Solid Volume Fraction Research Articles

Numerical study of unsteady thin film flow and heat transfer of power-law tetra hybrid nanofluid with velocity slip over a stretching sheet using engine oil

This paper explores the effects of velocity slip and power-law nanofluid flow on tetrahybrid nanofluids across a stretching sheet. Tetrahybrid nanofluids, which combine four distinct nanoparticles Ag, SiO2, CuO, and ZnO with engine oil as the base fluid, are investigated for their potential to enhance thermal performance. Engine oil plays a critical role in reducing friction and wear in mechanical systems by forming a protective layer on components such as cylinders, pistons, and bearings. Using MATLAB’s bvp4c, the study solves a set of ordinary differential equations derived from boundary layer equations, applying appropriate similarity transformations. It is observed that two unique velocity profiles intersect at a specific location, which shifts away from the stretching sheet as the velocity slip parameter increases. The findings indicate that tetrahybrid nanofluids offer superior heat transfer rates compared to standard nanofluids, showing improvements of 7.43, 6.27, and 5.35% over hybrid and tri-hybrid nanofluids, respectively. This study provides graphical representations of how various parameters, including the Prandtl number, power-law index, slip parameter, magnetic field parameter, and Reynolds number, affect temperature and velocity profiles. It is revealed that increasing the value of the solid volume fraction causes the tetrahybrid nanofluid velocity to decrease and its temperature to rise. The innovation of this work lies in its detailed examination of tetrahybrid nanofluids, extending beyond earlier research on simpler nanofluids and offering valuable insights for advanced thermal management solutions.

Irreversible effects for SWCNT‐MWCNT/water based flow with Coriolis force over rotating frame: A numerical study

AbstractIn this study, two different types of nanofluids are used: One is the simple nanofluid consist of single‐wall carbon nanotubes (SWCNT), and the other is the hybrid nanofluid composed of single and multi‐wall carbon nanotubes (SWCNT‐MWCNT). The famous Xue model is incorporated for the thermal energy analysis. An important property related to the nanoparticles is the Brownian motion and thermal‐migration, which is described by using Buongiorno's model. The appropriate similarity transformations are used to convert the governing nonlinear partial differential equations into the nonlinear coupled ordinary differential equations for the both velocity and temperature profiles. The numerical solution is obtained for the present problem by using bvp4c Matlab routine. This code is based on the finite difference method that implements the three‐stage Lobatto IIIa formula. The comparative analysis for the entropy generation in rotating frame due to heat transfer, viscous heating, and mass diffusion is the main focus in this study. The impact of different parameters such as, rotational motion , thermomigration and Brownian motion , volume fractions of SWCNT & SWCNT‐MWCNT ,, Eckert number , Lewis number , chemical reaction parameter , Brinkman number the temperature ratio parameter and concentration difference parameter on axial and transverse velocity, temperature profile, entropy generation, and Bejan number are obtained. The obtained results for these different variables are presented through graphs and tabular form. When the solid volume fraction is enhanced, the flow and heat distribution are observed to increase. The Nusselt and Sherwood numbers for both nanofluids are investigated. The decay in Nusselt number is observed as the values of the heat source/sink parameter, thermophoresis, Brownian motion, and Eckert number are increased. However, in the case of Sherwood enhancement an increment in the value of the chemical reaction parameter, thermophoresis, Brownian motion, and Lewis number is observed. The entropy generation is enhanced as a result of increment in Brinkman number and temperature ratio. However, in the case of Bejan number, opposite trend was seen in the entropy generation. For the hybrid nanofluid, the enhancement in both heat transmission and irreversibility effect is observed as compared to simple nanofluid.

