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The ternary hybrid nanofluids have potential in different technological arenas such as biomedical engineering, solar energy, atomic reactors, the automotive industry, and heat pipes. Given these facts, along with the recent advancements in nanotechnology and their extensive applications, this research focuses on the MoS₂-Fe₃O₄-ZrO₂/CH₃OH ternary nanofluid flow through bidirectional stretching sheets. We have transformed the coupled nonlinear partial differential equations for the advanced model into nondimensional ordinary differential equations using similarity transformations, and then semi-analytically apply the homotopy analysis methodology (HAM). We have displayed the physical features of potential factors graphically alongside the flowing factors based on velocity and temperature. We presented a physical evaluation in tabular format for the rate of heat transmission and compared the results with existing work to ensure their validity. These meaningful outcomes indicate that the axial fluid velocity is compressed by the magnetic interaction, inertial drag, porosity and stretchable ratio, while it is augmented by the Powell-Eyring factor and the changed Hartmann value. The effect of increasing transverse speed boosts inertial drag.

Plasma spraying is a prospective method frequently employed because of its increased effectiveness in ceramic coatings. Optimizing process parameters is necessary to maximize the coating performance. This study employed response surface methodology (RSM) to investigate the impact of process variables, including current, powder feed rate, and standoff distance, on the porosity and corrosive wear loss of Cr₃C₂$+$8YSZ composite coating. Experiments were done using the central composite design method, and quadratic regression models were created for the responses based on the completed trials. All parameters are observed to be most significant as the obtained p-value is under the threshold of 0.05 as per the analysis of variance (ANOVA) calculations. The optimal plasma spray process parameters were determined to be 500 A of current, a powder feed rate of 46gm/min, and a standoff distance of 3 inches for the expected lowest corrosive wear loss of 0.000025mm/year and a reduced area percentage porosity value of 0.93.

This paper is concerned with the electro-mechanical buckling analysis of different kinds of smart sandwich shells with functionally graded porous core and piezoelectric sensor–actuator face sheets. Different types of shallow shells with double curvature including convex shells, cylindrical shells and concave shells are analyzed. It is assumed that effective properties of the porous core are functionally graded to vary as a special function of the thickness parameter. The equilibrium equations are established for the doubly-curved smart sandwich shells using the energy method. The stability equations governing the equilibrium position of the smart sandwich shells are obtained as a set of coupled partial differential equations. Closed-form expressions are generated to obtain the critical buckling loads of the smart sandwich shells using the airy stress function. Sandwich shells under different types of electro-mechanical loadings including axial, lateral and hydrostatic pressures are analyzed. These numerical results show the effects of feedback gain, porosity coefficient and piezoelectric layer thickness on the buckling resistance of these smart sandwich structures.

The main goal of this research is to analyze the natural frequencies and dynamic response, and to utilize nonlinear control techniques for vibration control of a smart nanocomposite sector plate, while taking into consideration the effects of agglomeration and internal pores. The proposed composite configuration includes a porous core layer reinforced with agglomerated GPLs, as well as two layers of piezoelectric sensors and actuators. Both complete and partial agglomeration states are considered based on the Eshelby–Mori–Tanaka approach to predict the effective properties of the nanocomposite. The mechanical properties of the porous core are characterized using an open-cell metal foam with interconnected pores, notable for their low density and high surface area. The governing equations of motion are derived using Hamilton’s principle, which is based on the First-order Shear Deformation Theory (FSDT) plate theory and the finite element method. The nonlinear fuzzy PID controller is designed as a combination of a fuzzy PI component and a nonlinear PD component. The gains of the PD controller are dynamically adjusted using nonlinear gains to optimize its performance. In addition, a comprehensive analysis has been conducted to examine the effects of geometric dimensions, distribution of reinforcement, weight fractions of nanofillers, parameters of agglomeration, porosity coefficient, porosity pattern, and boundary conditions on the natural frequencies and dynamic response of smart porous nanocomposites. Numerical simulations demonstrate the efficacy of the proposed controller in significantly reducing vibration amplitudes compared to velocity feedback. The velocity feedback controller decreases deflection from 24.39$\mu \mathrm{\text{m}}$ to 8.37$\mu \mathrm{\text{m}}$, whereas the proposed controller achieves 3.66$\mu$m, representing a 56.27% improvement in performance.

