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To govern the complex rheological dynamics of fluid simulations, numerous mathematical approaches are being developed. The examination of such mathematical frameworks employs theoretical, iterative, empirical, and analytical methodologies. This work analyzes and evaluates the Laplace transforms to estimate the time-dependent mixed convective flow of hybrid nanofluid in a porous material. A hybrid nanofluid is produced through dispersing molybdenum disulfide (${\mathrm{\text{MoS}}}_2$) and silicone dioxide (${\mathrm{\text{SiO}}}_2$) nanoparticles in carboxymethyl cellulose ($\mathrm{\text{CMC }}-\mathrm{\text{water}}$). The objective of this study is to examine the heat transfer properties of a hybrid nanofluid (${\mathrm{\text{MoS}}}_2-{\mathrm{\text{SiO}}}_2)$/$(\mathrm{\text{CMC }}-\mathrm{\text{water}}$) flowing over a vertical sheet while being subjected to a thermal radiation and heat source and sink. The Laplace transform approach has been used in closed form to solve the resulting partial differential equations governing the flow. This study examines how hybrid nanofluids influence time-dependent flow and heat transmission in the presence of porous medium, heat radiation, and rate of heat generation. The computer program MATHEMATICA is used to emphasize the impact of each flow parameter. Graphs are used to analyze the results of radiation, heat source, magnetic, and nanoparticle volume fraction obtained using the Laplace transform technique for engineering variables like fraction and rate of heat, as well as velocity and thermal distribution. The velocity distribution is an increasing function of mixed convective parameter. Larger values of porosity variable and mixed convection variable result in accelerating the velocity of the fluid. Additionally, we conducted research with various ratios of nanoparticles and discovered several intriguing outcomes that can be used to solve various technical issues, particularly in the cooling process.

The relationship between thermal conductivity of porous material and fractal dimension is numerically simulated by using the finite element method. The solid matrix and pore space are generated randomly according to material porosity. Material parameters and element properties are changed by using ANSYS parameter design language. The effective thermal conductivity is derived according to thermal flux through some sections computed by FEM and Fourier heat transform law. The investigation shows that the effective thermal conductivity decreases with increasing porosity. The effective thermal conductivity will decrease exponentially with increasing fractal dimension of porosity space and increase exponentially with increasing fractal dimension of solid matrix.

Impact stress wave propagating through porous materials is investigated in order to examine the ability of the shock absorbing effect. The specimens are modeled as the porous medium with different porous diameters made of the acrylic resin plate. When these models are impacted with different impact velocities, the impact stress waves propagating before and after the porous parts are measured using the strain gages in the experiments. As the reduction effect of the impact stress wave propagating in the porous medium, we pay attention to the maximum stresses and the duration times from the histories of the impact stress waves. One-dimensional wave theory and dynamic element method simulated this model are applied in order to explain these phenomena.

Silicon nitride bonded silicon carbide (Si₃N₄-SiC) refractories are commonly used as the sidewall of aluminum electrolysis cells. They have to withstand an extremely corrosive molten electrolyte bath for long periods. The sidewall is normally protected with a layer of solidified electrolyte (called frozen ledge), which is sensitive to the thermal conductivity of the sidewall. In this work, through review of the literature on modeling methods for predicting the effective thermal conductivity of dense composites and porous materials, some selected methods were applied to calculate the effective thermal conductivity of Si₃N₄-SiC refractories. The model predictions were compared with the thermal conductivity of a commercial Si₃N₄-SiC refractory measured by using laser flash technique. The present study showed that, due to multi-phase nature and complex microstructure of Si₃N₄-SiC refractories, most of the selected modeling methods individually do not give satisfactory predictions in one step. Recursive applications of one method or combinations of different methods are capable of giving satisfactory predictions.

Porous Ni–Ti alloys were fabricated by reactive synthesis of Ni and Ti elemental powders. The corrosion behavior of porous Ni–Ti alloys was explored by electrochemical methods and weight change measurements at 298 K in seawater. The polarization curves and electrochemical impedance spectroscopy data show that porous Ni–Ti (6.5:3.5) alloys provide the best corrosion resistance. The values of corrosion current density and corrosion rate are 1.6944 × 10⁻⁴ mA/cm² and 1.9929 mm/a, respectively. The corrosion behavior and corrosion mechanism of porous Ni–Ti alloys are also discussed.

The purpose of this research is to analyze the general equations of double diffusive magneto-free convection in a rate type fluid presented in non-dimensional form, and apply to a moving heated vertical plate as in the boundary layer flow up, with existence of externally magnetic fields which are either moving or fixed consistent with the plate. Thermal transport phenomenon is discussed in the presence of constant concentration coupled with first-order chemical reaction with exponential heating. An innovative definition in power law (CF) and Mittag-Leffler (ABC) kernels form time fractional operators are implemented to hypothecate the constitutive mass, heat and momentum equations. The results based on special functions are obtained by using the technique of Laplace transformation to tackle the non-dimensional equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid is presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not to be zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations along with some special cases for the movement of the plate which are also studied.

