Solid Volume Fraction Research Articles

An MHD nanofluid flow with Marangoni laminar boundary layer over a porous medium with heat and mass transfer

ABSTRACT The current work considers two-dimensional incompressible fluid flow with heat transfer over a porous medium with mass transpiration and Marangoni boundary condition. The nanoparticles of graphene are mixed in water to improve thermal efficiency. It behaves as a heater upon increasing its solid volume fraction, Eckert number, and as a cooler upon increasing suction. This flow has remarkable interest due to its applications in glues, silicon wafers, heat exchangers, paints, crystal growth in space, etc. The ordinary differential equations (ODEs) are obtained from the considered partial differential equations (PDEs) using similarity transformation technique. Then the solutions are analytically recovered from the system of ODEs. The solutions of temperature and concentration fields are obtained in terms of Laguerre polynomial. The impacts of different parameters, such as Marangoni number, inverse Darcy number, Prandtl number, and Eckert number are analysed using graphical observations. Specially mentioned is Marangoni convection, which contains many industrial and engineering applications such as in nanotechnology, atomic reactors, soap films, semiconductor processing, and atomic reactors. This work adds the effect of graphene water nanofluid which enhance the thermal efficiency in a better way than the base fluid and explains the physical problem on the basis of chemically radiative Marangoni flow.

A modified CFD-DEM method for accurate prediction of the minimum fluidization velocity

Monodisperse fluidized bed experiments have been carried out on 13 kinds of particles with different particle sizes in a cylindrical fluidized bed. The accuracy of nine commonly used monodisperse drag models, including the Gidsapow, BVK, and Zhou–Fan models is verified. It is found that the Zhou–Fan model is the most accurate at low and moderate values of the particle Reynolds number. It is found that with the traditional computational fluid dynamics–discrete element method (CFD-DEM) method it is difficult to obtain an accurate minimum fluidization velocity owing to difficulty in obtaining an accurate value of the minimum fluidization solid volume fraction. A modified method is proposed to increase the accuracy of prediction of the minimum fluidized solid volume fraction by using a virtual particle size in the calculation of the particle collision process. The effectiveness of the modified method is verified by comparing the CFD-DEM simulation results with experimental results for Geldart-D particles. The relative error of the minimum fluidization velocity is found to be reduced from 24.6% to 2%.

LBM Simulation of Free Convection Heat Transfer of Cu/Water Nanofluid in Inclined Cavity with Non-Uniform Heating Temperature Distribution

In the present study, natural convection of Cu/water nanofluid in an inclined square cavity has been investigated numerically using lattice Boltzmann method (LBM). The left wall of the cavity is maintained at a constant hot temperature, while the right wall is subjected to non-uniform temperature distribution. The upper and lower walls are insulated. The fluid flow and heat transfer characteristics are investigated over a wide range of parameters, including Rayleigh numbers (Ra = 103, 104 and 105), solid volume fractions (Φ = 0%, 2%, 4% and 6%), amplitude ratio (A = 0, 0.5 and 1) and phase deviations of sinusoidal temperature distribution (Φ = 0, π/4, π/2, 3π/4 and π). The results are presented graphically in the form of streamlines, isotherms and Nusselt numbers for the different combinations of the considered parameters. The heat transfer rate inside the nanofluid increases as the Rayleigh number and the volume fraction of nanoparticles increase. Further, an increase in the amplitude ratio results in a decrease in the heat transfer rate, with a reduction of up to 8.67% at A = 1. On the other hand, changes in the phase deviation of the sinusoidal temperature distribution lead to an increase in the heat transfer rate, with a surge of up to 32.04% observed at Φ = π.

The effect of solid nitrogen on nucleate boiling heat transfer in a slush nitrogen pool

