Porous Square Research Articles

Lid driven cavity flow with two porous square obstacles

The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.

Natural convection heat transfer analysis of a nano-encapsulated phase change material (NEPCM) confined in a porous square chamber with two heat sources

This study focuses on the thermal behavior and performance of an insulated porous cavity containing square tubes, one as the hot block and the other as the cold block. The cavity is filled with a Nano-Encapsulated Phase Change Material (NEPCM) that combines the advantages of phase change materials (PCM) and nanofluid. The main purpose of this research is to examine the heat transfer mechanisms, phase change process, and overall thermal performance of the system. The governing equations of the NEPCM suspension are transformed into a dimensionless form and solved using the finite element approach. Various parameters, including nanoparticles concentration, fusion temperature, Darcy number, Rayleigh number, and Stefan number, are investigated to assess their impact on the system's thermal and dynamic performance. The results reveal that the optimal heat transfer performance is achieved when the NEPCM fusion temperature is set to 0.5. Moreover, a smaller Stefan number significantly improves the system's performance. Additionally, including NEPCM particles generally improves heat transfer, with a 33% increase in mean heat transfer observed when the volume fraction was raised from 0% to 2%.

Analysis of mixed convective-radiative heat transfer in a porous square cavity filled with various nanofluids

The present study examines the numerical simulation of mixed convective fluid movement and heat transference within the square cavity with various nanofluids. In this work, the nanofluids are prepared by suspending zinc oxide (ZnO)/silicon dioxide nanoparticles into water /kerosene /ethylene glycol base liquids. Features of various nanofluids flow inside cavity are investigated and this kind of studies may be useful in automobile applications and electrical gadgets. The vertical walls of the cavity are hot, the bottom wall is partially cooled, and the top wall is considered to be adiabatic. The Marker-And-Cell (MAC) method is utilized to solve the governing non-dimensional partial differential equations. The impact of heat generation/absorption (Q), nanoparticle volume fraction Darcy number (Da), Richardson number (Ri), Reynolds number (Re), and the thermal radiation parameter (Rd) are scrutinized. The outcomes are displayed informs of streamlines, isotherms, and local and average Nusselt numbers. The comparative study is performed and it finds a good accordance with the literature. As fluid flow and heat transfer are concerned, ZnO-Ethylene Glycol(EG) nanofluid explores the optimum features among the considered nanofluids. When 5% ZnO/SiO 2 nanoparticles are suspended into water, compared to SiO 2-water nanofluid, ZnO-water nanofluid has more than 10.81% mean rate of heat transmission. Suspension of 5% ZnO in water/kerosene/EG has the tendency to enhance the mean heat transfer rates of water/kerosene/EG up to respectively. The highest mean heat transfer rate is attained when the cavity’s aspect ratio is fixed as 1:1.

Effect of Hump Configurations of Porous Square Cavity on Free Convection Heat Transfer

Free convection is widely used in engineering applications, including solar energy, electronic devices, nuclear energy, and heat exchangers. A computational simulation utilizing Ansys Fluent-CFD was employed to examine the natural convection heat transfer inside a square cavity filled with pure water and saturated metal foam as a porous medium (porosity ɛ =0.9). The enclosure's lower wavy wall exhibits a high temperature (Th), while the side and upper walls have a low temperature (Tc). For different Rayleigh numbers, the study examines hump configuration and the bottom wall hump number (N). The predominant design of heat transmission was improved using the circular hump design parameters of ɛ=0.9, N=4 and Tc= 25C˚ for different Ra. This resulted in significant improvements in heat transfer enhancement and energy enhancement which were enhanced by 1.13 times, for both. The authenticity research included determining the optimal design for the square enclosure. This involved estimating the effects of hump configure and number of humps for bottom wall of enclosure. These parameters have not been studied yet. The optimum case showed the highest heat transfer coefficient (h) at circular hump, N=4 and Ra = 30´103. While the standard case had N=0 and Ra = 5´103. The CFD simulation results indicate that the primary objective of the study was achieved through the optimal design, which resulted in a significant enhancement of hydrothermal performance for both heat transfer enhancement and energy enhancement 1.13 times compared to standard case.

