Solid Volume Fraction Research Articles

Current advancements in fluid-flow Problems: A brief review

This specific article is a compilation of a few current studies on fluid flow issues. This article provides an overview of current research on the experimental and theoretical analysis of various nanofluids' thermal conductivity. The current study examines a number of variables that have a significant impact on a nanofluid's ability to transfer heat, including temperature, solid volume fraction, type, size, shape, magnetic field, pH, ultrasonic time, and surfactant. In addition, some plausible and appealing theories that enhance the thermal conductivity of nanofluids are mentioned. The final important heat transmission mechanisms that play a significant part in improving thermal conductivity are Brownian motion, thermophoresis, nanoclustering, interfacial nano-layer, and osmophoresis. Thus, consideration is given to the heat transmission properties of nanofluids. And also discussed some Numerical method to solve fluid flow problems.

Success and failure of the spreading law for large drops of dense granular suspensions

The spreading of large viscous drops of density-matched suspensions of non-Brownian spheres on a smooth solid surface is investigated experimentally at the global drop scale. The focus is on dense suspensions with a solid volume fraction equal to or greater than $40\,\%$ , and for drops larger than the capillary length, i.e. for which the spreading is governed by the balance of gravitational and viscous forces. Our findings indicate that all liquids exhibit a power-law behaviour typical of gravity-driven dynamics, albeit with an effective suspension viscosity that is smaller than the bulk value. When the height of the drop is of the order of the particle size, the power law breaks down as the particles freeze while the contact line continues to advance.

Influence of non-linear thermal radiation on the dynamics of homogeneous and heterogeneous chemical reactions between the cone and the disk

Abstract Purpose The current work presents a theoretical framework to boost heat transmission in a ternary hybrid nanofluid with homogeneous and heterogeneous reactions in the conical gap between the cone and disk apparatus. Furthermore, the impacts of non-linear thermal radiation on the ternary hybrid nanofluid composed of white graphene, diamond, and titanium dioxide dispersed in water are analyzed. Originality/value The combination of cone and disk systems is crucial for designing efficient heat exchange devices in the field of biomedical science for various purposes. For instance, in medical devices, the cone–disk apparatus is used to study the flow and heat transfer characteristics for better design and functionality. Hence, a sincere attempt has been made to study the impact of homogeneous and heterogeneous reactions on the nanofluid flow between the cone and disk in the presence of non-linear thermal radiation. Design/methodology/approach The mathematical model’s governing equations are partial differential equations (PDEs) which are then transformed into non-linear ordinary differential equations through appropriate similarity transformations. These transformed resultant equations are approximated by the Runge–Kutta–Fehlberg fourth/fifth order (RKF45) technique. The influence of essential aspects on the flow field, heat, and mass transfer rates was analyzed using a graphical representation. Findings The interesting part of this research is to discuss the power of parameters in three cases, namely, (1) rotating cone/disk, (2) rotating cone/stationary disk, and (3) stationary cone/rotating disk. Furthermore, the thermal variation of the fluid is analyzed by an artificial neural network with the help of the Levenberg–Marquardt backpropagation algorithm. The regression analysis, mean square error, and error histogram of the neural network are analyzed using this algorithm. From the graph, it is perceived that the flow field climbed up significantly with an increase in the values of radiation parameters in all cases. Also, it is noticed that temperature upsurges significantly by upward values of solid volume fraction of the nanoparticles ( ϕ \phi ).

Entropy generation analysis of unsteady MHD nanofluid flow in a porous pipe

This article presents a numerical investigation into the entropy production of nanofluids flowing through a porous medium in a permeable conduit, focusing on water-based solutions containing Titanium Carbide (TiC) and Silicon Carbide (SiC) nanoparticles. These nanoparticles are selected for their heat transfer properties. The flow system's governing equations are developed and solved using the Runge-Kutta-Fehlberg method. The study examines the influence of key nondimensional parameters, including the solid volume fraction of nanoparticles, radiation parameters, and Reynolds number, on temperature, velocity profiles, and entropy generation. The results show that Silicon Carbide-water nanofluids perform efficiently in terms of heat transfer and entropy minimization. Additionally, Silicon Carbide exhibits low skin friction at the pipe wall, with this effect increasing as the solid volume percentage of nanoparticles rises. The study also indicates that irreversibility due to heat transfer becomes more significant near the pipe wall as the solid volume fraction decreases and increases with higher radiation parameters and Reynolds number. These findings are presented graphically and in tabular form to illustrate the physical significance of the problem.

