Porosity Fraction Research Articles

Micromechanics and microstructure based machine learning approach: Unveiling the role of porosity and hydrated phases on the tensile behaviour of cement pastes

The fracture process and the mechanical performance of the cement paste rely significantly on its tensile behaviour. Machine learning methods have been recently developed to predict this behaviour based on numerous experimental measurements. Due to multi-phase heterogeneous nature of cement paste microstructure, evaluation of the role of each chemical phase on the cracking of cement paste is necessary to develop optimized binder systems. Numerous experimental tests would be necessary to determine the best cement pastes in a considered environment. Therefore, in this study, a hybrid approach based on an ensemble machine learning model and a microstructure informed micromechanical model is proposed for predicting the tensile behaviour of hydrated cement pastes. The model can be used as a quick prediction tool for tensile strength of a given microstructure or for deep analysis on the optimization of binder system. A Deep Neural Networks (DNN) model was developed by training and validating a large dataset detailing the chemical phase composition, phase volume fractions and the tensile strength of the cement pastes. This dataset covers an extensive range of Portland cements, hydration ages and water-to-cement ratios. It was developed by simulating cement thermodynamics and tensile behaviour using a damage micromechanical model; which is otherwise almost impossible to obtain through experimental means. Additionally, two generative algorithms, tabular generative adversial networks (TGAN) and conditional generative adversial networks (CTGAN), were employed for dataset augmentation as a sampling method for the sensitivity analysis. This machine learning study provides an in-depth investigation to identify the role of volume fraction of solid phases (C-S-H, ettringite, portlandite and hydrogarnet) and micro porosity (dry and filled) in affecting the tensile behaviour of hydrated cement paste. Optimization assessment of the microstructure was then performed using micromechanical analysis and damage propagation in hydrated cement paste phases and porous network.

The Influence of Iron Content on the Porosity of AlSi9 Alloy Intended for Alfining Piston Ring Inserts.

Due to its tendency to increase the power of engines, improving their reliability and operational efficiency, the compression ring in combustion engine pistons is embedded in a cast iron insert, which is subjected to the process of "alfining". This involves covering the insert with an Al-Si alloy, which increases the iron content. Research has shown that the β-Al5FeSi phases crystallizing in the area of the insert-piston connection are the main cause of an unstable connection between the silumin casting of the piston and the ring insert. Their unfavourable lamellar morphology and large dimensions are the main causes of weakening in the connection between the insert and the piston, resulting in an unacceptable number of defective products. It has also been found that up to approx. 0.59 wt.% Fe, the pore volume fraction is very small (up to 3%), and there is no correlation. However, after exceeding this value, both the volume fraction of the β-Al5FeSi phase and the number of pores increase monotonically to values of approximately 18% and 14%, respectively, and the correlation between the examined features is statistically significant. These results were compared with known theories of the influence of iron on the porosity of Al-Si alloys, showing that the precipitates of the β-Al5FeSi phase are more important in the porosity fraction than the two-layer oxide films called "bifilms". This research was carried out and verified under industrial conditions in one of the largest piston foundries (Federal-Mogul Gorzyce sp. z o.o., F-MG) on a separate line intended for alfining ring inserts intended for combustion pistons.

Effect of porosity gradient on fracture mechanics of bi-directional FGM structures: Phase field approach

This research aims to develop a computational model that can accurately predict the fracture behavior of porous bi-directional Functionally Graded Materials (FGMs). The Voigt model for homogenization, is established to account the effects of porosity fraction and gradient distribution within the FGMs, providing valuable insights about the brittle crack propagation. The study employs the UMAT subroutine in ABAQUS software and establishes an analogy between the phase field evolution law and the heat transfer equation, enabling efficient analysis of complex fracture problems. To validate the model, 2D fracture benchmark cases are analyzed, demonstrating its ability to capture different failure modes and the intricate material behavior of porous FGMs under fracture conditions. Furthermore, newly parametric analyses, that highlights the impact of various values of porosity’s volume fraction and FGM’s power law indexes on the brittle fracture path, are conducted to further validate the effectiveness of the newly developed phase field model in predicting the fracture behavior of bi-directional porous FGMs.

