Solid Volume Fraction Of Nanoparticles Research Articles

Numerical study of MHD mixed convection in a nanofluid filled lid driven square enclosure with a rotating cylinder

Abstract In this study, a numerical study of MHD mixed convection nanofluid filled lid driven square enclosure was performed. The bottom wall of the cavity is heated and the top wall is kept at constant temperature lower than that of the heater. Other walls of the square enclosure and cylinder surface are assumed to be adiabatic. The governing equations are solved with finite element method. The influence of the Richardson number ( 0.001 ⩽ Ri ⩽ 10 ), Hartmann number ( 0 ⩽ Ha ⩽ 50 ), angular rotational speed of the cylinder ( - 10 ⩽ Ω ⩽ 10 ) and solid volume fraction of the nanoparticle ( 0 ⩽ ϕ ⩽ 0.05 ) on fluid flow and heat transfer are numerically investigated. It is observed that 17% of heat transfer enhancement is obtained for Ri = 10 when compared to flow at Ri = 1. Averaged heat heat transfer decreases with increasing Hartmann number and 14.2% of heat transfer enhancement is obtained for Ω = - 10 compared to motionless cylinder case at Ω = 0 . When the solid volume fraction of nanoparticle is increased, heat transfer increases.

Analysis of the entropy generation in a nanofluid-filled cavity in the presence of magnetic field and uniform heat generation/absorption

This paper examines the natural convection in a square enclosure filled with a water–Al2O3 nanofluid in the presence of magnetic field and uniform heat generation/absorption. The left wall is hot, the right wall is cold and the horizontal walls are insulated. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. The entropy generation due to heat transfer, fluid friction and magnetic effect has been determined by the finite difference method. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra=103 to 106, Hartmann number varied from Ha=0 to 60, heat generation/absorption coefficient q=−10 to 10 and the solid volume fraction of nanoparticles between ϕ=0 and 6%. For Ra ≤105 and Ha≤30, the results show that the heat generation/absorption coefficient influences heat transfer rate, but it does not affect the entropy generation in the range −10<q<5. Also it is observed that adding nanoparticle reduces the entropy generation. The nanoparticle effect is more intense for high Hartmann number.

Yield stress and flow behavior of concentrated ferrofluid-based magnetorheological fluids: the influence of composition

In this paper, the magnetorheological (MR) and magnetoviscous properties of ferrofluid-based iron particle suspensions were investigated. The 2.1-µm mean size Fe particles were dispersed in high-concentration transformer oil-based ferrofluid, the iron particle volume fraction in the resulting nano-micro composite magnetorheological fluid samples varying from Φ Fe = 5 to 40 %. The ferrofluid carrier has φ p = 23 % solid volume fraction of magnetic nanoparticles stabilized with chemisorbed oleic acid monolayer and without any excess surfactant. In the absence of the field, the ferrofluid has a quasi-Newtonian behavior with a weak shear thinning tendency. The static yield stress shows an increase of about 3 orders of magnitude for an iron particle content of approx. Φ Fe = 25 % (Φ tot = 42.25 %), while above this value, a saturation tendency is observed. The dynamic yield stress (Bingham model) also increases with the magnetic induction and the particle volume fraction; however, the saturation of the MR effect is less pronounced. The relative viscosity change has a maximum at Φ Fe = (10–15) % due to the accelerated increase of the effective viscosity of the composite for higher Fe content. Addition of micrometer-sized iron particles to a concentrated ferrofluid without any supplementary stabilizing agent proved to be a direct and simple way to control the magnetorheological and magnetoviscous behavior, as well as the saturation magnetization of the resulting nano-micro composite fluid to fulfill the requirements of their use in various MR control and rotating seal devices.

Marangoni Mixed Convection Boundary Layer Flow in a Nanofluid

The problem of Marangoni mixed convection boundary layer flow and heat transfer that can be formed along the interface of two immiscible fluids in a nanofluid is studied using different types of nanoparticles. Numerical solutions of the similarity equations are obtained using the shooting method. Three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (23AlO) and titania (2TiO) are consideredby using a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter ϕ of the nanofluid. The influences of the interest parameters on the reduced velocity along the interface, velocity profiles as well as the reduced heat transfer at the interface and temperature profiles were presented in tables and figures.