A magnetohydrodynamic flow of a water-based hybrid nanofluid past a convectively heated rotating disk surface: A passive control of nanoparticles

Abstract One of the basic fluid mechanics problems of fluid flows over a revolving disk has both theoretical and real-world applications. The flow over a rotating disk has been the subject of numerous theoretical studies because it has many real-world applications in areas like rotating machinery, medical equipment, electronic devices, and computer storage. It is also crucial for engineering processes. Therefore, this article deals with a time-independent water-based hybrid nanofluid flow containing copper oxide and silver nanoparticles past a spinning disk. The Newtonian flow is taken into consideration in this analysis. The influence of magnetic field, thermophoresis, nonlinear thermal radiation, Brownian motion, and activation energy has been considered. The present analysis is modeled in a partial differential equation form and is then converted to ordinary differential equations using appropriate variables. A numerical solution using the bvp4c technique is accomplished using MATLAB software. The current results are matched with the previous literature and established a close relationship with previous studies. The purpose of this investigation is to numerically investigate the time-independent hybrid nanofluid flow comprising copper oxide and silver nanoparticles over a rotating disk surface. The results show that the increased magnetic parameters increase the friction force at the surface, which decreases the radial and azimuthal velocity distribution. At the sheet surface, the radial velocity of the hybrid nanofluid shows dominant performance compared to the nanofluid. On the other hand, the magnetic factor has dominant behavior on the azimuthal velocity component of the nanofluid flow compared to the hybrid nanofluid flow. The higher volume fraction and magnetic factor enhance the skin friction at the disk surface. Furthermore, greater surface drag is found for the hybrid nanofluid flow. The higher solid volume fraction, temperature ratio, and Biot number enhance the rate of heat transmission. Also, a higher rate of heat transmission is observed for the hybrid nanofluid flow.

Effect of thermal radiation and inclined magnetic field on thermosolutal mixed convection in a partially active wavy trapezoidal enclosure filled with hybrid nanofluid

This work focuses on the examination of the magneto-thermosolutal convection in a lid-driven wavy trapezoidal enclosure in the presence of thermal radiation. The wavy cavity is filled with radiative Fe3O4-Cu-H2O hybrid nanoliquid. In this work, two cases are considered depending on the location of heat and concentration sources. A portion of the vertical walls are kept hot and in high concentration while the remaining parts are in adiabatic condition. The adiabatic flat upper lid is moving towards the right with equal speed. In addition, the lower wavy border is cold and low concentration. The governing Navier–Stokes equations are modeled to describe thermosolutal phenomena within the wavy enclosure. These equations are solved by reconstructing a recently developed compact scheme. Computed outcomes are presented in terms of streamlines, isotherms, iso-concentrations, average Nusselt and Sherwood numbers to evoke the thermosolutal phenomena for various physical parameters. Also, computing in-house code is validated with the published numerical and experimental and literatures. This investigation surveys the roles of several well-defined parameters such as Richardson number (Ri), Lewis number (Le), Buoyancy ratio number (N), Radiation parameter (Rd), Hartmann number (Ha), inclination of angle (γ), undulation of the wavy surface (d) and solid volume fraction (ϕhnp) of the hybrid nanofluid. An increase in the Lewis number (Le) enhances species diffusion within the system but diminishes thermal transport. This work reveal that a change in ϕhnp from 0% to 4%, heat transfer is upgraded up to 4.28% in Case I and 3.93% in Case II while mass transfer is declined by 2.24% in Case I and 1.60% in Case II. Results indicate that Case I performed better than Case II in the case of energy and solutal transfer. This work has many practical applications such as heat exchangers, electronic device cooling, food processing and porous industrial processes.

Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

AbstractResults from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between $$\phi _b=0.2$$ ϕ b = 0.2 and 0.6, and the Coulomb friction coefficient is either $$\mu _c = 0$$ μ c = 0 or 0.5. The main objectives are to unravel the influence of (1) $$\phi _b$$ ϕ b and $$\mu _c$$ μ c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing $$\phi _b/\Phi _R$$ ϕ b / Φ R , where $$\Phi _R$$ Φ R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration $${\bar{\phi }}/\phi _m$$ ϕ ¯ / ϕ m , where $$\phi _m$$ ϕ m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number $$I_v$$ I v in the core region, where the macroscopic friction coefficient $$\mu $$ μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for $${\bar{\phi }}/\phi _{mp}$$ ϕ ¯ / ϕ mp as function of $$I_v$$ I v , where $$\phi _{mp}$$ ϕ mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond $$\phi _{m}$$ ϕ m at high $$\phi _b$$ ϕ b and maximum core concentrations below $$\phi _m$$ ϕ m at lower $$\phi _b$$ ϕ b .

A CFD and experimental study of hydrodynamic and heat transfer behavior in ribbed fluidized beds

Abstract The study focuses on enhancing the performance of fluidized bed systems, which are widely used in industrial processes requiring efficient heat and mass transfer. By integrating ribs at angles of 135, 150, and 165° on the riser wall, the research assesses their impact on hydrodynamic behavior and heat transfer using CFD simulations. The simulations, confirmed through experimental data, revealed that the 150° ribbed model outperforms others by improving particle mixing and achieving the highest heat transfer coefficient. The investigation also covered static pressure, solid volume fraction, and particle velocities at different bed heights (30, 60, 90, and 120 mm), showing that ribbed models significantly enhance turbulence and particle distribution, with the 150° ribs providing a balance between dynamic mixing and stable flow.

Heat transfer augmentation in a double lid-driven trapezoidal porous cavity with heated block using hybrid nanofluid

This study intends to understand the fundamental characteristics of hybrid nanofluids (HNF) in a porous cavity using computational modeling, which will aid in developing HNF within hydrodynamics and enable adaptability. The present research investigates the enhancement of the transmission of heat in a double lid-driven trapezoidal porous cavity containing a heated block, utilizing a HNF composed of aluminum oxide/copper-water (Al2O3/Cu-H2O) employing the Finite Element Method (FEM) based on Galerkin weighted residual (GWR). Additionally, the Darcy-Brinkman-Forchheimer comprehensive approach has been used to demonstrate fluid flow in the porous media. The governing parameters such as the Darcy number (10−4 ≤ Da ≤ 10−2), the porosity of the porous medium (0.6 ≤ ε ≤ 0.9), inclined angle (π/16 ≤ ϕ ≤ π/3), and solid volume fraction (0.001 ≤ δ ≤ 0.05) have been chosen to evaluate the impact within dimensionless time (0.1 ≤ τ ≤ 1). The simulation outcomes of flow and thermal fields are shown through streamlines, isotherms, average heat transfer rate at the hot surfaces, and average temperature inside the cavity. The outcomes of this study show that the HT rate rises by 41.02% when increasing the solid volume fraction (svf) from 0.1% to 5%. Also, it has been found that if the inclined angle is enhanced from π/16 to π/3 at non-dimensional time τ = 0.5, the average HT augmented by 63.16%.

Influence of multimodal fiber distribution on the permeability of fibrous media

This article deals with the impact of fiber size distribution on the permeability of nonwoven fibrous media, a major issue in the general field of filtration. The conventional method to determine the permeability of nonwoven fibrous media involves equating complex fibrous media with structures composed of a single equivalent fiber diameter. Based on numerical simulations of flow through tridimensional structures with polymodal and polydisperse fiber size distributions, we proposed a new equivalent diameter. In conjunction with a packing density function, the approach is compared to experimental data and simulations available in the scientific literature and shows better permeability predictions than other existing models for a wide range of solid volume fractions (1 % to 20 %) and fiber diameters (1.5 µm to 30 µm). This predictive model of permeability is an essential step in developing a decision-making tool for the design of fibrous media.