Carbonation resistance of fly ash/slag based engineering geopolymer composites

Engineering geopolymer composites (EGC) are promising environmentally friendly building materials with excellent mechanical properties. However, the durability of EGC is compromised by gradual carbonation from atmospheric exposure. For the first time, this study provided an insight of the carbonation of EGC by comprehensively investigating the effect of mix design, such as fly ash/ground granulated blast furnace slag ratio (FA/GGBS ratio), alkali content, water/binder ratio (W/B ratio) and polyethylene (PE) fibre content, on its carbonation resistance. Our results showed the components in EGC affected the carbonation through the alternation of microstructures. An increase of FA content and W/B ratio significantly increased the carbonation depth by 206.6 % and 116.3 % respectively due to the increased porosity and transition pore fraction, resulting in more than 30 % reduction in tensile strength and 15 % reduction in compressive strength. However, increased alkali and fibre content prevent carbonation with around 60 % and 26 % decrease of the carbonation depth, leading to a less loss of the mechanical properties. Furthermore, we tested the pH values of the EGC along the carbonation depth, proposing a novel approach to assess the carbonation degree by dividing the area into completely carbonated area (pH around 9.21–10.44) and non-carbonated area (pH around 12.58–13.37). These findings provide insights for mitigating carbonation effects in EGC and facilitate the widespread use of this sustainable material in construction applications, ensuring long-term durability and reliability.

Multiscale model for concrete cured under geothermal environment: Theoretical analysis and experimental validation

Concrete poured as linings of geothermal tunnel would deviate normal curing condition. A multiscale model based on continuum micromechanics, accounting for temperature-dependent factors, is established from the cement paste level to the concrete level. This model predicts the physical properties and compressive strength of concrete and is validated against measured strength, which incorporates the impact of high-temperature curing on the hydration degree, density of C-S-H, and chemical shrinkage of cement. Evolutions of the average hydration degree and compressive strength of concrete were experimentally investigated to this end, and then simulated with multiscale approach. The specimens were subjected to curing temperature 20°C, 40°C, 60°C, and 80°C for first 7 days while maintaining constant relative humidity of 100 %, and then water curing at 20°C for the rest days till tests. The high-temperature curing accelerates the hydration process, but the variance in hydration degree between standard temperature (20°C) and high-temperature conditions diminishes with prolonged water curing. An enhancement in compressive strength is also observed in the early stages of high-temperature curing, succeeded by a decline compared with standard curing after the 50th curing day. Quantitative analysis reveals that volume fractions of hydrates and porosity subjected to high-temperature curing show a substantial increase in the first 7 curing days, and the denser layer of hydration products formed on cement slows down the hydration in later curing ages. The complex evolution of strength in concrete undergoing high-temperature curing is influenced by temporal consideration (the hydration degree) and spatial considerations (the density of C-S-H and the chemical shrinkage of cement). The surge in hydration significantly contributes to strength promotion in early stages. However, the pivotal factor leading to strength deterioration is the increase of porosity when the difference in the hydration degree is less than 0.065.

Tailoring Solid-State Battery Performance through Computationally Tuning the Composition of LLZO-LCO Composite Cathodes

The composite cathode consisting of garnet-type solid-electrolyte Li7La3Zr2O12 (LLZO) and active material LiCoO2 (LCO) is one of the most promising solutions for the cathode design of all-solid-state lithium batteries. The transport properties of Li within the LLZO-LCO composite cathode are known to be sensitively dependent on the composition and microstructural features. This study focuses on computationally refining the performance of solid-state batteries by modifying the porosity and volume fractions of the LLZO-LCO composite cathode while considering the variations in the microstructural features. Various 2D and 3D microstructures were synthesized using a stochastic stacking particle model and the corresponding effective diffusivity of Li is calculated using a numerical homogenization method, which allows for a systematic assessment of the impact of composition on lithium transport within the microstructure. By identifying the optimal ratio between LLZO and LCO phases and porosity, this research yields crucial insights for improving the performance of solid-state batteries by tailoring the composite cathode.Figure 1: A) An example 3-dimensional microstructure with 20.3% percent vacuum (white space) and 39.25% percent LCO (yellow) and 40.45% LLZO (orange). B) The highest effective diffusivity (purple) is found when the LLZO percentage is highest. Once the vacuum percentage is 30% or higher, minimal effective diffusivity (red) is observed.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Figure 1