The nucleate boiling heat transfer in a slush nitrogen pool has been studied across a heat-flux range from 5 to 400 kW/m2 and a system pressure range from 12.5 kPa (triple point pressure) to 101 kPa (atmospheric pressure). The effect of solid nitrogen on the heat transfer process was found to vary with the heat flux and the pressure. Experimental results reveal that the nucleate boiling heat transfer coefficient (HTC) of slush nitrogen is higher than that of subcooled liquid nitrogen at the low heat flux, which can be attributed to the fact that the solid nitrogen particles (with their latent heat of melting) absorb heat in the thermal boundary layer and form a sharper temperature gradient near the boiling surface. However, at the high heat flux, the HTC of slush nitrogen is lower than that of subcooled liquid nitrogen, which can be attributed to the invasion and inhibition occurring between the solid nitrogen particles and the bubbles during boiling, leading to the accumulation of vapor phase with low thermal conductivity on the boiling surface, thereby the heat transfer will be suppressed. As a result, a dual effect for the nucleate boiling heat transfer in slush nitrogen can be observed. Furthermore, the critical heat flux (CHF) of slush nitrogen is obtained and compared with the CHF of subcooled liquid nitrogen. According to the CHF model, the bubble period is the dominant parameter in determining the CHF. A calibrated CHF correlation for slush nitrogen is developed based on the hypothesis that the bubble period is prolonged as the effective viscosity of slush nitrogen increases with the solid volume fraction. The CHF values of slush nitrogen with the solid volume fraction of 10%, 20% and 30% are 0.96, 0.91 and 0.84 times those of subcooled liquid nitrogen, respectively, at the pressures higher than 50 kPa. Consequently, the solid volume fraction of slush nitrogen and the degree of subcooling of subcooled liquid nitrogen are found to have opposite effects on CHF.

Waste discharge concentration and quadratic thermal radiation influences on time-dependent nanofluid flow over a porous rotating sphere

The nature of waste discharge concentration on time-dependent nanofluid flowing over a rotating sphere is examined in the conducted research. The linear and quadratic radiation influences are considered in the energy transport equation. The flow generation occurs due to a sphere’s revolution with time-dependent angular velocity. The term external pollutant concentration is modeled in the concentration equation. Titanium dioxide ( Ti O 2 ) nanoparticles are inserted into base-liquid water ( H 2 O ) . Similar variables are reported for the conversion of the problem. The converted problem is computed through the Runge–Kutta–Fehlberg (RKF) scheme. The study outcomes obtained from a numerical scheme are presented with the help of graphs. The rise in the linear and quadratic thermal radiation factors will enhance the thermal profile. Improvement in local pollutant external source and external pollutant source parameters will improve the concentration profile. The mass transfer rate will improve by adding the solid volume fraction and escalated values of local pollutant external source constraints.

Study on surface erosion threshold and erosion mass of bentonite applied in nuclear waste repository based on fractal structure characteristics

Bentonite exhibits good self-sealing performance and low permeability after hydration, and therefore is selected as a buffer material for high-level radioactive waste repositories, isolating the canisters containing nuclear waste from the external environment. The bentonite cushion directly contacts the surrounding rock and generates gels at the contact interface with fracture water. Surface erosion occurs once the shear stress exerted by the flowing water exceeds the erosion threshold of the bentonite gel, resulting in gel particle detachment from the soil–water interface and transport through fissure. The mass loss of the buffer by erosion will weaken its functionality as designed and directly endanger the long-term safety of the repository. The erosion behavior of bentonite is related to the structure of the gel formed by bentonite hydration. In this paper, the X-ray small-angle scattering experiments were used to prove that the gel structure has fractal characteristics and to obtain the mass fractal dimension. Based on the fractal structure of the bentonite gel, the erosion threshold that determines whether erosion will occur was quantified as a function of the solid volume fraction of the gel by taking the inter-particle attractive bond as the primary source of resistance. Furtherly, the cumulative erosion mass model that evaluates the extent of erosion was constructed to reveal the relationship between the cumulative erosion mass and cumulative water flow after the erosion has achieved stability. The proposed relations are verified by the experimental results from published literature and are of great significance for judging whether erosion will occur and evaluating the degree of erosion.

CFD-DEM numerical investigation of the effects of water content and inclination angle on interactions between debris flows and slit dam

Debris flows, composed of sediment–water mixtures, can pose significant risks to downstream populations and infrastructure in mountainous regions. Slit dams have been demonstrated as being effective measures for decreasing the destructivity of debris flows. Reliable evaluations of the interactions between debris flows and slit dams are challenging if the complicated component characteristics of debris flows, such as the water content, are not considered. Here, a multi-scale study of debris flows impacting a slit dam is conducted via computational fluid dynamics and discrete element method (CFD-DEM) simulations to understand the influences of the water content (controlled by solid volume fraction in this study) and the channel inclination angle on flow–slit dam interactions. The results indicate that both the initial solid volume fraction and the channel inclination angle have significant effects on the impact kinematics of flow–slit dam interactions and regulation functions of the slit dam: (i) For gentle slopes, the deposition of debris flows is primarily influenced by flume basal friction, and the normalized peak total impact forces have little difference for a given inclination angle, whereas for steep slopes, an overtopping can occur, further result in the increasing of the normalized peak total impact forces with the increase of solid volume fraction. (ii) The run-up height and retention efficiency are also analyzed to provide a scientific reference for optimizing the design of slit dams.