Thermal management and power generation characteristics in a bifurcating channel by using a piezo-embedded inclined elastic fin assembly during turbulent forced convection of ternary nanofluid

Numerous engineering systems use piezoelectric energy harvesters (PE-EHs), which have several benefits including low cost, simplicity, better power density, and ease of installation. They can be used in different applications for energy harvesting and different external sources such as wind and vortex induced vibrations due to fluid–structure interaction can be utilized. This study uses a unique elastic fin PE/EH assembly for power generation, thermal management, and flow control in a bifurcating channel. Performance of the system is improved by using ternary nanofluid in the channel cooling system. Galerkin weighted residual FEM with ALE is used as the solution method. The convective heat transfer performance and power generation by the EH device are investigated in relation to the varying following parameters: Reynolds number (Re between 10000 and 30000), PE-EH inclination (γ between 0 and 60), fin horizontal location (xf between −H and H), and nanoparticle loading in the base fluid (ϕ between 0 and 0.03). The vortex size and distribution near the junction are significantly influenced by the fin inclination and horizontal location of the fin assembly within the bifurcating channel. When varying other parameters of interest, using nanofluid at the highest loading results in significant deflection of the fin assembly and power generation within the PE-EH. Enhancement factors (EFs) for power generation becomes 15.6 and 39.8 when cases of lowest and highest Re are compared with pure fluid and nanofluid while they are 2.93 and 3.38 for thermal performance improvements. Fin inclination of γ=30 is found as the optimum inclination for achieving the highest power from the assembly. Higher inclination of elastic fin/PE-EH assembly results in cooling performance deterioration while average Nu reduces by a factor of 2.94 by varying inclination from γ=30 to γ=60 with nanofluid. For power generation, effects of using nanofluid with varying inclination is significant and EF becomes 252 from γ=0 to γ=30. There are opposing tendencies for the device’s power generation and cooling performance enhancement when the fin’s horizontal placement is changed. EF for average Nu is 7.25 for varying fin location. As the loading of nanoparticle inside the base fluid increases, the average Nu and generated power exhibit non-linear rising characteristics. Polynomial type correlations are provided for the average Nu and power from the device by varying elastic fin assembly inclination and nanoparticle solid volume fraction. Potential of using hybrid nanofluid in PE-EH embedded thermo-fluid system is shown. The design, development, and optimization of self-sufficient power production systems that may be used to various thermo-fluid systems, such as electronic cooling and thermal control in a range of heat transfer devices, may benefit from the findings.

A data-driven method for fast predicting the long-term hydrodynamics of gas–solid flows: Optimized dynamic mode decomposition with control

Data-driven methods are of great interest in studying the hydrodynamics of gas–solid flows. In this paper, we developed an optimized dynamic mode decomposition with control (DMDc) method for long-term and fast prediction of one physical field with the aid of another physical field. Using the computational fluid dynamics-discrete element method (CFD-DEM) simulation results as the benchmark, the prediction ability of the standard DMDc method and the optimized DMDc method is evaluated. It was shown that the optimized DMDc method is superior when the order of magnitude of the predicted data is much larger than that of the auxiliary data, which cannot be addressed by using scaled or dimensionless data, for instance, the prediction of gas pressure with the aid of solid volume fraction; on the other hand, both DMDc and optimized DMDc methods can reasonably predict the long-term behavior of gas–solid flows, when the magnitude of the elements of the predicted field is comparative to that of the auxiliary field. This study proposes a fast and relatively accurate method for predicting the hydrodynamics of gas–solid flows with the aid of a known field.

