 (ISPH) method to simulate the natural convection flow from an inner heated Y-fin inside Y-shaped enclosure filled with nanofluid.

The dimensionless governing partial differential equations are described in the Lagrangian form and solved by an implicit scheme of the ISPH method. The embedded Y-fin is kept at a high temperature T_h with variable heights during the simulations. The lower area of Y-shaped enclosure is squared with width L = 1 m and its side-walls are kept at a low temperature T_c. The upper area of the Y-shaped enclosure is V-shaped with width 0.5 L for each side and its walls are adiabatic.

The performed simulations revealed that the height of the inner heated Y-fin plays an important role in the heat transfer and fluid flow inside the Y-shaped enclosure, where it enhances the heat transfer. Rayleigh number augments the buoyancy force inside the Y-shaped enclosure and, consequently, it has a strong impact on temperature distributions and strength of the fluid flow inside Y-shaped enclosure. Adding more concentration of the nanofluid until 10% has a slight effect on the temperature distributions and it reduces the strength of the fluid flow inside Y-shaped enclosure. In addition, the average Nusselt number is measured along the inner heated Y-fin and it grows as the Rayleigh number increases. The average Nusselt number is decreasing by adding more concentrations of the nanofluid.

An improved ISPH method is used to simulate the natural convection flow of Y-fin embedded in the Y-shaped enclosure filled with a nanofluid.

The purpose of this study is to apply an incompressible smoothed particle hydrodynamics (ISPH) method to simulate the Magnetohydrodynamic (MHD) free convection flow of a nanofluid in a porous cavity containing rotating hexagonal and two circular cylinders under the impacts of Soret and Dufour numbers.

The inner shapes are rotating around a cavity center by a uniform circular motion at angular rate ω. An inner hexagonal shape has higher temperature T_h and concentration C_h than the inner two circular cylinders in which the temperature is T_c and concentration is C_c. The performed numerical simulations are presented in terms of the streamlines, isotherms and isoconcentration as well as the profiles of average Nusselt and Sherwood numbers.

The results indicated that the uniform motions of inner shapes are changing the characteristics of the fluid flow, temperature and concentration inside a cavity. An augmentation on a Hartman parameter slows down the flow speed and an inclination angle of a magnetic field raises the flow speed. A rise in the Soret number accompanied by a reduction in the Dufour number lead to a growth in the concentration distribution in a cavity.

ISPH method is used to simulate the double-diffusive convection of novel rotating shapes in a porous cavity. The inner novel shapes are rotating hexagonal and two circular cylinders.

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 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 study the unsteady ferrofluid flow with a hot source helix inside a cavity under the impacts of a variable magnetic field by using the incompressible smoothed particle hydrodynamics method.

The governing equations are formulated by considering the basics of the magnetohydrodynamic and ferrohydrodynamics. Different locations of a variable magnetic source outside the geometry are investigated. The helical coils are extensively applied in the cooling and heating of air conditioners and heat pumps. Computations were carried out for different lengths of the heated helix (0.2 ≤ L_h ≤ 0.8), different locations of the magnetic source, (a = 0.5, b = −0.01), (a = 0.5, b = 1.01), (a = 1.01, b = 0.5), (a = −0.01, b = 0.5), different numbers of the inner helix (one helix, two helixes and three helixes) and different values of the nanoparticles volume fraction (0% ≤ ϕ ≤ 10%).

The outcomes of the investigations revealed that an increase in the lengths of a helix by 0.4 results in a reduction of the stream function by 25.60%. In addition, when the magnetic wire is located near the center of the right wall, the maximum values of the average Nusselt number are obtained while the smallest values of the average Nusselt number are given when the magnetic source is located near center of the top wall.

The novelty of this paper is investigating the natural convection flow from two different models of an inner hot helix inside a cavity with considering different locations of variable magnetic sources.

This study aims to explore the evolving field of physics-informed neural networks (PINNs) through an analysis of 996 records retrieved from the Web of Science (WoS) database from 2019 to 2022.

WoS database was analyzed for PINNs using an inhouse python code. The author’s collaborations, most contributing institutes, countries and journals were identified. The trends and application categories were also analyzed.

The papers were classified into seven key domains: Fluid Dynamics and computational fluid dynamics (CFD); Mechanics and Material Science; Electromagnetism and Wave Propagation; Biomedical Engineering and Biophysics; Quantum Mechanics and Physics; Renewable Energy and Power Systems; and Astrophysics and Cosmology. Fluid Dynamics and CFD emerged as the primary focus, accounting for 69.3% of total publications and witnessing exponential growth from 22 papers in 2019 to 366 in 2022. Mechanics and Material Science followed, with an impressive growth trajectory from 3 to 65 papers within the same period. The study also underscored the rising interest in PINNs across diverse fields such as Biomedical Engineering and Biophysics, and Renewable Energy and Power Systems. Furthermore, the focus of the most active countries within each application category was examined, revealing, for instance, the USA’s significant contribution to Fluid Dynamics and CFD with 319 papers and to Mechanics and Material Science with 66 papers.

This analysis illuminates the rapidly expanding role of PINNs in tackling complex scientific problems and highlights its potential for future research across diverse domains.