Structure and Conformation of Individual Molecules upon Adsorption of a Mixture of Benzoporphyrins on Ag(111), Cu(111), and Cu(110) Surfaces.

The front cover artwork is provided by the groups of Prof. Dr. Hans-Peter Steinrück and Prof. Dr. Norbert Jux at the Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg. The image shows a mixture of six 2H-tetrakis-(3, 5-di-tert-butyl-phenyl)(x)benzoporphyrins (2H-diTTBP(x)BPs, x = 0, 1, 2-cis, 2-trans, 3, or 4) molecules forming a porous square structure on Ag(111) as observed in scanning tunneling microscopy (STM) at room temperature. Read the full text of the Research Article at 10.1002/cphc.202300355.

Entropy generation and natural convection analyses in a non-darcy porous square cavity with thermal radiation and viscous dissipation

This study investigates the phenomena of fluid flows, general heat transfer and entropy generation on transient natural convection in a square cavity occupied with a saturated non-Darcy porous medium with dissipation effects and thermal radiation. The governing equations for the fluid flows and heat transfer, with corresponding boundary and initial conditions in the porous system are solved with the use of the alternate direct implicit method (ADI). The impact of the dimensionless parameters on the flow and thermal effect including entropy generation, with the fluid structure interaction cases are discussed. The following ranges have been used for simulations for the relevant dimensionless parameters: Grashof Number (103≤Gr≤107), Rayleigh number (103≤Ra≤106), Eckert number (0≤Ec≤5×10-5), the Forschheimer resistance (0≤Γ,γ≤10), radiation parameter (0≤Rd≤5) and Prandtl number (0≤Pr≤10). The present numerical work, compared with previously published work are made, and excellent agreement is discovered. According to the simulation results, the top right wall and base of the heated wall are where entropy is being generated most. Furthermore, as the Forschheimer resistance increases the flow rate, the heat transfer, and entropy production reduce. As Pr decreases at Ra=105 the buoyancy force takes control of the flow fields when the porous medium’s resistance weakens. As a result, the fluid flow becomes stronger.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

Numerical computation on MHD natural convective ternary nanofluid flow and heat transfer in a porous square cavity: Marker-and-cell technique

PurposeThe analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.Design/methodology/approachThe cavity inclination angle is fixed ω = 0 in case (I) and in case (II). The traditional fluid is water, and is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.FindingsThe average heat transfer rate is computed for four combinations of ternary nanofluids: and under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.Practical implicationsThe purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.Social implicationsThe current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.Originality/valueTo the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.

Numerical Study of Natural Convection Flow in a Square Porous Enclosure Filled with Casson Viscoelastic Fluid

The present simulation, a numerical investigation of natural convection of Casson viscoelastic fluid in a porous square enclosure has been reported. Darcy-Boussinesq approximation mathematical model has been considered. The enclosure has been uniformly heated from the left wall and uniformly cooled from right side wall. The developed partial differential equations of the present computational domain are employed by using stream function approach along with finite difference scheme. The house-computational numerical algorithm has been validated against with the previous work and the computational results have been registered a good correlation. All the important results as shown by streamlines, isotherms, and local Nusselt numbers, the impact of Casson fluid parameter (β), Rayleigh number (Ra) is examined. It has been observed that with the increase in Casson fluid parameter (β), the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Casson fluid parameter (β), for which the heat transfer inside the enclosure takes place solely by conduction mode. It has been also observed that at high Casson viscoelastic fluid the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Casson viscoelastic fluid.

An optimization approach for studying the effect of lattice unit cell's design-based factors on additively manufactured poly methyl methacrylate cranio-implant