Enhancing Heat Transfer Efficiency Through Controlled Magnetic Flux in a Partially Heated Circular Cavity Using Multi-Walled Carbon Nanotube Nanofluid and an Internal Square Body

Applications including aircraft systems and electronics cooling depend on effective heat transfer. This study investigates magnetohydrodynamic (MHD) free convection and thermal radiation for heat transfer in a circular cavity filled with multi-walled carbon nanotube (MWCNT) nanofluid and containing a square obstruction. This study examines the impact of the internal geometry on heat transfer and fluid flow dynamics under three distinct boundary conditions, and it presents a comprehensive analysis based on a wide range of Hartmann (Ha) and Rayleigh (Ra) numbers. MWCNT nanofluid with high thermal conductivity was employed to enhance heat transfer efficiency, using a solid volume fraction (SVF) of 4% for MWCNTs and assuming Newtonian behavior for computational simplification. Magnetic properties were imparted to the nanofluid by assuming the dispersion of carbon nanotubes in a base fluid containing magnetic nanoparticles. Other walls were insulated, the bottom wall was heated, and a magnetic field (MF) with Ha ranging from 0 to 100 was applied. It was observed that raising Ra from 103 to 106 improved the Nusselt number (Nu) from 0.08 to 7.1 using the Galerkin finite element method. Ha increased from 0 to 100 and reduced Nu by 35%. Three boundary conditions for the square body showed that the heated conditions provided the largest Nu. By means of an increase in SVF from 0 to 0.04, the MWCNT nanofluid improved heat conductivity by 18%. Radiation effects with the radiation parameter Rd = 0.5 increased heat transmission by 22%. These results underline the importance of considering MHD and nanofluid characteristics in maximizing heat transfer for commercial purposes, and the approaches employed in this study contribute to a deeper understanding of the behavior of thermal systems under the influence of MHD and internal geometry.

Particle dynamics at fluid interface by pseudo-potential lattice Boltzmann method coupled with smoothed profile method

Fluid–solid coupling widely exists in some natural phenomena and industrial applications. However, it is still an important challenge to correctly capture the transient changes of particles at fluid interface. We develop a lattice Boltzmann model for particle dynamics at fluid interface, which adopts a coupling strategy by combining the pseudo-force (Shan-Chen) multiphase multicomponent model and the smoothed profile method. In the coupling strategy, a novel extrapolation boundary condition is applied for fluid–solid interface, a repulsive force (bounce-back force) between solid node and fluid node is introduced in the coexistence region (at the fluid–solid interface), to form the interaction between fluid and solid particle. Thanks to the proposed fluid–solid coupling method, the drag force on solid particles can be correctly described, especially for situations of high solid volume fractions. It is found that the wetting angle θ between fluid interface and particle surface is basically linear with the repulsive force coefficient difference ΔG. What is more, to further validate the reliability of our proposed model, we performed two groups of simulations for different Bos = 0.51 (0.84) and 0.83 (1.35), they are the single particle trapped under gravity at deformed fluid interface and the falling single particle impacts fluid interface in the presence of gravity, respectively, and good agreements between simulation results and experimental ones in the description of the relationship between the inertial force and the interfacial tension are obtained, and their correlations are both close to 1, which proves the reliability of our proposed model.

Mechanisms of air bubble rise in cement suspensions studied by X-ray analysis

The de-airing of fresh concrete is a crucial step in ensuring sustainable and durable concrete structures. Currently, proper de-airing is ensured by adjusting the fresh concrete consistency i.e. its rheological properties, without any knowledge whether this will actually guarantee sufficient de-airing. The exact relationship between the rheological properties and air bubble dynamics in concrete is not yet understood. In this paper, a detailed study was carried out in which air bubbles of different size and volume were injected in fresh cement suspensions with varying solid volume fractions (i.e. varying rheological behaviour). The air bubbles were visualised by means of X-ray radiography and the rise behaviour was evaluated with image based algorithms. It was found that in more viscous suspensions (i.e. higher particle contents) the bubble speed increases with decreasing suspension viscosity. For suspensions with higher flowability (i.e. less particle content), the inertial forces dominate the viscous forces, with the viscosity playing a subordinate role. The shear rate induced by an ascending air bubble is sufficient to locally reduce the dynamic viscosity of the suspension. In addition, it leads to shear-induced particle migration, with less concentrated regions in the ascending channel. Consequently, subsequent bubbles are influenced by changes of viscosity in this channel, rising faster and having different bubble shapes.