This paper seeks to study and investigate the wave dispersion behavior in porous functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) beams. The beams comprise four patterns of single-walled carbon nanotubes (SWCNTs) distributed in the polymer matrix. The mixture rule is used to estimate the CNTR beams’ material properties. Innovative to this study are three porosity models describing the porosity distributions within the matrix and a three-unknown integral higher-order shear deformation theory (HSDT) modeling analytically the CNTRC beams with a novel shape function expressing the distributions of shear stresses and strains. The equations of motion for CNTRC beams are derived based on Hamilton’s principle. The stiffness and mass matrices are formulated by a generalized solution of harmonic wave propagation to express the wave dispersion relations. Numerical comparisons with previously published works verify the applicability of this mathematical model. The paper studies the effects of CNTs patterns through the polymer matrix, porosity models, and volume fractions of the porosity and CNTs. Based on the analytical results, augmenting the porosity and CNTs volume fractions leads to faster phase and group velocities. Furthermore, the impact of CNTs volume fractions, porosity models, and porosity volume fractions becomes more pronounced as the wavenumber increases.

This work aims to examine the stability of rectangular hollow section (RHS) beams with functionally graded (FG) thin walls that are subjected to thermo-mechanical loads and different boundary conditions. A nonlinear analytical model for predicting thermal buckling that introduces distortional deformation and takes porosity into account is presented. Using Ritz’s method, coupled nonlinear equilibrium equations are established and then the tangential matrix is formed to obtain critical values. Material properties vary continuously and progressively across the thickness according to a power law of the porous volume fraction and are assumed to be unrelated to the temperature. A finite element (FE) simulation using the FE ABAQUS software is employed to verify the applicability of the current model in predicting lateral torsional buckling (LTB) resistance. Several numerical examples are used to illustrate the impacts of temperature, porosity, power-law index, and axial loads on the instabilities of FG box beams.

Numerical simulation is significant for investigating impact performance of functionally graded SiC${}_{\mathrm{\text{p}}}$/Al6061 composite plate. Existing numerical studies rely on stress–strain characteristics derived from theoretical models which hardly consider damage softening and porosity effect. In this work, an effective modeling method is developed to generate geometric models of representative volume elements (RVEs) of SiC${}_{\mathrm{\text{p}}}$/Al6061 composites. It avoids the limitations of traditional methods in generating RVEs with high ceramic content. Finite element (FE) models for uniaxial compression of RVEs are established with consideration of elastoplastic behaviors of constituent materials and interfacial damage. Stress–strain curves of SiC${}_{\mathrm{\text{p}}}$/Al6061 composites are obtained from FE simulation results by a homogenization method. The stress–strain curves can reproduce the damage softening, and the predicted elastic moduli agree well with those estimated by Mori–Tanaka theory. Low-velocity impacts of a functionally graded SiC${}_{\mathrm{\text{p}}}$/Al6061 composite plate are simulated using the stress–strain curves. The simulation results are close to those using stress–strain curves obtained by a theoretical method, however, overestimate contact forces in comparison with experimental results. Novel porous RVE FE models are further developed to consider the porosity effect. The models give an improved prediction for stress–strain characteristics of the composites and low-velocity impact response of the functionally graded composite plate.

This research presents an analysis on the nonlinear dynamics of rotating sandwich disk with different edge conditions subjected to the transverse pulse loadings. It is assumed that the annular sandwich plate is made from Titanium alloy face sheets and a metal-based porous composite core reinforced by graphene nanoplatelets (GNPs). The aluminum core of the sandwich plate is assumed to be multi-layered as each layer have different porosities. The effective material properties of the porous nanocomposite core are predicted by a generic Halpin–Tsai model where the porosity is included. In the framework of the first-order shear deformation theory and the von-Kármán nonlinearity, the nonlinear equations of motion are formulated using Hamilton’s principle. The nonlinear governing equations are reduced by employing the Galerkin method and the fourth-order Runge–Kutta technique is applied to solve the final differential equations. The influences of material properties and geometrical parameters on the nonlinear dynamic response of the annular sandwich plate are investigated in detail.