In craniomaxillofacial surgery the inclusion of lattice structure on the Cranio-implants for the surgical procedure of cranial defects is difficult. Additive manufacturing open ups a huge space for the development of intricate profiles for complex surgical practices. Designing lattice structures with various design topologies has gained more interest in the medical community for reducing the weight of the implants in the cranial region. This research proposes the mimicking of cranial defective portion concerning bone-like porous structure by means of Poly methyl methacrylate (PMMA) material via 3D printing technology. The experiments were optimized by incorporating square-type porous lattice structure in the development of cranial implants. The design-based factors of the unit cell were enhanced with the aid of the Design of experiments (DOE) technique. L9 orthogonal array is developed by incorporating various design-based factors of the lattice unit cell like unit cell size (mm), skewing angle (°), wall thickness (mm), and unit cell orientation (°). The experiments are optimized with respect to obtaining better compressive strength and compressive strength/density of the prepared lattice structure incorporated polymeric samples. The result shows that for obtaining the maximum compressive strength in the porous square lattice-structured PMMA compression samples will be a lower cell size of 2 mm, a higher skewing angle of 30°, a higher wall thickness of 1 mm, and a unit cell orientation of 90°. The experimental optimized condition results of the design-based factors achieve the maximum compressive strength and compressive strength/density of 83.37 MPa and 189.73 MPa/g mm−3. The lattice structure orientated with 90° has a significant contribution towards reducing the development of structural deviations of incorporating square lattice structure on the PMMA polymeric material. Therefore, the topologically modified square lattice structure incorporated 3D printed PMMA material has a potential scope for the replacement of conventional maxillofacial cranial implants.

Flow around porous square cylinders with a periodic and scalable structure

This study experimentally explores the effect of permeability as an isolated control parameter on the downstream wake structure and the aerodynamic properties of the porous square cylinder. An addictive manufacturing technique was utilized to fabricate the porous cylinder, comprised of a simple cubic lattice structure. This unique manufacturing technique, coupled with a periodic and scalable lattice structure, allows us to decouple the permeability from the porosity. Based on permeability measurements in this study, Darcy number (Da) of the porous cylinder varies in a range of 2.44×10−5−4.07×10−4, while its porosity (Φ) is fixed at 0.7. Interesting features in the downstream wake are observed due to the mutual interaction between longitudinal and lateral bleeding flows. This mutual interplay prevents wake entrainment, relocating a recirculation bubble downstream and making its size smaller with increasing Da. When Da>2.0×10−4, in particular, a steady wake is observed in the near-wake despite the low degree of porosity. Finally, we proposed a new approach to defining the length scale of the flow adjustment that is suitable for the porous square cylinder and comparable to the porous cylinder with a circular cross-section.

Ferrofluid treatment with insertion of electric field inside a porous cavity considering forced convection

The electro-hydrodynamic (EHD) ferrofluid flow through a porous square shaped enclosure is simulated with different shapes of nanomaterial in the presence of constant heat flux. The flow is governed by coupled partial differential equations and is simulated with the well-established computational technique of control volume finite element method (CVFEM). The effects of the enhancing medium permeability and electric field strength on the flow are displayed through contour plots of streamlines and isotherms. The calculations are performed for different governing parameters namely, porosity, applied electric field , radiation effect , and nanomaterial shape factor over the Nusselt number . It is found that the medium augmenting permeability depreciates the ferrofluid streaming in the absence as well as in the presence of the applied electric field. The temperature of the ferrofluid augments with the medium increasing porosity in the absence of an external electric field, while an opposite effect is observed on the temperature in the presence of the electric field. The enhancement in the medium porosity makes the ferrofluid flow more regular in the absence as well as in the presence of an external electric field.

Bejan’s heatline and mulitphysics analysis of double diffusive free convection in a doubly stratified non-Darcian porous enclosure with heat generation

The current article illustrates the characteristics of the MHD free convective transport phenomenon in the thermal and mass stratified fluid-saturated Darcy-Forchheimer porous square cavity under the action of the cross-diffusion (Soret and Dufour effects) heat generation and chemical reaction effects. To acquire the spatial distribution of thermal fluxes along with directional propagation in chemically reactive and heat generative non-Darcy fluid flow, a newly developed heatline model for multi-force effect following the heat function theory is proposed in this study. In addition to the thermal profile visualization tools, the solutal free convective fluid flow fields are visually demonstrated by the massline contours curves using a novel mass-function model analogous to the heat function methodology. On the other hand, for the numerical solution of the non-dimensional form of the partial differential equations governing the study, the finite element method is applied. Moreover, the non-Darcy fluid flow attributes subjected to the multiple forces are graphically portrayed by the streamlines, isotherms, iso-concentrations, cumulative Nusselt/Sherwood number plots, heatlines, and masslines for the related dimensionless parameter. Here, these visuals delineate the contra-rotating fluid flow transition under both the thermal and concentration stratification forces. Especially, forceful retardation in both the thermal and concentration flux’s movements is noticed when magnetic forces are intensified. An upward geometrical shift of the higher concentration region is seen with increasing chemical reaction parameter.

