Values Of Solid Volume Fraction Research Articles

Interpolation of probability‐driven model to predict hydrodynamic forces and torques in particle‐laden flows

AbstractThe development of hydrodynamic force/torque closure models with physical fidelity is crucial for ensuring reliable Euler–Lagrange simulations in particle‐laden flows. Our previous work (Seyed‐Ahmadi and Wachs. J Fluid Mech. 2020;900:A21) proposed a microstructure‐informed probability‐driven point‐particle (MPP) method to construct a data‐driven particle‐position‐dependent closure model, incorporating the effect of surrounding particle positions on forces/torques. However, the MPP model is not pluggable in Euler–Lagrange simulations due to the computation of constant coefficients through linear regression and reliance on statistical arguments to obtain the probability map for a pair of values of solid volume fraction (Φ) and Reynolds number (Re). To overcome this limitation, we propose an interpolated MPP (iMPP) method, involving interpolation in the Φ and Re spaces. Our results demonstrate that the iMPP method can capture over 70% of the total fluctuations in hydrodynamic forces/torques in approximately 97.8% of the tested cases. This advancement contributes to a more versatile closure model suitable for integration into E‐L simulations.

Numerical study on thermal performance of TiO2, Fe3O4 and NiCr/engine oil in an inclined wavy pip

The essential intention of the existing article is to illustrate the effect of wall properties on flow and thermal behavior, through a sinusoidal inclined wavy pipe. To succeed this phenomena we assume a sinusoidal pipe consist of wavy surface, whose walls traveling down to its borders and located at an inclined position, moreover titanium dioxide (TiO2), ferrosoferric oxide (Fe3O4) and nichrome (80% Ni and 20% Cr) are considered as nano-particles and unused engine oil is assumed as a base fluid. The arising mathematical equations for thermal and flow ratio with wall slip impact are solved by mathematica. Also, evaluate graphically the thermal and flow behavior of nanofluids for multi values of solid volume fractions (η), rigidity parameter (M1), stiffness parameter (M2), viscous damping parameter (M3), Grashof number (Gr), slip parameter (β) and heat generation parameter (H) also discuss the streamlines for different values of solid volume fraction.

Numerical investigation of hybrid nanofluid with gyrotactic microorganism and multiple slip conditions through a porous rotating disk

The current mathematical configuration mainly focuses on the boundary layer flow of hybrid nanofluid with gyrotactic microorganisms and porous medium across the rotating disk. The heat and mass transport evaluation is done with double diffusion theory, Joule heating effect, and chemical reaction. The surface of the disk experiences multiple slip boundary conditions. The two nanoparticles, Ag and MgO, are mixed into water to form a hybrid solution. The flow model is transferred into self-similar nonlinear ODEs with appropriative transformation. These nonlinear ODEs are numerically explained using the BVP4C MATLAB approach. The physical quantities are also discussed withthe tabulated data, and the assessment is done with previous research. It is worth noting that higher values of solid volume fraction improved the velocity field and the temperature of the fluid . Stronger estimation of porosity parameter and inertia coefficient decline the velocity distribution.

Numerical treatment for Casson liquid flow in a microchannel due to porous medium: A hybrid nanoparticles aspects

In the current investigation a mathematical model is simplified to explore the numerical treatment for the thermal and flow behavior in a magneto hydrodynamics Casson fluid through a micro channel by taking [Formula: see text] nanoparticles. The combined effects of temperature jump, porous medium and velocity slip are incorporated. Using the dimensionless variables one can obtain the governing differential equations thereafter resolved numerically using RKF45 method. The velocity, temperature, skin friction and Nusselt number coefficient are addressed for different pertaining parameter. The upshots of the current investigation are visualized through graphically elucidation. Out comes shows that larger values of solid volume fraction decreases both velocity and temperature field. Furthermore drag coefficient is increases for increase in magnetic parameter, also hybrid nanofluid gives more impact than nanofluid.

Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profiles. The analytical expressions for the pressure gradient and wall shear stresses are obtained. The term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. The final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas the opposite behaviour is depicted near the left wall due to ciliated tips, whereas the temperature is an increasing function of B and γ and a decreasing function of Φ.