Dual Solutions of Two-Dimensional Hybrid Nanofluid Flow and Heat Transfer Past a Porous Medium Permeable Shrinking Sheet with Influence of Heat GenerationAbsorption and Convective Boundary Condition

In this study, the dual solutions of two-dimensional hybrid nanofluid flow and heat transfer past a porous medium permeable shrinking sheet with influence of heat generation/absorption and convective boundary condition were examined using the bvp4c solver with the MATLAB computational framework. The utilization of two-dimensional hybrid nanofluid flow and heat transfer in the presence of a porous medium permeable shrinking sheet, considering the effects of heat generation/absorption and convective boundary conditions, has wide-ranging applications in industries such as cooling systems, aerospace, chemical engineering, biomedical applications, energy systems, microfluidics, automotive thermal management, industrial drying, and nuclear reactor cooling, etc. These applications employ the improved thermal characteristics of hybrid nanofluids and the efficient heat control offered by porous media and convective boundary conditions. The governing partial differential equations (PDEs) are transformed into a collection of higher-order ordinary differential equations (ODEs) together with their corresponding boundary conditions. These equations are subsequently shown both numerically and graphically. The main objective of this inquiry is to examine the relationship between the solid volume fraction of copper and the permeability parameter of the porous medium, specifically focusing on the values of f''(0) and - (0) according to the suction effect. The current research has also integrated the temperature and velocity profile of a hybrid nanofluid flow, which corresponds to the influence of porous medium permeability, heat generation/absorption, and convective boundary condition. Dual solutions are acquired by certain combinations of parameters. Non unique solutions are obtained when the critical point reaches , for suction effects. Increasing the intensity of heat generation absorption and convective boundary condition leads to a more pronounced temperature profile and thicker boundary layer.

Experimental study of solid-liquid two-phase flow field in a centrifugal pump volute under multiple working conditions

In order to study the variation law of the solid-liquid two-phase flow field in the volute of centrifugal pump and the distribution law of the solid particles in the volute, based on PIV technology, the dynamic and static interference flow field of the volute under different flow conditions (30 m3/h, 40 m3/h, 50 m3/h, 60 m3/h, 70 m3/h) and different solid phase volume fractions (1 %, 1.5 %, 2 %) is studied. It is found that with the increase of the solid phase volume fraction, the head and efficiency of the centrifugal pump gradually decrease, and the addition of the solid phase has little effect on the pump head when the solid phase volume fraction is small under the condition of the large flow. The high turbulent kinetic energy area in the volute is mainly concentrated near the outer wall of the volute and the area where the tongue is located. Under the same solid phase volume fraction, the turbulent kinetic energy in the volute increases with the increase of the flow rate. The turbulent kinetic energy in the volute decreases with the increase of the solid phase volume fraction. The absolute velocity component of the flow field in the volute is significantly affected by the flow condition.

Transport of a Mixture of Sand and Water Through a Pump Characterized by Dual Inlets and a Double-Layered Impeller

A centrifugal pump incorporating two inlets and a double-layered impeller is proposed for transporting a mixture of sand and water. The double-layered impeller (primary impeller) encircles a secondary impeller. To reveal the operating and flow characteristics of such a pump, numerical work is conducted with a validated numerical method. The effects of the feed rate of sand and the rotational speed of the impeller are investigated. The results show that the pump efficiency is not monotonically related to the solid volume fraction. At a feed rate of sand of 2.10 m3/min and a rotational speed of 950 rpm, the lowest pump efficiency is reached. In the volute chamber, vortices of various sizes are evidenced. With increasing rotational speed, the overall solid volume fraction in the pump decreases. Meanwhile, when the solid volume fraction attains 0.28, sand particles tend to accumulate near the outer rim of the volute chamber. The axial force acting on the primary impeller increases with the rotational speed. Under different operating conditions, the radial forces point unanimously toward the third and fourth quadrants.