Influence of space conjugate temperature varying non-uniform heat sink/source on hydromagnetic slip water-EG (50:50) nanofluid

Significant cooling is an essential requirement in the field of aeronautical and bio-medical engineering, nuclear reactor system, solar collectors, and in development of electronic chips etc. Involving rotating conical geometries. In view of this, flow and heat transfer over conical geometries subject to different constraints of motion are highly needed. Implementation of magnetic field subject to flow pattern controls the fluid motion thereby imparting better cooling. Consideration of nanofluid instead of regular fluid yields prominent cooling of the associated surface. Such relevance has motivated the authors to work on magnetohydrodynamics and heat transfer investigation of water-EG (50:50) mixture based Al2O3 and Fe3O4 past heated and rotating down-pointing upright cone subject to impact of space and temperature varying non-uniform heat source or sink. Numerical solution of dimensionless governing equations is accomplished by implementing Runge-Kutta method. The findings indicate that swirl and axial velocities peter out with rise in magnetic parameter while both exhibit opposite impact in response to slip parameter. Temperature profiles upgrade due to amplification of space and temperature dependent parameters. Skin friction and heat transportation upsurge with growth of solid volume fraction of nanoparticle.

Packing properties assessment of cement and alternative powders: Artefacts and protocols

This paper introduces three major recommendations for the assessment of the maximum packing fraction of mineral powders through compressive rheology. First, our results show that a minimum compressive stress is required for the measured solid volume fraction to tend towards a constant jamming fraction. Second, we show that the modification of the particles surface properties, especially their friction coefficient, by polymer adsorption, allows for this jamming fraction to get closer to the particle maximum packing fraction. Finally, we show that a minimal value of the initial solid volume fraction of a sample is necessary to prevent particle size separation during testing. We moreover show that the measured jamming fraction depends on the initial solid volume fraction of cement-based samples. We suggest that such a peculiar behavior finds its origin in the dependency of early hydrates volume or morphology on the initial supersaturation.

Effect of instantaneous local solid volume fraction on hydrodynamic forces in freely evolving particle suspensions

Particle Resolved Simulations (PRS) for freely evolving sphere suspensions at solid volume fractions (φ) between 0.1 and 0.4, Reynolds number Re from 10 to 300 and particle-fluid density ratios ρsρf of 2, 10 and 100 are used to investigate the effect of Voronoi tessellation based particle local solid volume fraction (φv)on particle drag and lateral forces. Findings reveal the instantaneous suspension mean drag force is positively correlated with the variance of φv among particles in the suspension. It is also shown that using the conditioned instantaneous φv of each particle in existing mean drag force correlations can significantly improve the prediction accuracy. Suspension mean lateral force ranges up to 60 % of the drag force while individual particles exhibit values as high as 90 % of the drag force. An instantaneous lateral force correlation is proposed based on suspension-averaged flow variables and φv.

Flow and coherent structures generated by a circular array of rigid, emerged cylinders in a shallow channel

The study investigates the flow structure, dynamics of the large-scale coherent structures, drag forces and sediment entrainment mechanisms generated by a circular array of diameter D containing rigid emerged circular cylinders of diameter d placed in a smooth-bed channel of depth h under strong shallow flow conditions (D/h = 20, d/D = 0.0125 and 0.025). Eddy resolving simulations are conducted with different values of the solid volume fraction 0.025 ≤ SVF ≤ 0.1 and non-dimensional frontal area per unit volume (2.56 ≤ aD ≤ 10.2, where for the present configuration, a = SVF(1/d)4/ ${\rm \pi}$ ) and a fixed channel Reynolds number (Reh = 10 000). The flow conditions are such that a vortex street (VS)-type of shallow wake is expected to form for a solid cylinder of diameter D. Findings are compared with previous results obtained for cases with moderately shallow conditions 2.5 ≤ D/h ≤ 3.5 and with the limiting case of flow past a solid cylinder with D/h = 20. For moderately shallow conditions, the core of the main horseshoe vortex (HV) forming around the array occupies a small fraction of the water column and its coherence is the largest in front of the array. By contrast, for very shallow conditions, multiple HVs form around the array and their cores occupy a large fraction of the water column. Moreover, the coherence of most of these HVs peaks close to the sides of the array. Only for relatively large aD values, the main HV extends over the whole upstream face of the array, similar to the limiting case of a solid cylinder. For sufficiently high aD, a secondary instability is present inside the near wake that leads to the formation of parallel horizontal vortices in the vicinity of the wake roller vortices. The changes in the wake structure with decreasing SVF and aD are qualitatively similar to those observed for cases with moderately shallow flow conditions, with the antisymmetric wake shedding mode being suppressed for aD ≤ 2.5. However, the Strouhal number associated with the shedding of wake rollers, which is still close to 0.2 for a solid cylinder with D/h = 20, can be as high as 0.4 for aD = 2.5. The paper also discusses how the steady wake and total wake lengths and the strength of the bleeding flow vary with the SVF. Simulation results show that the capacity of the flow to entrain sediment inside and around the array peaks for SVF = 0.05 and aD = 5.2, with sediment entrainment monotonically increasing with the SVF outside the array and monotonically decreasing inside the array. Despite the differences in the flow structure next to and inside the array, the variation of the mean, time-averaged streamwise drag coefficient of the solid cylinders ${\bar{C}_d}$ with aD is close to that observed for arrays with moderately shallow flow conditions. The combined drag coefficient for the array decreases with increasing flow shallowness, with the decay being stronger for relatively large values of aD.