In this paper, the steady and transient heat transfer behaviours of multidirectional (1D/2D/3D) functionally graded composite plates are investigated. Also, two different porosity types, i.e., even and uneven distributions, are considered along with material gradation. Here, the spatial/temperature-dependent effective material properties of these highly heterogeneous composites with porosity are evaluated using the extended Voigt’s homogenisation scheme via multi-variable power-law functions and further verified with the representative volume element (RVE) scheme. In continuation, generalised mathematical models are developed by including material nonlinearity using the cubic-polynomial-based temperature-dependent constitutive model. The Poisson’s and Laplace’s equations are utilised for steady and transient heat transfer problems, respectively, and the weak form is derived using the Galerkin method. Further, coupled finite element method (FEM)–finite difference method (FDM) is adopted via Picard’s successive iteration and Crank–Nicolson technique to compute the nonlinear transient temperature. The proposed model is verified by comparing it with the previously reported results. In addition, the effects of heterogeneity, porosity, power-law indices and boundary conditions on the steady/transient heat transfer responses of multidirectional functionally graded plates are examined and discussed in detail. At last, the optimum material distributions are obtained using the response surface methodology (RSM) by minimising the heat transfer responses.

In various industries, for advanced cooling, electronic device thermal management, and solar thermal systems ethylene glycol (EG)-based nanofluids are presented as efficient heat transfer agents. The proposed oxide tri-hybrid nanofluids comprising multiple oxide nanoparticles, i.e., Al₂O₃, TiO₂ and SiO₂ have significantly enhanced thermal properties and stability compared to mono and binary nanofluids. The current investigation aims at the transportation of heat characteristics of an EG-based tri-hybrid nanofluid over a curved Riga surface filled with a porous substance. The study focuses on thermal radiation effects. Moreover, the Riga plate is a magnetic device with alternating electrodes and magnets that provide a significant electromagnetic forcing mechanism for flow behavior. The designed mathematical model with their dimensional form needs transformation to their corresponding dimensionless form with the utility of similarity rules. Further, a numerical technique based on shooting is employed for the solution of the model for the attainment of physical factors. The physical properties of these factors are presented briefly through graphs followed by a comparative analysis.

In this paper, for some classes of weight functions $w$ on $G$, we study $\sigma$-$c$-lower porosity of the set

This study undertakes a numerical investigation into the two-phase magnetohydrodynamic (MHD) flow of a novel Al₂O₃-Ag/ethylene glycol (30%)–water dusty Maxwell hybrid nanofluid within a porous stretched cylinder incorporates the influential factor of thermal radiation. Notably, it pioneers exploration into the flow characteristics of Maxwell nanofluids and hybrid nanofluids containing dust particles over a porous cylinder, an uncharted domain in the existing literature. By adeptly simplifying the governing partial differential equations into nonlinear ordinary differential equations (ODEs) using judiciously chosen similarity variables, our research employs MATLAB’s bvp4c scheme to obtain numerical solutions, presented both graphically and in tabular form. Our results unveil significant insights: the Maxwell fluid parameter and magnetic parameter exhibit a dual effect of enhancing heat transfer while mitigating velocity gradients. Moreover, increasing the curvature parameter exerts a favorable influence on the velocity and temperature profiles of both phases. Furthermore, the fluid-particle interaction parameter emerges as a pivotal factor shaping velocity and temperature profiles in the dust phase, while the radiation parameter notably amplifies heat transfer rates. Remarkably, our investigation reveals a notable 26% increase in total skin friction and a nearly 13.5% enhancement in heat transfer within the dusty Maxwell hybrid nanofluid configuration compared to the dusty Maxwell nanofluid arrangement. These findings hold profound practical implications for addressing real-life engineering challenges, offering invaluable insights into optimizing heat transfer and velocity profiles across diverse technical applications. They pave the way for the development of enhanced cooling mechanisms and highly efficient heat exchangers, crucial for tackling multifaceted engineering challenges.

The combined influences of porosity, elasticity of tangential end constraints, nonlinear elastic foundations and initial geometrical imperfection on the buckling and postbuckling of functionally graded material (FGM) beams under uniform temperature rise are investigated in this paper. The pores are distributed into FGM according to the even and uneven types. The properties of constituent materials are assumed to be temperature-dependent and effective properties of porous FGM are determined using a modified rule of mixture. Two ends of beams are assumed to be simply supported or clamped and under tangentially elastic constraints. Equilibrium equations are derived based on Timoshenko beam theory taking into account the von Kármán nonlinearity, initial geometrical imperfection and interactive pressure from nonlinear elastic foundation. Analytical solutions are assumed and Galerkin method is used to obtain the expressions of buckling loads and nonlinear load–deflection relation. An iteration process is adopted to determine the critical buckling temperatures and postbuckling temperature–deflection curves. Parametric studies are carried out to analyze the effects of porosity, degree of in-plane constraints of ends, out-of-plane boundary conditions, imperfection, slenderness ratio and elastic foundations on the thermal buckling and postbuckling behaviors of porous FGM beams.