Coir fiber from coconut husk is an important agricultural waste in Malaysia. The porous structure of fiber makes it an eligible material for acoustical absorption. In previous studies at Universiti Kebangsaan Malaysia, single layer coir fiber showed low acoustical absorption in medium and low frequencies; e.g. absorption coefficient of a 20 mm industrial prepared coir fiber sample was below 0.3 for frequencies less than 1.5 kHz. Current research was initiated to improve the shortcoming by mixing industrial prepared coir fiber with air gap layers. Analyzes were based on two approaches, namely; Delany–Bazley with acoustic transmission analysis (ATA) and Allard elastic model with transfer matrix analysis. Experimental measurements were conducted in impedance tube to validate the analytical results. Outcomes described that Delany–Bazley-ATA technique was an approximate solution showing overall absorption path without giving any accurate information about the peaks and resonances. Allard method took the elasticity of material into account and transfer matrices were able to characterize the whole structure as a combination of single layers. Results were close to experimental values and predicted the path and resonances very well. Further analyzes were conducted by Allard method and derived that having a fiber layer backed by an air gap was better than leaving the same gap in between that layer. The explanation was that, in the first arrangement, the sound field impacted a solid layer with higher thickness and followed a longer transmission path which caused a higher acoustical absorption. Furthermore, it was noticed that a reasonable thickness of backing air gap improved the overall sound absorption. Increase in the gap thickness produced more peaks and moved them to lower frequencies which caused better absorption in low frequencies. The cause of this phenomenon was increase in impedance of the panel due to rise in the air-gap thickness. This moved the acoustical resonances to lower frequencies and improved the sound absorption in this frequency span. Finally, it was concluded that other acoustic absorption techniques such as adding perforated plate may be combined with coir fiber-air gap structure to improve the low frequency acoustic absorption coefficient without any need to highly increase the air gap thickness.

The purpose of this work is to simulate uncertainties existing in microscopic field of spherical porous material so that the homogenized property of interest can be predicted with high reliability. Moreover, the final goal is to build a bridge of feedback between microstructure design and fabrication to predict microstructure morphology by limited measurement data of macroscopic property. The uncertainties are identified as parametric variables in constituent material property and nonparametric variables in morphological fluctuation such as disordering and clustering in microstructure. First-order perturbation, based stochastic homogenization (FPSH) method together with mixture distribution technique is employed for probabilistic prediction. Furthermore, the update of prediction is accomplished in the case of an assumed virtual experimental trial. Two numerical examples show that the probabilistic prediction has given a better decision in microstructure design than deterministic prediction. The main conclusion coming from the new method derived by gap between measured data and prediction showed that, when the update is used for morphology prediction of microstructure, it is almost perfect agreement with parameters’ setup of virtual experiment. After it is applied for update of probabilistic homogenized property, it could make the updated homogenized property closer to measurement data so that it becomes more realistic.

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i₁ – i₂ plane, the normal stress in the third axial direction (i₃) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

The finite element analysis (FEA) of porous NiTi shape memory alloys (SMAs) remains a challenge due to irregularity and complexity of pore structure. In this paper, the real finite element model (FEM) is established based on the geometrical reconstruction. Through a SMA constitutive model, the mechanical behavior and stress-induced martensitic (SIM) phase transformation are analyzed with the real FEM. The results show that the stress–strain curve of FEA is in good agreement with the experimental curve and the calculation can reflect the mechanical behavior well in the compressive process. With the increase of load, the SIM first appears pore walls or weak parts of struts, then spreads to the center of matrix, and finally happens to most of matrix. When the slope of the stress–strain curve shows obvious changes, the SIM has happened in quite a part of matrix.

Porous carbon nanospheres (CNSs) have wide applications. A big challenge in materials science is synthesis of discrete ultrasmall porous carbon nanospheres. Herein, we report a facile reverse microemulsion-hydrothermal method to prepare discrete porous CNSs. The obtained CNSs possess an average diameter of 20nm and pores of 0.7nm and 3.4nm. Our work has provided a convenient method for the controllable synthesis of ultrasmall porous CNSs with potential applications.

A model for predicting thermal waves within a surface-heated porous structure has been developed. The relevant phenomena for the moisture, pressure and temperature fields are coupled. Considering mass and energy transfer processes, a set of governing differential equations is presented. The solution of the problem has been obtained with a finite difference scheme.

It is the special structure to make the porous materials have the unique performance and application. As new structural and functional material, porous materials are being paid much more attention in the world and found application in many industrial fields. Classifications, properties, fabrication methods and application are summarized in this paper. Finally, we indicate the developing tendency of porous materials.

The alumina thin films with brilliant structural colors have been fabricated by means of electrochemical oxidation in phosphoric electrolyte under the condition of room temperature. The relationship of the structural colors with the anodization time and the angle of incidence of illuminating light are discussed. The microstructures of the films have been characterized as well. The effective refractive index of film is calculated according to Maxwell-Garnett theory. The maximum reflection wavelength of films is calculated by Bragg's equation, and the generation mechanism structural color has also been discussed. In the end, organic-assist covering method has been applied to obtain the intricate multicolor pattern on the same alumina thin film. This thin film with brilliant colors may have potentials in color displays, decoration and anti-counterfeiting technology.