Vibration analysis of a composite sandwich plate with a viscoelastic auxetic core, FG-CNTRC interior, and MEE–FGP exterior face sheets

This research has been conducted to analyze the free vibration behavior of a five-layered composite plate with a viscoelastic auxetic core. The plate comprises a viscoelastic auxetic core layer, functionally graded carbon nanotube reinforced composite (FG-CNTRC) interior, and magneto-electro-elastic functionally graded porous (MEE–FGP) exterior skins, which is rested on Winkler–Pasternak foundation. According to the magnetic–electric boundary conditions and Maxwell equations, the electric and magnetic potentials of the plate are determined. The macro-mechanical properties of the auxetic core have been derived based on Gibson’s model; the three-parameter Zener model has also been utilized to describe its viscoelastic behavior. Additionally, the equations of motion of the plate are obtained and solved by using Reddy’s third-order shear deformation theory (TSDT) and the Galerkin method, respectively. Moreover, various aspects of the current research have been validated by comparing the numerical results with those reported in the literature section. Overall, in the numerical result section, the effects of different parameters and conditions such as geometrical parameters, position of the plate’s interfaces of layers (thickness of the core and face layers), various distribution patterns and volume fractions of both CNT and porosity, external work parameters of the MEE skins, boundary conditions, Winkler–Pasternak stiffness coefficients, the relaxation time, and other parameters of the viscoelastic core on the natural frequency and loss factor of the composite plate are represented.

Modeling the dependence of electrolyte design on lithium-sulfur battery performance

Herein, we offer two electrochemical models, a zero-dimensional (0-D) and a one-dimensional (1-D) model, to mechanistically explore the impact of the electrolyte-to-sulfur (E/S) ratio and electrolyte properties on the discharge behavior of a lithium-sulfur (Li-S) cell. The electrochemically active area in both models is defined based on the carbon weight fraction and reference porosity, so the influence of the carbon loading and E/S ratio on the reaction kinetics is included. Mass transfer of the species must be considered to model the reliance of the discharge capacity on the current density. Instead, the 0-D model is more responsive to the influence of the E/S ratio on the discharge capacity. The effect of electrolyte properties can be modeled implicitly through model parameters. The 0-D model is less sensitive to the variance in model parameters than the 1-D model in terms of the predicted capacity.

Sensitivity analysis of hydraulic erosion and calibration of the erosion coefficient

Hydraulic erosion may pose a threat to the safety and sustainability of geo-related infrastructure, yet quantifying the intricate process of hydraulic erosion still poses a significant scientific and technical challenge. One important step in meeting this challenge is the formulation of a hydraulic erosion model with the erosion coefficient as a central controlling parameter. Calibration of the erosion coefficient (or rate) remains one of the main obstacles to improving predictive modelling, particularly in scenarios lacking long-term laboratory test data. In this study, sensitivity analysis of the key erosion indicators on the parameters controlling hydraulic erosion is conducted. A novel calibration method for the erosion coefficient is presented based on sensitivity analysis. After validating against simulation results and laboratory test findings, the proposed calibration method is applied to a hypothetical long-term hydraulic erosion case. The results show that the maximum hydraulic erosion time is sensitive to all considered parameters (erosion coefficient, initial fraction of fluidized solid particle, initial porosity and maximum porosity), while the erosion curve shape is only sensitive to the initial porosity and the maximum porosity. The validation by existing simulation results shows that the proposed calibration method is robust and internally consistent. The validation by experimental results indicates that the proposed calibration method also has high external validity. Finally, the proposed calibration method is applied to hypothetical long-term erosion in a grouted area. The results show that the hydraulic erosion effect in the grouted area becomes increasingly severe over time. This study contributes toward a more efficient calibration of the erosion coefficient, especially for scenarios in the absence of testing porosity evolution data. The research outcome provides a theoretical foundation for the safety assessment and sustainability analysis of geotechnical structures that are subject to hydraulic erosion.