Analysis of single and multi-wall carbon nanotubes (SWCNT/MWCNT) in the flow of Maxwell nanofluid with the impact of magnetic dipole

The study of non-Newtonian fluids flow over diverse geometries with significant physical implications has numerous applications in the manufacturing and engineering field. On the other hand, carbon nanotubes (CNT) have wide-ranging applications in nanotechnology, energy storage, industry, chemical sensors, conductive plastics, optics, and structural composite materials. Hence, the flow of Maxwell nanoliquid embedded with SWCNT/MWCNT over a stretching sheet with the consideration of thermal radiation and magnetic dipole is examined. The partial differential equations (PDEs) specifying the flow of liquid are transformed into ordinary differential equations (ODEs) with the assistance of suitable similarity transformations. The reduced ODEs are numerically solved by using Runge-Kutta Fehlberg 45 order (RFF 45) method with the aid of shooting scheme. Major result outcome unveils that, fluid velocity decreases with an upsurge of ferromagnetic interaction parameter thermal distribution enhances rapidly for heightening of Biot number and thermal radiation parameter. Rate of heat transfer growths with higher values of Biot number and thermal radiation parameter. Surface drag force enhances with heightens values of solid volume fraction but decreases for viscous dissipation parameter.

Multiple shaped nano-particles influence on thermal conductivity of fluid flow between inflexible and sinusoidal walls

An approximate approach is used to evaluate the effect of different shaped nano-particles on the thermal behavior and flow performance of nanofluid flow through inflexible and sinusoidal walls in the existence of heat generation effect. To achieve this phenomena we considered boehmite alumina in different shapes like, blade, platelet, brick and cylinder as nano-particles and methanol as a base fluid. The model considered here is pumping of methanol in combination with boehmite alumina through inflexible and sinusoidal walls, which inspired due to the reality that thread injection is a probable technique for assigning clinical implantation's in the humanoid frame with least clinical trauma. The interior cylinder is endoscope (stiff and uncompromising) rotating with constant velocity (V) and the external cylinder is sinusoidal (wave traveling down to its wall). The resulting mathematical relations are simplified with the help of low Reynolds number and long wavelength, the resulting non-linear partial differential equations are converted into ordinary differential equations by using perturbation approach. After finding the analytic solutions we graphically compare the different shapes (platelet, blade, cylinder and brick) of nano-particles to evaluate which shape of nano-particles give batter performance. To observe the performance we compare the friction forces on interior and exterior cylinders, pressure gradient, pressure rise, velocity and temperature profiles for different values of solid volume fraction and also presented the streamlines for all shapes of nano-particles.

Assessment of Arrhenius activation energy in stretched flow of nanofluid over a rotating disc

AbstractThe study of shape effects in nanofluids plays a vital role in the fluid flow as well as heat propagation. Hence, the different shape factors of molybdenum disulfide MoS2 on a stretchable disc with rotation under the effect of the magnetic field, chemical response, and activation energy are examined. The set of partial differential equations is converted into ordinary differential equations (ODEs) by using von Karman's transformations, and the obtained ODEs are solved by using Runge‐Kutta‐Fehlberg 45 and shooting techniques. The numerical computations are made by utilizing well‐known maple 17 software. The different physical parameter effects on velocity, temperature, and concentration curves, as well as skin friction and Sherwood numbers, are analyzed through graphs. It is noted that the larger values of solid volume fraction enhances the drag coefficient and reduces the rate of heat transfer. It is further observed that the curve of a viscous fluid is always lesser than curve of a nanofluid.

Investigation into the rheology of a solid sphere suspension in second-order fluid using a cell model

The rheology of suspensions of solid spheres in viscoelastic background media is analytically calculated for dilute values of solid volume fraction. A mean-field cell model is used to express the influence of the solid particles in a suspending fluid, which obeys the second-order fluid model. A semi-analytical constitutive equation is created for the whole suspension, itself a second-order fluid with modified material parameters. The resulting rheology of the whole suspension is presented in simple shear, which shows predictions for the behavior of viscometric functions past explicitly dilute concentrations.

Thermo-magneto-hydrodynamical effects on merging flow of TiO2–water nanofluid

The steady flow of a nanofluid (mixture of titanium dioxide and water) in a rectangular channel under the influence of an inclined magnetic field is studied. The channel contains an upstream hot splitter plate in alignment with the upper and lower plates of the channel. It may be said that two incoming channel flows merge to form a single channel flow. This setup may apply to the heating chamber in which titanium dioxide can be used to enhance the thermal transfer rate. It is observed that the position of the splitter plate (that may act as an electric heater) affects the velocity and temperature of the fluid. Therefore, in order to ensure these facts, the examination of the flow behavior and the temperature distributions in the channel if the splitter is placed at different positions in the upstream have been probed. In addition, the effect of nanoparticles on the convection process has been probed. The streamlines are almost similar for a clear fluid as well as for a nanofluid (for low values of solid volume fraction of nanoparticles (i.e.$$\varphi < 0.05$$)) for all values of the Reynolds number. However, the rise in the temperature is noted for the nanofluid if the concentration of nanoparticles is increased. The increase in the Reynolds number also supports the enhancement of the Nusselt number and, hence, the thermal transfer rate of the nanofluid. The Nusselt number is dominant in the vicinity of the trailing edge of the splitter because the trailing edge exhibits as a stagnation point. In addition, the maximum Nusselt number for nanofluid at moderate Reynolds number (e.g., Re = 100) is enhanced to 0.3% with respect to the clear fluid. Moreover, obtained results for this particular case are compared with the existing literature, and the results compare well.

Numerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method

PurposeThis study aims to apply the lattice Boltzmann method to investigate the natural convection flows utilizing nanofluids in a semicircular cavity. The fluid in the cavity is a water-based nanofluid containing Al2O3 or Cu nanoparticles.Design/methodology/approachThe study has been carried out for the Rayleigh numbers from 104 to 106 and the solid volume fraction from 0 to 0.05. The effective thermal conductivity and viscosity of nanofluid are calculated by the models of Chon and Brinkman, respectively. The effects of solid volume fraction on hydrodynamic and thermal characteristics are investigated and discussed. The averaged and local Nusselt numbers, streamlines, temperature contours for different values of solid volume fraction and Rayleigh number are illustrated.FindingsThe results indicate that more solid volume fraction corresponds to more averaged Nusselt number for both types of nanofluids. It is also found that the effects of solid volume fraction of Cu are stronger than those of Al2O3.Originality/valueNumerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method in the presence of water-based nanofluid containing Al2O3 or Cu nanoparticles.

Effects of slip on Cu–water or Fe $$_{3}$$ 3 O $$_{4}$$ 4 –water nanofluid flow over an exponentially stretched sheet

This study aims to report the boundary layer flow of nanofluid over an exponentially stretched sheet in the presence of velocity slip as well as thermal slip. Utilising similarity transformations, the governing momentum and temperature equations are converted into ordinary differential equations and then solved numerically by shooting technique. An interesting behaviour of the solution for the converted self-similar equations is noted: dual solutions are obtained for some particular range of values of the governing parameters for the flow past an extended sheet. A comparison is made between the boundary layer flow of Cu–water and Fe $$_{3}$$ O $$_{4}$$ –water nanofluids. Both fluid velocity and temperature increase due to the enhancement in the velocity slip parameter. With the rising values of solid volume fraction, velocity diminishes but temperature increases.

Simulation of natural convection heat transfer using nanofluid in a concentric annulus

In the present study, natural convection of nanofluids in a concentric horizontal annulus enclosure has been numerically simulated using the lattice Boltzmann method. A water-based nanofluid containing Al2O3 nanoparticle has been studied. Simulations have been carried while the Rayleigh number ranges from 103 to 105 and solid volume fraction varies between 0 and 0.04. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics such as average and local Nusselt numbers, streamlines, and isotherm patterns for different values of solid volume fraction, annulus gap width ratio and Rayleigh number are investigated and discussed in detail.

동심이중관내 나노유체의 자연대류열전달에 관한 수치적 연구

In the present study, the homogeneous model is used to simulate the natural convection heat transfer of the CuO-water nanofluid in a concentric annular enclosure. Simulations have been carried while the Rayleigh number ranges from <TEX>$10^3$</TEX> to <TEX>$10^6$</TEX>, solid volume fraction ranges from 0.01 to 0.04 and the radius ratio varies between 0.1 and 0.7. Results are presented in the form of streamlines, isotherm patterns and averaged Nusselt numbers for different values of solid volume fraction, radius ratio of the annulus and Rayleigh numbers. The results show that by decreasing the radius ratio and/or increasing the Rayleigh number, the averaged Nusselt number increases. Also the heat transfer rate increases as increased solid volume fractions.