Effect of Porosity and Transverse Magnetic Field on the Wake Separation and Detachment around a Porous Square Cylinder

Effect of Porosity and Transverse Magnetic Field on the Wake Separation and Detachment around a Porous Square Cylinder

A New Microporous Lanthanide Metal-Organic Framework with a Wide Range of pH Linear Response.

Lanthanide metal-organic frameworks (Ln-MOFs) have attracted extensive attention because of their structural adjustability and wide optical function applications. However, MOFs with a wide linear pH response and stable framework structures in acidic or alkaline solutions are rare to date. Here, we used 4,4',4″-s-triazine-2,4,6-triyltribenzoate (H3TATB) as an organic ligand, coordinated with lanthanide ions (Eu3+/Tb3+), and synthesized a new metal-organic framework material. The material has a porous three-dimensional square framework structure and emits bright red or green fluorescence under 365 nm UV light. The carboxyl group of the ligand is prone to protonation in an acidic environment, and negatively charged OH- and ligand (TATB3-) have a competitive effect in an alkaline environment, which could affect the coordination ability of ligand. The luminescence degree of the framework decreases with the increase in the degree of acid and base. In particular, such fluorescence changes have a wide linear response (pH = 0-14), which can be used as a potential fluorescence sensing material for pH detection.

Dynamic analysis of porosity dependent functionally graded sigmoid piezoelectric (FGSP) plate

This paper analyzes the vibration behaviour of the functionally graded sigmoid piezoelectric (FGSP) plate subjected to electrical and mechanical loading of a porous and non-porous plate. The sigmoid law is used for the variations of material properties along with the direction of thickness with different porosity types, i.e. even and uneven types. The plate incorporates the geometrical nonlinearity with von Kármán strains and First-order shear deformation theory (FSDT) based displacement field. For getting the nonlinear governing equation from Hamilton's principle or energy principle and higher-order numerical formulation with nine nodded isoperimetric elements and the six degrees of freedom per node. The perfect FGSP plate shows multi-periodic excitation with two strong attractors for SSSS boundary conditions, while quasi-periodic responses and 3-T periodic responses are observed for CCCC and CFFF boundary conditions. For evenly distributed porous SSSS FGSP square plate, the center displacement increases with an increase of the porosity from 0.2 to 0.4, while for un-evenly distributed porous center displacement reduces with a rise of the porous exponent from 0.2 to 0.4. The current analysis outcomes can be used for perfect and porous functionally graded piezoelectric smart structure applications under different electromechanical loading environments.

Radiative effects on unsteady MHD natural convection flow in an inclined wavy porous cavity using hybrid nanofluid containing a square obstacle

The introduction of hybrid nanofluids is a significant notion in several engineering and industrial applications. It is utilized prominently in diverse engineering applications, such as low-pressure drop, wider absorption range, generator cooling, good thermal conductivity, nuclear system cooling, heat exchangers. The present model describes the unsteady MHD free convection flow in an inclined wavy permeable enclosure using hybrid nanofluid (Aluminum oxide/Copper-water) containing a square obstacle with the effects of radiation and heat generation/ absorption. The flow is buoyancy-driven and is subjected to heat radiation (Rd) and an angled magnetic field that is constant (B0). The left wall of the cavity is partially heated and cooled by the wavy-right wall, while the remaining sides are adiabatic and contain a square solid block. A numerical Finite difference technique is utilized to resolve the governing PDEs formulated in stream function, temperature and nanoparticle volume fraction. The acquired results are validated with previous numerical studies. The parameters number in this study are discussed as the inclination angle 0°⩽α⩽π/2, Dimensionless heat source length (0.2 ≤ B ≤ 0.8), porosity of the porous medium 0.1⩽ε⩽0.9 dimensionless location of the left heater (0.3 ≤ D ≤ 0.7), Heat generation -2⩽Q⩽2, nanoparticles volume fraction (0.01 ≤ φ ≤ 0.02), thermal radiation 0⩽Rd⩽10 and the Hartmann number (0 ≤ Ha ≤ 100). The results show that improving the porosity raises the average Nusselt number; however, the rate of increase is greater at higher heat flux locations. The average Nusselt number grows when the nanoparticle volume fraction raises in Rd. The distribution of isothermal lines is slightly reduced for the higher value of the Hartman number. Natural convective hybrid nanofluid flow in a wavy porous square cavity combined with heat source/sink has a vital role in various engineering and industrial processes such as solar collector electric machinery, creation of constructing shelters and attics.