Effect of maximum packing fraction of powders on the rheology of metakaolin-based geopolymer pastes

In this work, we study the effect of maximum packing fraction of powders on the rheology of geopolymer pastes. A large range of metakaolin powders is generated either by blending or grinding powders. Blends of metakaolin with quartz and limestone are also studied. We show that the compressive packing model is able to predict correctly over a wide range of values the maximum packing fraction of these powders. We show that an increase of the maximum packing of powders leads to a decrease of the viscosity of geopolymer suspension at a constant solid volume fraction. We finally show that the viscosity of studied geopolymer suspensions can be well predicted by the Krieger Dougherty relation. We suggest that the highest potential degree of freedom allowing for the control of the viscosity of geopolymer pastes without modifying the composition of the suspension lies in the maximum packing fraction of the solid powders.

Segregation–rheology feedback in bidisperse granular flows: a coupled Stokes’ problem

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes’ problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles’ relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles’ relative friction is modified via a frictional coefficient ratio, by analogy with the particles’ size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation–momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation–rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

Rheological properties and shootability of sprayable geopolymer mortar

Geopolymer presents a promising alternative to Portland cement for shotcrete, offering reduced environmental impacts, favorable mechanical performance, and improved durability. At present, small-scale applications have been implemented, but the fresh performances of spayed geopolymer are still rarely studied, restricting its further large application. This research investigates the rheological properties and shootability of sprayable fly ash/slag/silica fume based geopolymers considering the effects of different mix parameters. The water to binder (W/B) ratio has the greatest effect on the yield stress, and the dynamic yield stress is increased from 64.47 Pa to 388.64 Pa as the W/B ratio is reduced from 0.32 to 0.28. The change in dynamic yield stress is mainly related to either the formation of hydration products or the solid volume fraction. Mixtures with the highest thixotropic indexes are ideal for achieving both pumpability and shootability, while also exhibiting relatively low characteristic time. A modified equation for pumpability assessment is presented, which is more reasonable and consistent with the experimental results. The static yield stress is recommended for evaluating the build-up thickness of the designed fresh mixture, as there is a recognized strong correlation between them. In addition, the build-up thickness decreases with the increase of flowability, which could be used as a potential indicator. With the increasing sand to binder ratio, the mechanical strength exhibits a valley, which could be linked to the critical volume fraction of aggregate that corresponds to an effective interacting network, below which the sand-induced defects cause damage to strength and above which the interacting skeleton could contribute to strengthening. The strong environment savings of the current material are demonstrated, with the reduction in carbon emissions more than 50%. This study provides valuable information towards regulating and controlling the shootability of sprayable geopolymer and expands its broader application.

Performance characteristics of the airlift pump under vertical solid–water–gas flow conditions for conveying centimetric-sized coal particles

In this study, the installation of an airlift pump with inner diameter of 102 mm and length of 5.64 m was utilized to consider the conveying process of non-spherical coal particles with density of 1340 kg/m3 and graining 25–44.5 mm. The test results revealed that the magnitude of increase in the solid transport rate due to the changes in the three tested parameters between compressed air velocity, submergence ratio, and feeding coal possibility was not the same, which are stand in range of 20%, 75%, and 40%, respectively. Hence, creating the optimal airlift pump performance is highly dependent on submergence ratio. More importantly, we measured the solid volume fraction using the method of one-way valves in order to minimize the disadvantages of conventional devices, such as fast speed camera and conductivity ring sensor. The results confirmed that the volume fraction of the solid phase in the transfer process was always less than 12%. To validate present experimental data, the existing empirical correlations together with the theoretical equations related to the multiphase flow was used. The overall agreement between the theory and experimental solid delivery results was particularly good instead of the first stage of conveying process. This drawback can be corrected by omitting the role of friction and shear stress at low air income velocity. It was also found that the model developed by Kalenik failed to predict the performance of our airlift operation in terms of the mass flow rate of the coal particles.