Analysis of MHD mixed convection in a flexible walled and nanofluids filled lid-driven cavity with volumetric heat generation

In this study, MHD mixed convection in a CuO-nanofluid filled lid-driven cavity having an elastic side wall and volumetric heat generation is numerically investigated. The left vertical wall is moving with constant velocity in the +y direction. The left vertical wall of the cavity is maintained at constant cold temperature while the right vertical wall is at hot temperature and the other walls of the cavity are insulated. The governing equations are solved with finite element method. The Arbitrary Lagrangian–Eulerian method is used to describe the fluid motion with the elastic wall in the fluid–structure interaction model. The influence of Richardson number (between 0.01 and 100), internal Rayleigh number (between 103 and 106), Hartmann number (between 0 and 50), inclination angle of the magnetic field (between 0° and 90°), Young's modulus of flexible wall (between 5×102N/m2 and 106N/m2), and nanoparticle volume fraction (between 0 and 0.05) on the fluid flow and heat transfer were numerically investigated. The effect of Brownian motion on the effective thermal conductivity was taken into account. The averaged heat transfer decreases with decreasing values of Richardson number and increasing values of Hartmann number and internal Rayleigh number. Absolute value of the averaged heat transfer enhances by 14.34% and 8.83% at Richardson number of 1 and 100 and deteriorates by 6.51% at Richardson number of 0.01 for Young's modulus of the elastic wall 500 when compared to configuration for Young's modulus of 106. The local and averaged heat transfer enhance as the value of solid volume fraction of the nanoparticle increases and this is more effective for higher values of Richardson number where heat transfer process is effective.

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic (MHD) stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge–Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.

MIXED CONVECTION HEAT TRANSFER IN A DOUBLE LID-DRIVEN INCLINED SQUARE ENCLOSURE SUBJECTED TO Cu-WATER NANOFLUID WITH PARTICLE DIAMETER OF 90 nm

In this article, mixed convection flow in a two-sided lid-driven cavity at different inclination angles filled with Cu−water nanofluid (with diameter of 90 nm) is studied numerically using the finite volume method. For different values of solid volume fraction of nanoparticles, flow is induced by the top and right-hand sidewalls sliding at constant speed. The left-hand sidewall is kept constant at higher temperature (Th), while the right moving wall is maintained at a lower temperature (Tc), thereby introducing natural convection. In this study, bottom and top walls were assumed isolated; Richardson number ranged from 0.001 to 10, nanoparticles solid volume fraction (φ) up to 0.06 were investigated, and cavity inclination angle from 0° to 90° was considered and the Grashof number was set to 104. The influence of inclination angle and φ of the nanofluids on hydrodynamic and thermal characteristics is discussed. The results indicated that increase in φ for a constant Ri enhances heat transfer. Also, heat transfer was increased as Ri was decreased for a particular φ. Moreover, where natural convection is dominant (i.e., higher Ri), the flow form seems to be influenced more by φ.

Lattice Boltzmann simulation of natural convection heat transfer in nanofluids

In this study, lattice Boltzmann method is applied to investigate the natural convection flows utilizing nanofluids in a square cavity. The fluid in the cavity is a water-based nanofluid containing Al 2O 3 or Cu nanoparticles. The study has been carried out for the Rayleigh number 10 3–10 6 and the solid volume fraction 0–0.05. The effective thermal conductivity and viscosity of nanofluid are calculated by Chon and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics are investigated and discussed. The average and local Nusselt numbers, streamlines, temperature contours and vertical component of velocity for different values of solid volume fraction and Rayleigh number are illustrated. The results indicate that by increasing solid volume fraction, the average Nusselt number increases for both nanofluids. It is found that the effects of solid volume fraction for Cu are stronger than Al 2O 3.

Microstructural effects on distortion and solid-liquid segregation during liquid phase sintering under microgravity conditions

Tungsten heavy alloys with compositions ranging from 78 to 98 wt pct tungsten were liquid phase sintered at 1507 °C under microgravity conditions for 120 minutes. The sintered microstructures were quantitatively measured for solid volume fraction, grain size, connectivity, and contiguity. Links between these microstructural parameters were analyzed and compared to previously derived empirical equations. The macrostructures of the samples were also quantified and correlated to the underlying microstructures. Critical values of solid volume fraction, contiguity, and connectivity required for free-standing structural rigidity were defined for various degrees of bond rigidity as represented by the dihedral angle. The results are used to predict the degree of solid-liquid segregation due to density differences between the solid and the liquid.

On the solution of a lubrication problem with particulate solids

The lubrication characteristic of a fluid with solid particles is studied using the continuum theory of mixtures. The governing equations are formulated and appropriate boundary conditions are introduced for an arbitrary-shaped lubricant film thickness. As a special case, closed-form analytical perturbation solutions up to ε 1 order for pressure and shear stress are obtained for a mixture of a conventional oil and solid particles with small values of solid volume fraction sheared in the clearance space of an infinitely long slider bearing. It is found that when compared with a pure fluid, the mixture of the fluid and solid generates a higher pressure and therefore a higher load-carrying capacity with the added advantage of a reduction in the coefficient of friction.