Fast shot speed induced microstructure and mechanical property evolution of high pressure die casting Mg-Al-Zn-RE alloys

In this study, the effects of fast shot speeds during high pressure die casting on the microstructure and mechanical properties of Mg-Al-Zn-RE (RE: rare earth) alloys were systematically investigated. The optimum mechanical performance was achieved at a fast shot speed of 6 m/s, and the ultimate tensile strength, yield strength, and elongation of the castings reached 290 MPa, 190 MPa, and 10.5 %, respectively. With an increase in fast shot speed, the yield strength, ultimate tensile strength, and elongation of the Mg-Al-Zn-RE alloy increased by 17 MPa, 82 MPa, and 8.2 %, respectively. These improvements are primarily attributed to the decreased area fraction of externally solidified crystals (ESCs) and the reduced volume fraction of pores. Furthermore, the enhancement in yield strength is due to grain boundary strengthening, solid-solution strengthening, and second-phase strengthening. The reduction in the area fraction of ESCs and porosity are the main contributors to the improvement in plasticity. The findings of this study provide valuable guidance for the intelligent design of novel high pressure die casting Mg alloys.

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Abstract Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

Modeling sub‐resolution porosity of a heterogeneous carbonate rock sample

AbstractAccurately estimating the petrophysical properties of heterogeneous carbonate rocks across various scales poses significant challenges, particularly within the context of water and hydrocarbon reservoir studies. Digital rock analysis techniques, such as X‐ray computed microtomography and synchrotron‐light‐based imaging, are increasingly employed to study the complex pore structure of carbonate rocks. However, several technical limitations remain, notably the need to balance the volume of interest with the maximum achievable resolution, which is influenced by geometric properties of the source–detector distance in each apparatus. Typically, higher resolutions necessitate smaller sample volumes, leading to a portion of the pore structure (the sub‐resolution or unresolved porosity), that remain undetected. In this study, X‐ray microtomography is used to infer the fluid flow properties of a carbonate rock sample having a substantial fraction of porosity below the imaging resolution. The existence of unresolved porosity is verified by comparisons with nuclear magnetic resonance (NMR) data. We introduce a methodology for modeling the sub‐resolution pore structure within images by accounting for unresolved pore bodies and pore throats derived from a predetermined distribution of pore throat radii. The process identifies preferential pathways between visible pores using the shortest distance and establishes connections between these pores by allocating pore bodies and throats along these paths, while ensuring compatibility with the NMR measurements. Single‐phase flow simulations are conducted on the full volume of a selected heterogeneous rock sample by using the developed pore network model. Results are then compared with petrophysical data obtained from laboratory measurements.

Characterization of porosities and optimization of mix design of pervious concrete using image analysis

Although pervious reduces surface runoff and replenishes groundwater resources, industrial applications are hindered by uncertainty in properties during mass productions. Most experimental studies correlated design parameters to performance parameters predominantly analysing porosity measured from water replacement method. This explains only a fraction of porosity and leads to inappropriate correlations between the influencing parameters. This study quantified porosity using a novel image analysis. 480 samples of pervious concrete were cast varying aggregate to cement ratio and compaction levels and performance parameters such as, wet-density, compressive strength, apparent, actual and effective porosities were assessed. The developed novel image analysis method facilitates accurate computation of porosity and actual, apparent and effective porosities was analysed quantified and optimised. An optimum A/C ratio was observed as 4.0 corresponding to 30 blows of compaction and a resultant actual porosity of approximately 0.2. Further the study establishes relationships between different types of porosities and their performance implications.

SEM Image Processing Assisted by Deep Learning to Quantify Mesoporous γ-Alumina Spatial Heterogeneity and Its Predicted Impact on Mass Transfer.