Modelling of filtered drag force for clustered particle-laden flows based on interface-resolved simulation data

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

Direct numerical simulation of turbulent flow and heat transfer in a particle-laden turbulent channel flow

Direct numerical simulation (DNS) is conducted to investigate the impact of solid particles on heat transfer in a plane channel flow. For comparison, two corresponding DNSs of unladen channel flow are also performed. The numerical simulation of the particle-laden case employs a two-way coupled Eulerian–Lagrangian computational model, which allows for the consideration of momentum transfer between the two phases: discrete particles and the continuous fluid phase. The presence of particles results in an increase in the mean temperature, the root mean square (rms) of temperature fluctuations, and the streamwise turbulent heat flux within the core region. Furthermore, particles exert a more significant influence on these characteristics at higher solid volume fractions. Additionally, the correlation between velocity and temperature is affected by the presence of particles. When comparing heat transfer in particle-laden channel flow to that in the corresponding unladen channel flow, it is observed that the difference in heat flux arises from changes in the rms of the wall-normal velocity and temperature fluctuations. The impact of particles on turbulent heat flux transport is significant in the vicinity of the wall, while their influence within the core region is relatively small.

Improving the thermal properties of water by adding MWCNTs, cerium oxide, and MgO hybrid nanoparticles at different temperatures and volume fraction of nanoparticles: Experimental investigation

This study aimed to investigate the thermal conductivity (TC) of various nanofluid compositions, including water/MWCNT-MgO-cerium oxide ternary hybrid nanofluids (THNFs) with solid volume fractions (SVFs) ranging from 0.1% to 0.6%. Additionally, the thermal conductivity of water/MWCNT-cerium oxide, water/MWCNT-MgO, and water/MgO-cerium oxide hybrid nanofluids (HNFs), as well as water/MWCNT, water/cerium oxide, and water/MgO mono nanofluids (MNFs), was measured at SVF=0.1% and 0.3%. The experimental temperature was varied between 20, 30, 40, and 50°C for all samples. The MWCNT, MgO, and cerium oxide nanoparticles (NPs) were suspended in the water base fluid (BF) to create the nanofluids (NFs) in a two-step process. MWCNT NPs are 20–30 nm in size, MgO NPs are 20 nm, and cerium oxide NPs are 10–30 nm in size. DLS and zeta potential experiments, which demonstrate the correct stability of NFs, were used to evaluate the stability of NFs. The KD2-Pro instrument was used to test the samples' TC after making sure they were stable. The data obtained demonstrate a rise in TC with rising SVF and rising temperature. The MWCNT/water MNF exhibits the largest rise in TC in SVF=0.3%, with a TC increase of 19.16% at T=40°C. It should be noted that the largest increase in TC is 26.09% compared to the BF for water/MWCNT-MgO-cerium oxide THNF at SVF=0.5% and T=40°C. Finally, a mathematical connection was shown with the comparisons done to estimate the data. The results demonstrate the postulated relationship's high degree of accuracy.

Development of a XGBoost-based drag force model for freely evolving particle suspensions

An XGBoost-based drag model is developed using data from Particle Resolved Simulations (PRS) of freely evolving spherical particle suspensions, encompassing Reynolds numbers from 10 to 300, solid volume fraction between 0.1 and 0.4, and particle-to-fluid density ratio of 2, 10 and 100. Drag force data from 150 continuous time instances in PRS are divided into two sets: the first set that includes data from the initial 120 instances is used for training the model and interpolation testing, while the second set comprises drag forces from the final 30 instances is used exclusively for extrapolation testing. Both interpolation and extrapolation tests demonstrate significantly improved accuracy compared to traditional drag correlations. Notably, the model achieves its highest prediction accuracy for particles with density ratios of 100, which is attributed to the increased influence of unsteady drag forces at lower density ratios that cannot be fully captured by instantaneous particle distributions alone.