Comparative study of copper nanoparticles over radially stretching sheet with water and silicone oil

Abstract Copper nanoparticles are widely used in many sectors and research endeavors owing to their unique properties, including a large surface area, catalytic capabilities, and high thermal and electrical conductivity. The selection of the base fluid for copper nanoparticles should be contingent upon the anticipated application requirements since various fluids exhibit distinct characteristics that could potentially impact the mobility of the nanoparticles. The present investigation analyzes heat transfer phenomena occurring across a radially stretched surface. The research explores the effects of different states of Cu nanoparticles when combined with base fluids, such as water and silicone oil, on the heat transfer process. The momentum and energy equations are transformed into nonlinear ordinary differential equations by applying the similarity transformation. The boundary value problem-fourth-order (BVP4C) method numerically solves the governing ordinary differential equation for the modeled problem. In addition, the influence of various factors such as the slip parameter, solid volume fraction, Eckert number, Prandtl number, and unsteadiness parameter are examined. It has been discovered that blade-shaped nanoparticles transfer heat as quickly as possible via silicone oil and water. However, for platelet-shaped nanoparticles, a minimum heat transfer rate has been noted. The maximum skin friction coefficient is observed in platelet-shaped nanoparticles, while blade-shaped nanoparticles have the lowest skin friction coefficient.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression.

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the range mm /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

Investigating the thermal properties of single-grade engine oil (SAE 50) with the simultaneous addition of MWCNT and CuO nanoparticles

This study examines the MWCNT-CuO (20%–80%)/SAE50 nanofluid (NF) by considering the temperature changes, solid volume fraction (SVF), and shear rate (SR) parameters. The temperature range is 30–50 °C and SVF of 0.0625, 0.125, 0.25, 0.5, 0.75 and 1%, and different SRs are investigated. Viscosity is obtained using a Brookfield CAP 2000+ viscometer. The results show that the NF has a non-Newtonian behavior and the values of the power-law index are variable. Increasing the temperature of the NF decreases the viscosity because the intermolecular distance increases and the intermolecular forces decrease. Increasing the SVF in all SVFs except SVF = 0.0625 and 0.125% increases the viscosity, and therefore the SVF = 0.0625 and 0.125% have special importance. Modeling the viscosity of NF with the response surface methodology (RSM) has good accuracy so that the values of R2 and R2-adj are equal to 0.9993 and 0.9992, respectively. The sensitivity of NFs increases by adding 10% of the SVF in higher SVFs.

Thermal Analysis of MHD Hybrid Nanofluid on Stretching/Shrinking Non-Parallel Walls with Uncertain Volume Fractions

This study examines the heat transmission of magneto-hydrodynamic (MHD) hybrid nanofluid (Ag–[Formula: see text]O) flows between two stretchable or shrinkable walls. The nanoparticle volume fraction is considered an uncertain parameter and is represented using triangular and Gaussian fuzzy numbers. The governing radial momentum and energy equations are transformed into nonlinear ordinary differential equations using a similarity transformation and with the required boundary conditions. A generalized homotopy approach is used to analyze the impacts of embedding parameters, including the Reynolds number, stretching/shrinking parameter, opening angle, radiation parameter, Magnetic parameter, and solid volume fraction on velocity and thermal profiles in crisp and uncertain cases. The findings demonstrate that fluid velocity and temperature distribution increase as the stretching parameter increases. The correctness of the suggested technique is validated by comparing the results with the available numerical solution. It has been observed that there is a great agreement between the present results and the numerical ones.

Efficient cooling system design by using different shaped nanoparticles and rotating cylinders in channel system for photovoltaic thermal management

Research focusing on improving the efficiency and performance of renewable energy systems requires the development of cooling systems (CSs) with effective solutions, including photovoltaic (PV) thermal management. The current work proposes a unique cooling method that uses double rotating cylinders (RCs) and different shaped alumina nanoparticles (NP; spherical, blade, brick, and cylindrical) in water for conductive panel’s cooling channel. The numerical study is performed for different values of Reynolds number (Re: 100–600), rotational Re (Rew: 0–20), size of the cylinders (Rc: 0.01H–0.2H), and solid particle volume fractions (svf: 0–0.03). It is observed that vortex size and numbers behind the cylinders can be controlled by varying Re and Rew. A 16 °C temperature drop of the panel is achieved at the highest Re at svf = 0.03. When rotations are active, the average Nu increases 99% and 37% for water and nanofluid (NF) at Rew = 20 and Re = 250 while temperature drops of 15 °C and 7.5 °C are obtained. The highest performance coefficient (PEC) is obtained as PEC = 1.38 when NF is used at Rew = 15. Large cylinders results in lower PEC values. When rotations are not active, the average Nu rises by about 26.8%, 13.5%, 12.8%, and 3.5% for cylindrical, blade, brick, and spherical-shaped particles while average cell temperature drops by about 5.5 °C, 4.5 °C, 4.3 °C, and 1 °C. The highest PEC value is obtained as 1.23 when cylindrical particles at the highest loading are used for stationary cylinders. Proper orthogonal-based model is considered for estimation of spatially varying panel temperature.