Atmospheric Bubbling Fluidized Bed Risers: Effect of Cone Angle on Fluid Dynamics and Heat Transfer

Abstract In this paper, a comparative study of fluid flow behavior and thermal characteristics of sand particles has been carried out numerically and experimentally in bubbling fluidized beds for five-cone angles of the riser wall having 0 deg, 5 deg, 10 deg, 15 deg, and 20 deg. An Eulerian model with a k–ε turbulence model is used to explore the numerical analysis, and the findings are compared to those of the experiments. For the study, the inlet air velocity is fixed at 1.5 m/s with sand particles filled up to 30 cm to maintain bubbling conditions in the risers. The results indicate that increasing the cone angle up to 10 deg while maintaining the amount of bed materials constant leads to a reduction in pressure drop. The expansion of particles along the riser is observed to decrease with the increase in the cone angle up to 10 deg. The radial solid volume fraction profile transforms to a U shape from the W-type profile as the cone angle increases up to 10 deg. Correspondingly, the solid velocity is found to have an inverted U-type and W-shaped profile for the risers. The granular temperature is also found to increase with a decrease in the solid percentage at any location. The average bed temperature, interphase, and bed-to-wall heat transfer coefficient at a location of 10 cm axial height also increase with the cone angle increase up to 10 deg. As a result, the conical riser, when designed with a greater cone angle up to 10 deg, exhibits more efficiency in terms of heat transfer characteristics. The 3D simulation results are in strong concurrence with the experimental results in all investigations.

Numerical investigation of fluid flow and heat transfer of a nanofluid around two circular cylinders arranged in tandem in horizontal duct

In this study, two-dimensional unsteady laminar convective heat transfer from two isothermal cylinders arranged in tandem in horizontal duct has been numerically investigated. The numerical study is performed by solving the governing equations (continuity and momentum) and energy equations using a finite volume-based code ANSYS Fluent. The present study was conducted using nano sized copper particles suspended in water. The Prandtl number Pr of the resulting suspension being equal to 7. The range of solid volume fractions studied is and the flow Reynolds number is equal to 100.The spacing ratio of the two cylinders was varied from 2 to 5 while the blockage ratio was kept constant β=0.25. A detailed discussion has been provided regarding the variation of flow structure and the characteristics of flow, including total drag and lift coefficients, as a function of the dimensionless parametersIn order to visualize the flow and heat transport, streamlines, vorticity contours and isotherms were generated. In addition, the local and average Nusselt numbers for the upstream and downstream cylinders are calculated. The results demonstrate that the force coefficients, the wake structure behind the cylinders, and the Nusselt number are significantly influenced by the value of the spacing ratio and the volume fractions of nanoparticles. The results demonstrate a significant enhancement in heat transfer efficiency relative to the base fluid. The aforementioned improvement is more pronounced in the case of higher gap ratios and higher nanoparticle volume fractions.