Mechanically-grown morphogenesis of Voronoi-type materials: Computer design, 3D-printing and experiments

The present work introduces a novel and versatile computer-design and experimental strategy to obtain random Voronoi-type geometries, called M-Voronoi (from mechanically grown), with smooth void shapes and variable intervoid ligament sizes that can reach very low relative densities. This is achieved via a numerical, large strain, nonlinear elastic, void growth mechanical process. Originally small circular voids embedded in a cell of arbitrary shape (triangle, circle, rectangle, trapezoid) grow when subjected to displacement (Dirichlet) boundary conditions. The deformed voids evolve into smooth Voronoi-type geometrical shapes leading to macroscopic isotropy or anisotropy depending on the prescribed boundary conditions. The void growth process is a direct consequence of mass conservation and the incompressibility of the surrounding nonlinear elastic matrix phase and the final achieved relative density may be analytically estimated in terms of the determinant of the applied deformation gradient. In order to study the mechanical properties of the M-Voronoi materials, we focus on two-dimensional porous polymer square representative isotropic and anisotropic geometries in terms of void size and realization, which are 3D-printed and experimentally tested under uniaxial compression. For comparison, we also test random polydisperse porous materials with circular voids, standard eroded Voronoi geometries and hexagonal honeycombs. The first two are also isotropic while the latter are only isotropic in the linear elastic regime. We show that the randomness of the M-Voronoi geometry and their non-uniform intervoid ligament size leads to enhanced mechanical properties at large compressive strains with no apparent peak-stress and strong hardening well before densification. By comparing them with the hexagonal geometries, which tend to exhibit a peak-stress and a plateau-type response, we show that the hardening response of the M-Voronoi is mainly due to their geometrical characteristics and less due to the polymer hardening response. Anisotropic M-Voronoi are also produced and tested indicating that anisotropy only enhances the initial stiffness along the longitudinal direction but instead leads to lower buckling loads and hardening rates than the corresponding isotropic M-Voronoi in the nonlinear regime.

Unsteady Natural Convection in a Porous Square Cavity Saturated by Nanofluid Using Buongiorno Model: Variable Permeability Effect on Homogeneous Porous Medium

This paper investigated numerically a natural convection in a porous cavity saturated by nanofluide. The left and right wall of the cavity are maintained at the hot-cold temperature respectively, the other walls are adiabatic. The two-phase Buongiorno model has been adopted to take account Brownian and thermophoretic diffusion in order to demonstrate the spatial distribution of the local nanoparticles concentration. After following the temporal evolution of the different structures (0<τ<5), Numerical simulations are performed to explore the effect of density buoyancy (104<Ra<106), the permeability of the homogeneous porous medium (10-5<Da<10-2), on the hydrodynamic, thermal and mass behavior. An original motivation was also introduced in our work to examine the effect of linearly variable permeability along the opposite direction of the cavity by varying the initial Darcy number from (10-5<Da<10-2) and fixing the final Darcy number Daf =10-5. The dimensionless partial differential equations are solved using the finite element method. The effects of the governing parameters on heat transfer are analyzed. Results indicate that the stationary regime is formed after the unsteady regime at dimensionless time τ = 0.3. The movement of nanofluide is strongly influenced by thermal buoyancy forces and depends on the Darcy number, heat transfer is accentuated for the homogenous medium compared to this one with variable permeability. It is found that the convective flow in a homogeneous porous medium is considerably affected by the variation of permeability and consequently the heat transfer is reduced.

Bioconvection in Porous Square Cavity Containing Oxytactic Microorganisms in the Presence of Viscous Dissipation

Bioconvection in Porous Square Cavity Containing Oxytactic Microorganisms in the Presence of Viscous Dissipation