An improved semi-resolved computational fluid dynamics-discrete element method for simulating liquid–solid systems with wide particle size distributions

Vertical hydraulic transport of particles with wide particle size distributions is a crucial process for coal physical fluidized mining. In the present study, an improved semi-resolved computational fluid dynamics (CFD)-discrete element method was developed to simulate particle flows with wide particle size distributions. In this model, the CFD cells allocated to the particle volume and the momentum source term were defined as the dependent domain and the influential domain, respectively. On this basis, the two-way domain expansion method and the one-way domain expansion method were adopted for the liquid–solid simulation of coarse and fine particles, respectively. The dependent domain expansion coefficient and the influential domain expansion coefficient were proposed to determine the spatial range of the dependent domain and influential domain for the coarse particles, and the optimal modeling strategy for the dependent domain and influential domain expansion coefficient for the coarse particles was determined. Furthermore, a volume expansion method and a momentum source expansion method were proposed for calculating the solid volume fraction of the dependent domain and the source term of the influential domain for the coarse particles. Furthermore, the sample point method was adopted to obtain the solid volume fraction in the dependent domain for the fine particles, and the momentum source term was only updated to the particle-located cell. Subsequently, single-particle settling and binary-particle fluidizing numerical experiments were used to verify the calculation accuracy of the model. The investigation can provide a new method for numerical simulation of liquid–solid flow with wide particle size distributions.

Stagnation-Point Slip Flow of Hybrid Ferrofluid Past Exponentially Stretching Sheet in Darcy-Forchheimer Space

Objectives: The present article provides a detailed analysis on the Darcy-Forchheimer hybrid nanofluids flow past an exponentially stretching sheet in the presence of mixed convection with slip conditions and the impacts of different relevant parameters of the fluid flow for velocity and temperature profiles. Methods: In order to create hybrid nanofluids, two magnetic nanoparticles, magnetite ( ) and cobalt ferrite ( ), are taken into consideration. The governing boundary layer coupled partial differential equations are transformed into a system of non-linear ordinary differential equations, which are then solved numerically by using the bvp4c solver available in the Matlab software. A comprehensive parametric analysis has been performed to show the effects of the convective parameter, velocity ratio parameter, porosity parameter, forchheimer parameter, solid volume fractions of and , velocity slip and temperature jump on the fluid velocity and temperature profiles as well as the local skin-friction coefficient and local Nusselt number within the boundary layer. Findings: For higher values of , , , , the velocity field grows, and it declines for , Fr, and A. The temperature field thickness is higher for , Fr, , and A, while decreases for and . The local skin friction coefficient diminishes as rise in the values of , , , Fr, , , A and B. The local Nusselt number shows increasing behaviour for increasing amount of , , , Fr, , , A and B. Novelty: The novelty of the current work is the analysis of the flow of Darcy-Forchheimer hybrid nanofluids across an exponentially stretched sheet in the presence of mixed convection with slip conditions. Here, water is used as base fluid and magnetite, cobalt ferrite being used as hybrid nanoparticles for the present study. Keywords: Hybrid nanofluids, Exponentially stretching sheet, Mixed convection, Velocity slip, Temperature jump

Composite material in the sea urchin Cidaris rugosa: ordered and disordered micrometre-scale bicontinuous geometries.

The sponge-like biomineralized calcite materials found in echinoderm skeletons are of interest in terms of both structure formation and biological function. Despite their crystalline atomic structure, they exhibit curved interfaces that have been related to known triply periodic minimal surfaces. Here, we investigate the endoskeleton of the sea urchin Cidaris rugosa that has long been known to form a microstructure related to the Primitive surface. Using X-ray tomography, we find that the endoskeleton is organized as a composite material consisting of domains of bicontinuous microstructures with different structural properties. We describe, for the first time, the co-occurrenceof orderedsingle Primitive and singleDiamond structures and of a disordered structure within a single skeletal plate. We show that these structures can be distinguished by structural properties including solid volume fraction, trabeculae width and, to a lesser extent, interface area and mean curvature. Indoing so, we present a robust method that extracts interface areas and curvature integrals from voxelized datasets using the Steiner polynomial for parallel body volumes. We discuss these very large-scale bicontinuous structures in the context of their function, formation and evolution.