Analytical and Numerical Studies on Hydromagnetic Flow of Water Based Metal Nanofuids Over a Stretching Sheet with Thermal Radiation Effect

Hydromagnetic flow of an incompressible viscous water based nanofluid over a stretching sheet with radiation effect is investigated. The radiation heat flux is described by the Rosseland diffusion approximation in the energy equation. The resulting non-linear partial differential equations are transformed into a set of ordinary differential equations using scaling transformations. The dimensionless governing equations for this investigation are solved analytically using hyper geometric functions and numerically by Nachtsheim–Swigert shooting iteration technique together with fourth order Runge–Kutta integration scheme for different nanoparticles. The influence of pertinent parameters such as magnetic parameter, solid volume fraction of nanoparticles, Prandtl number, radiation parameter, Nusselt number and skin friction coefficient are discussed.

Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids

The present study aims to identify effects due to uncertainties of thermal conductivity and dynamic viscosity of nanofluid on boundary layer flow and heat transfer characteristics due to permeable stretching tube in the presence of heat source/sink. Water-based nanofluid containing various volume fractions of different types of nanoparticles is used. The nanoparticles used are Cu, Ag, CuO, and TiO2. Four models of thermal conductivity and dynamic viscosity depending on the shape of nanoparticles are considered. The results are presented to give a parametric study showing influences of various dominant parameters such as Reynolds number, the suction/injection parameter, solid volume fraction of nanoparticles, type of nanoparticles, the heat generation/absorption parameter and skin friction coefficient. The results indicate that the skin friction coefficient decreases as the Reynolds number and the suction/injection parameter (γ) increase, while the local Nusselt number increases as the Reynolds number and the suction/injection parameter (γ) increase. The results are compared with another published results and it found to be in excellent agreement.

A lattice Boltzmann simulation of enhanced heat transfer of nanofluids

Due to its distinctive characteristics nanofluid has drawn much attention from academic communities since the last decade. Compared with conventional fluids, nanofluid has higher thermal conductivity and surface to volume ratio, which enables it to be an effective working fluid in terms of heat transfer enhancement. Recent experimental works have shown that with low nanoparticle concentrations (1–5vol.%), the effective thermal conductivity of the suspensions can increase by more than 20% for various mixtures. Although many outstanding experimental works have been carried out, the fundamental understanding of nanofluid characteristics and performance is still not sufficient. Much more theoretical and numerical studies are required. Over the past two decades, the lattice Boltzmann method (LBM) has experienced a rapid development and well accepted as a useful method to simulate various fluid behaviours. In the present study, the LBM is employed to investigate the characteristics of nanofluid flow and heat transfer. By coupling the density and temperature distribution functions, the hydrodynamics and thermal features of nanofluids are properly simulated. The effects of the parameters including Rayleigh number and volume fraction of nanoparticles on hydrodynamic and thermal performances are investigated. The results show that both Rayleigh number and solid volume fraction of nanoparticles have influences on heat transfer enhancement of nanofluids; and there is a critical value of Rayleigh number on the performance of heat transfer enhancement.

An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid

A study of natural convective flow, heat transfer and entropy generation in an odd-shaped geometry is presented here. The geometry considered is a combination of the horizontal and vertical enclosure shapes. The cavity is filled with Cu–water nanofluid. The numerical study focuses specifically on the effect of natural convection parameter and solid volume fraction of nanoparticle on the average Nusselt number, total entropy generation and Bejan number. Also isotherms, stream function and entropy generation due to heat transfer are presented for various Rayleigh number and solid volume fraction. The governing equations are solved by using penalty finite element method with Galerkins weighted residual technique. The results reveal that increasing Rayleigh number causes increase of the average Nusselt number as well as the heat transfer term of entropy generation and decrease of the viscous term. The proper choice of Rayleigh number could be able to maximize heat transfer rate simultaneously minimizing entropy generation.

Heat transfer and entropy generation through nanofluid filled direct absorption solar collector

Sustainable energy generation is one of the most important challenges facing society today. Solar energy is one of the best sources of renewable energy with minimal environmental impact which offers a solution. The present work investigates the heat transfer performance and entropy generation of forced convection through a direct absorption solar collector. The working fluid is Cu–water nanofluid. The simulations focus specifically on the effect of solid volume fraction of nanoparticle and Reynolds number on the mean Nusselt number, mean entropy generation, Bejan number and collector efficiency. Also Isotherms and heatfunction are presented for various solid volume fraction and inertia force. The governing partial differential equations are solved using penalty finite element method with Galerkins weighted residual technique. The results show that both the mean Nusselt number and entropy generation increase as the volume fraction of Cu nanoparticles and Reynolds number increase. The results presented in this study provide a useful source of reference for enhancing the forced convection heat transfer performance while simultaneously reducing the entropy generation.