Bridging micro nature with macro behaviors for granular thermal mechanics

The connection between micro-level characteristics and macroscopic properties in granular heat transfer and mechanics is fundamental and crucial. This study proposes a novel discrete element approach incorporating granular heat transfer, contact bonding, and granular stress tensor models to investigate the mechanical and thermal responses of continuum media composed of constituent spheres. Eight benchmark tests were devised to bridge the long-standing gap between micro and macro properties in granular materials. Through these tests, the numerical solutions obtained from discrete element modeling match well with existing analytical or finite element solutions derived from continuum-based theory. This validation underscores the rationality and reliability of the granular heat transfer model, contact bonding model, and granular stress tensor model. Moreover, the study highlights the consistency between continuum-based theory and discontinuum-based theory. A minor distinction between continuum-based models and discrete element models emerges near the boundaries due to variations in the specification of boundary conditions. This discrepancy can be clarified by Saint-Venant's Principle, thus validating the accuracy of the microscale heat transfer and mechanics theory for granular materials. Five mono-disperse packing structures, including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), hexagonal close packing (HCP), and random packing (Random), were further analyzed to examine their influence on heat transfer performance. Numerical results reveal that higher coordination numbers and solid volume fractions correspond to higher apparent thermal conductivity of granular assemblies, thus elucidating the connection between micro packing configurations and macroscopic heat transfer properties. The apparent thermal conductivity for different crystal configurations follows the sequence: HCP ≒ FCC > BCC ≒ Random > SC. To improve the accuracy and physical relevance of the proposed model, the effect of particle contact area needs to be further incorporated into the granular heat transfer model.

Analysis of magneto-natural convection and second law of thermodynamics of Cu-Al2O3-hybrid nanofluid in a vertical wavy cabinet having a localized non-uniform heat source

Improvements in thermal transference rate and minimization of entropy generation are critical issues in many industrial and engineering applications where heat transfer coefficient is essential to achieve optimal performance and minimal energy consumption. In the present investigation, a computational analysis has been conducted to analyze the impact of magnetic field on magneto-free convection and entropy generation inside a vertical wavy cabinet filled by Cu-Al2O3/H2O hybrid nanosuspension. In the geometry of this model, vertical boundaries of the chamber are designed as wavy and kept as cooled temperature (Tc), whereas the horizontal boundaries are modeled as square and are designed to be thermally adiabatic, except the centrally heated portion on the bottom wall. The centered bottom heated section is supposed to be isothermal with linearly changing temperature, and it changes linearly from Th1 to Th2, whereas it is modelled as a non-isothermal condition. The main focus, in this investigation, is on the entire chamber filled with the combination of hybrid nanoparticles regarded the volumetric concentration of copper and alumina nanoparticles (Cu-50 %+Al2O3-50 %) along with base liquid (H2O). The transformed dimensionless partial differential equations were solved by using finite volume method (FVM) with power law differencing scheme. The simulated flow and temperature fields are scrutinized by streamlines, isotherms, entropy formations, total entropy generation and average convective Nusselt number associated with varying number of undulations (0 ≤ N≤3) volume fraction of hybrid nano liquid (0 ≤ φ ≤ 0.04) magnetic orientation angles (0° ≤ ς ≤ 135°), Hartmann number (Ha = 0 and 50), and dimensionless temperature drop (Ω = 0.001–0.1). From this study, it is found that the average Nusselt number and entropy generation increase as the solid volume fraction of hybrid nanoadditives increases, while opposite trend is observed when the values of Hartmann number rises. The findings show that growth of undulation number (N) causes the reduction of convective heat transfer rate as well as average entropy production intensity. The obtained outcomes concluded that hybrid nano liquid is more effective and finest choice for the improvement of cooling of heat transfer process and minimal energy loss than single nanoliquid. According to the new proposed criterion (TPC), the results show that square-shaped enclosure (N=0) manifests the better cooling performance among the considered governing parameters. The novelty of this study is to scrutinize the flat/ vertical wavy boundaries of the cabinet which can be represented as a model of heat transfer controller, in which it manages the thermal and flow field characteristics. Predominantly, the isothermal line source is used to boost the overall convective heat transfer which is applied in buildings and fluid-mounted heaters. Additionally, many investigators have focused only on the enhancement of heat transfer. As it is known, to increase the thermodynamic efficiency of a system, optimization of entropy generation is an excellent tool which reduces the loss of energy. Hence, it recently does a good engineering sense to highlight an entropy irreversibility.