Applying different machine learning algorithms to predict the viscosity behavior of MWCNT–alumina/water–ethylene glycol (80:20) hybrid antifreeze

While machine learning has become the new way of analyzing data, neutral networks form the basis of this revolutionary technology. In this work, we shall employ the power of neural networks to analyze and demystify the processes in nanofluids. By combining the precision of neural networks with the optimization capabilities of genetic algorithms, we aim to create a more accurate and efficient prediction model for MWCNT-alumina/water-ethylene glycol (80:20) hybrid antifreeze. Our approach entails using an MLP neural network and several training functions (LM, GD, BFGS, BN) with an adjustable number of neurons. The inputs of the network are φ (solid volume fraction or ϕ), temperature (T), and shear rate (γ), and the output is μnf of MWCNT-alumina/water-ethylene glycol (80:20) hybrid anti-freeze. To improve the accuracy of the final model, we use genetic optimization to make final adjustments to the parameters of the neural network. Utilizing the detailed analysis of the primary characteristics of these algorithms, we conclude that the BFGS function is the best to obtain neural network training. Steady performance achieved by this function—0.99828 of the R-value and RMSE value significantly equal to 0.213—illustrates good stability and accuracy of the suggested model. This work contributes to progressing the existing knowledge about the behavior of nanofluids and can stimulate further improvement in heat transfer and energy utilization.

Effect of ZrB2 addition on microstructure and mechanical properties of 95W-HEA alloys

In tungsten heavy alloys, the substitution of conventional binders with novel high entropy alloys and the addition of rare metal borides have demonstrated considerable promise in enhancing comprehensive performance. In this study, 95W-5CoCrFeNiMn -x ZrB2 (x = 0.1, 0.2, 0.4, 0.6, 0.8) was synthesized by powder metallurgy method and characterized. The results show that: the spherical tungsten grains are distributed in binder network, and the added ZrB2 reacts with oxygen to generate ZrO2 and B2O3, which will affect the microstructure and properties of the alloys. An increase of ZrB₂ content results in a reduction in alloy density, accompanied by an enhancement in hardness; the changes in grain size, contiguity, and solid volume fraction present a trend of first falling and then rising, and the minimum value is obtained when the addition is 0.4 wt%. At this time, 95WHEAs-0.4 ZrB2 presents the best comprehensive performance, exhibiting an average grain size of 16.80 μm, a relative density of 96.10 %, a hardness of 411.68 HV1, and a compressive strength of 2457.64 MPa. The primary fracture mode observed in the alloys is W-binder interfacial separation, with a minor occurrence of tungsten cleavage when the ZrB2 addition is within an optimal range.

Effect of Water-based Alumina-Copper MHD Hybrid Nanofluid on a Power-Law Form Stretching/Shrinking Sheet with Joule Heating and Slip condition: Dual Solutions Study

The application of hybrid nanofluid is now being employed to augment the efficiency of heat transfer rates. A numerical study was conducted to investigate the flow characteristics of water-based-alumina copper hybrid nanofluids towards a power-law form stretching/shrinking sheet. This study also considered the influence of magnetic, Joule heating, and thermal slip parameters. This study is significant because it advances our understanding of hybrid nanofluids in the presence of magnetic fields, power-law form stretching/shrinking sheet, and heat transfer mechanisms, providing valuable insights for optimizing and innovating thermal management systems in various industrial applications such as polymers, biological fluids, and manufacturing processes like extrusion, plastic and metal forming, and coating processes. The main objective of this study is to examine the impact of specific attributes, including suction and thermal slip parameters on temperature and velocity profiles. In addition, this exploration examined the reduced skin friction and reduced heat transfer in relation to the solid volume fraction copper and magnetic effects on shrinkage sheet and thermal slip parameter on suction effect. To facilitate the conversion of a nonlinear partial differential equation into a collection of ordinary differential equations, it is necessary to incorporate suitable similarity variables into the transformation procedure. The MATLAB bvp4c solver application is utilized in the conclusion process to solve ordinary differential equations. No solution was found in the sort of when , and . As the intensity of the Eckert number increases, the temperature profile and boundary layer thickness also increase. The reduced heat transfer rate upsurged in both solutions for solid volume fraction copper for shrinking sheet, while the opposite actions can be noticed in both solutions for thermal slip parameter for suction effect. Finally, the study conducted an analysis to identify two distinct solutions for shrinking sheet and suction zone, while considering different parameter values for the copper volume fractions, magnetic and thermal slip condition effect.

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.

Heat transfer enhancement in magnetohydrodynamic hybrid nanofluids over a Bi-directional extending sheet with slip and convective conditions

The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

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.

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%.

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.