The pore network architecture of porous heterogeneous catalyst supports has a significant effect on the kinetics of mass transfer occurring within them. Therefore, characterizing and understanding structure-transport relationships is essential to guide new designs of heterogeneous catalysts with higher activity and selectivity and superior resistance to deactivation. This study combines classical characterization via N2 adsorption and desorption and mercury porosimetry with advanced scanning electron microscopy (SEM) imaging and processing approaches to quantify the spatial heterogeneity of γ-alumina (γ-Al2O3), a catalyst support of great industrial relevance. Based on this, a model is proposed for the spatial organization of γ-Al2O3, containing alumina inclusions of different porosities with respect to the alumina matrix. Using original, advanced SEM image analysis techniques, including deep learning semantic segmentation and porosity measurement under gray-level calibration, the inclusion volume fraction and interphase porosity difference were identified and quantified as the key parameters that served as input for effective tortuosity factor predictions using effective medium theory (EMT)-based models. For the studied aluminas, spatial porosity heterogeneity impact on the effective tortuosity factor was found to be negligible, yet it was proven to become significant for an inclusion content of at least 30% and an interphase porosity difference of over 20%. The proposed methodology based on machine-learning-supported image analysis, in conjunction with other analytical techniques, is a general platform that should have a broader impact on porous materials characterization.

Sensitivity analysis of natural convection in a porous cavity filled with nanofluid and equipped with horizontal fins using various optimization methods and MRT-LB

In the present study, natural convection heat transfer is investigated in a porous cavity filled with Cu/water nanofluid and equipped with horizontal fins. Optimization and sensitivity analysis of the fin’s geometry, porous medium and nanofluid properties to maximize heat transfer rate is the aim of this work. To achieve this purpose, a design space is created by input parameters which include length, number of fins, distance between fins, porosity, Darcy number and volumetric fraction of the nanoparticles. Several tools have been used to implement optimization methods including the Taguchi method (TM) for design points generation, sensitivity analysis of design variables by using signal-to-noise ratio (SNR) and analysis of variance (ANOVA), response surface method (RSM) for interpolation and regression by using nonparametric regression, and genetic algorithm (GA) for finding optimum design point. The double multi-relaxation time lattice Boltzmann method (MRT-LBM) is used to analyze and simulate the flow field and heat transfer in each design point. The results show that the optimal configuration leads to an average Nusselt number of 5.56. This optimal configuration is at the length of fins L/2, the number of fins 2, the distance between fins L/12, porosity 0.8, Darcy number 0.1, and the volumetric fraction of the nanoparticles 0.02. By using the SNR results, the Darcy number and the number of fins have the most and the least effect in maximizing the average Nusselt number, respectively. The ANOVA results and global sensitivity analysis (GSA) findings further validated this conclusion.

Nonlinear bending characteristics of multidirectional functionally graded porous panels using higher-order finite element solution with parametric optimization

The current study aims to investigate the nonlinear bending behavior of unidirectional (1D) and multidirectional (2D/3D) functionally graded porous shell panels. Here, the material properties of the multidirectional functionally graded (FG)-panels are estimated by employing the representative volume element method and Voigt’s micromechanical homogenization scheme. The nonlinear mathematical model of the FG-panel is developed by incorporating Green-Lagrange type nonlinear strains in higher-order-midplane kinematics. The minimum potential energy principle is used to obtain the final form of the equilibrium equation for the multidirectional FG shell panel and further solved by using Picard’s iterative-based 2D-isoparametric finite element method via quadrilateral Lagrangian elements. The efficacy and robustness of the present model are checked by comparing its results with previously reported literature. Numerous examples are solved to analyze the impact of material parameters, such as volume fraction index and porosity index, and geometrical parameters, such as aspect ratio and support conditions, on the nonlinear deformation behavior of multidirectional FG shell panels. In addition, parametric optimization is carried out to minimize the flexural response by using the response surface methodology and, hence, determining the optimal values of multidirectional porous FG-panel. The results demonstrate that, within the defined ranges of FG-panel, lower values of porosity index and volume fraction index yield lesser deflection.

Coupling μ-computed tomography and multi-scale modelling to assess the mechanical performance of material extrusion metal components

The porosity defects arising in objects produced by metal Material Extrusion (MEX) additive manufacturing affect the macroscopic mechanical behaviour. This paper presents a new approach integrating μ-computed tomography (μXCT) and multi-scale finite element analysis to evaluate the mechanical performance of components fabricated by metal MEX. The porosity information from μXCT is mapped into the finite element model, allowing to define the volume fraction of porosity to each finite mesh element. Then, the Mori-Tanaka homogenization technique is used to estimate the effective mechanical properties in each integration point, assuming a representative volume element composed by a metal matrix with a void. The reliability of the proposed approach was assessed using tensile specimens of stainless steel 316L produced by metal MEX. The numerical predictions were compared with experimental measurements, namely the strain field evolution measured by digital image correlation (DIC). The results highlight the detrimental influence of the porosity distribution, evaluated in the specimen using μXCT, on the strain distribution during the loading stage. The numerical predictions are in agreement with the experimental measurements, i.e. the difference is lower than 11%. Therefore, the proposed approach offers valuable insights for evaluating the mechanical performance of components produced by metal MEX, focusing on the detrimental effects of porosity defects.