The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in dense environments. Starting from sub-critical states of ordinary percolation the system evolves under the diagenetic rules to critical percolation configurations. Our numerical simulation results in two dimensions indicate that the stable configuration has the same critical behavior as the ordinary percolation.

A honeycomb model is designed according to the leaf veins, which is expressed as a function of porosity and tortuosity, and there is no empirical constant in this model. We mainly applied it to the leaf venation network, and the prediction in our model are compared with that from available correlations obtained by matching the numerical results, both of which are consistent with each other. Our model and relations may have important significance and potential applications in leaf venation and porous media. They also have a certain guiding significance to fluid heat transfer and thermal diffusion, as well as biotechnology research, e.g. veins and the neural networks of human.

We study the scaling properties of a hybrid deposition model that considers random deposition (RD) and ballistic deposition (BD) with next-nearest-neighbor aggregation. The BD occurs with probability p and competes with RD with probability $(1-p)$. It is found that the dynamics of the growing interface follows the same universality class as that of the correlated BD and obeys the generalized scaling ansatz of Family–Vicsek, as proposed by Horowitz and Albano. The deposition process leads to porous structure in the bulk. We have shown that the saturated porosity scales as a power law with the probability of mixing p, which can be described well by extending the scaling arguments as that for the surface.

The impact damage of an Al₂O₃-coated soda-lime glass under tensile and compressive stress conditions was investigated by an impact test using a steel ball (2mm dia.). The size of the glass specimens was 40×40×5(mm). In order to change the porosity percent of each specimen, the target distance was set at 120mm and 70mm. Also, the effect of the thickness of the coating layer was shown by two amounts (100 μm and 50 μm). The velocity of the steel balls was set between 30 and 60m/s. After the impact test, the crack patterns and lengths were measured using a stereo-microscope. The tensile and compressive specimens were prepared by inflation and deflation of air pressure within a pressure vessel. It was confirmed that the crack length of the glass under tensile stress was longer than that of glass under compressive stress. Also, the optimum conditions were a target distance of 70mm and 100 μm of a coating thickness, thus resulting in a minimization of porosity percent and area.

The A raw C/C composite with a density of 1.40g/cm³ was used in order to investigate the high temperature erosion behavior and mechanical properties of liquid silicon infiltrated C/SiC composites. The microstructures of the as-received and infiltrated composites were examined with an optical (OM) and a scanning electron microscope (SEM). The volume fraction of residual silicon and porosity was measured by using an image analyzer. The flexural test for as-received as well as melt Si infiltrated C/C composites was performed to estimate the mechanical strength of the C/SiC composites. Severe fiber damage was occurred after infiltration. SiC was formed by reaction between carbon of fiber surface and molten Si. Flexural strength was decreased after melt Si infiltration and pull-out of fiber was observed at the fracture surface of as-received material.

In this study, a novel method two-step foaming method (TSFM) has been proposed to fabricate Al alloy foams with irregular shapes. The two steps Al alloy foaming process and cell-structures evolution have been investigated experimentally. The relationship between foamable precursor, foaming parameters and cell-structures of the final foam samples has been observed. Moreover, the Al foam samples with regular and irregular shapes prepared by TSFM are shown in this paper.

Aluminium has good corrosion properties and a high strength to weight reduction which makes it favourable in many applications. The increased use of aluminium casting in the automotive industry does also imply that the need for design data for aluminium increases. Especially for castings, the influences of casting defects are always an issue. For this reason fatigue properties for as-cast sand and permanent mould specimens with different contents of porosity have been studied. The cast aluminium specimens of two different porosities were fatigue tested in cyclic axial test at R=-1. Prior to fatigue test specimens were examined by CT-scan and sorted into two quality groups depending on the porosity level.

The aim of this work was to investigate the fatigue life for cast AC4C-T6 alloy with different amounts of inherent porosity. An additional aim was to predict the durability for cast components with defect constrained in a specified volume of components, by using a commercial program MSC. Fatigue.