Free vibration analysis of hybrid CNT/GPL-reinforced Porous composite plates under fluid-loading

The present study aims to explore free vibration analysis of hybrid reinforced porous composite plates subjected to fluid loading. The hybrid composite comprises a porous core layer covered by two reinforced porous face sheets. Graphene Platelets (GPLs) and Carbon Nanotubes (CNTs) are considered as reinforcement materials. The linear three-dimensional piezo-elasticity theory is employed to model the structural part of the system, while the classical Rayleigh integral is used to obtain the fluid interaction part. The accuracy and reliability of the proposed model are validated by comparing the calculated natural frequencies of the plate in vacuum and water-loaded conditions with those reported in the literature. For the first time, several parametric studies are performed to investigate the effects of dimension ratios, porosity distributions, reinforcement dispersion pattern, porosity coefficient, and weight fraction of nanofiller on the natural frequency of hybrid reinforced porous composites. The results indicate that adjusting the porosity and weight fraction of the face sheets can enhance stiffness without changing the mass, emphasizing the importance of hybrid composites for achieving optimal stiffness while maintaining a constant mass. Furthermore, the influence of core layer porosity distributions on the composite behavior differs from that of porosity distributions in the face layers. Additionally, the effectiveness of the reinforcement pattern depends on the type of porosity distribution in the face layers.

Exploring the effects of TiO2${\rm TiO}_2$–Ag/water hybrid nanofluid on MHD flow over a permeable exponentially stretching–shrinking sheet with radiative heat transfer and slip conditions

AbstractThe objective of this article is to study the importance of velocity and thermal slip in the exponentially stretching or shrinking sheet with the megnetohydrodynamic (MHD) hybrid nanofluid flow along with magnetic field, radiative, heat generation effects. This study has practical importance in enhancing heat transfer efficiency, improving energy conversion and optimizing thermal management systems. The findings can also contribute to the development of sustainable energy systems and aid in assessing the stability and safety of nanofluid applications. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformation. The ODEs are solved using bvp4c solver in MATLAB. The dual solutions are achieved for specific range of the stretching or shrinking parameter and mass suction parameter. The first solution is physically significant after considering stability analysis. The hybrid nanofluid has numerous real‐life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical, and drug reduction. The skin‐friction increases but Nusselt number decreases over the stretching sheet whereas the opposite effect shows over shrinking sheet for the both solution with the increasing velocity slip parameter. On the other hand, The Nusselt number decreases over the shrinking or stretching sheet for both solutions with the increasing in the thermal slip parameter. The skin friction increases over shrinking sheet but decreases over stretching sheet for the first solution with increasing silver volume fraction parameter and porosity parameter (). Enhancing magnetic field parameter leads to the skin friction increases over the shrinking sheet but decreases over stretching sheet but Nusselt number shows opposite trend. The Nusselt number decreases over shrinking sheet but increases over stretching sheet for the first solution with increasing porosity parameter (). The Nusselt number decreases over shrinking or stretching sheet as the increases heat generation () and variable thermal conductivity parameter () but Nusselt number shows opposite trend as the increases radiative parameter ().

Effect of Porosity on the Free Vibration Analysis of a Rotating Pretwisted Sandwich Blade with a Functionally Graded Core in the Thermal Environment

This work deals with the investigation of the effect of porosity on the natural frequencies of the rotating pretwisted sandwich blade with a functionally graded core in the thermal environment. The top metallic and the bottom ceramic surfaces are exposed to ambient temperature and high inlet temperature, respectively. A finite element approach using a layerwise theory is developed. Two different porosity distributions are assumed here. The effect of the volume fraction index, rotational velocity, porosity model and temperature gradient on the natural frequencies of the pretwisted sandwich blade is studied.