Stagnation-point Flow and Heat Transfer of a Nanofluid Adjacent to Linearly Stretching/Shrinking Sheet: A Numerical Study

In this study, the steady stagnation point flow and heat transfer of three different types of nanofluid over a linearly shrinking/stretching sheet is investigated numerically. A similarity transformation 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 effects of the governing parameters on the nanofluid flow and heat transfer characteristics are analyzed and discussed. Numerical results for the local Nusselt number, skin friction coefficient, velocity profiles and temperature profiles are presented for different values of the solid volume fraction (&phi) and for three different types of nanoparticles (Cu, Al₂O₃ and TiO₂) in stretching or shrinking cases. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for Cu-water nanofluid compared to the Al₂O₃-water and TiO₂-water nanofluids. Furthermore, it was seen that the effect of the solid volume fraction of nanoparticles on the heat transfer and fluid flow characteristics is more important compared to the type of the nanoparticles.

ANALYSIS OF LAMINAR MIXED CONVECTION IN AN INCLINED SQUARE LID-DRIVEN CAVITY WITH A NANOFLUID BY USING AN ARTIFICIAL NEURAL NETWORK

This study has focused on laminar mixed convection in an inclined square ventilated lid-driven cavity filled with a copper−water nanofluid. The governing equations in the two-dimensional space are discretized by using the finite volume method with the SIMPLER algorithm. The effects of independent parameters, including the Richardson number, Reynolds number, inclination angle, and the solid volume fraction of nanoparticles, on the streamlines, isotherm lines, and the average Nusselt number along the heat source have been studied. It is found that both the inclination angle and solid volume fraction, especially the second one, have remarkable effects on the fluid flow and heat transfer characteristics in the cavity. Artificial neural networks (ANN) used to extract a relation involve independent parameters for calculating the Nusselt number. The back propagation-learning algorithm with the tangent sigmoid transfer function is used to train the ANN. Finally, analytical relations for the nanofluid mixed convection in a lid-driven cavity are derived from the available ANN. It is found that the coefficient of multiple determinations (R2) between the real values and ANN results is equal to 0.9999, the maximum error being less than 0.5829 and the mean square error being equal to 5.37 × 10−5.

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.

Natural Convection Heat Transfer of Copper–Water Nanofluid in a Square Cavity With Time-Periodic Boundary Temperature

This paper presents a numerical study of natural convective heat transfer of copper–water nanofluid in a square enclosure where the temperature of the left vertical sidewall is sinusoidally oscillated with a constant average temperature, the right sidewall is cooled at a relatively low temperature, and the other walls are kept adiabatic. The influence of pertinent parameters such as Rayleigh number, solid volume fraction of copper nanoparticles, and dimensionless time period on the heat transfer characteristics is studied. The results show that the heat transfer rate increases using copper nanoparticles.

Heat transfer and entropy generation analysis of nanofluids flow in an open cavity

Mixed convection and entropy generation of nanofluids flow are numerically investigated in an open cavity heated from below with uniform temperature. Finite volume method was employed to solve the dimensionless governing equations of physical problems. The obtained results were presented by average Nusselt number, average entropy generation, Bejan number, streamlines and isotherms with various pertinent parameters, namely, Reynolds number (100⩽Re⩽500), Richardson number (0.05⩽Ri⩽1) and solid volume fraction of nanoparticles (0⩽φ⩽0.1), for three aspect ratios of the cavity (1, 1.5 and 2) and various types of nanoparticles (Cu, Al2O3, CuO and TiO2). It was found that the heat transfer and the entropy generation increase with the increase of Reynolds number, Richardson number and volume fraction of nanoparticles, and vary with the aspect ratio of the cavity and nanoparticle types. The choice of these parameters is important to obtain maximum enhancement of heat transfer with minimum entropy generation.

Effect of Nanofluid Variable Properties on Natural Convection in a Square Cavity Using Lattice Boltzmann Method

In this paper, laminar natural convective of a nanofluid in a square cavity is studied using Lattice Boltzmann Method (LBM). The main objective is to investigate the effects of variable thermal conductivity and dynamic viscosity models for Al2O3–water and TiO2–water nanofluids on flow and heat transfer in this geometry. Hydrodynamics and thermal fields are coupled using the Boussinesq approximation. The influence of pertinent parameters such as solid volume fraction of nanoparticles (0≤φ≤5%), Rayleigh number (Ra =103-106) and the type of nanoparticles on flow and heat transfer are investigated. Good agreement was observed between the present results and those of previous numerical simulation and experimental published work. It is found that fluid flow and temperature field are affected by addition of nanoparticles into water especially for higher Rayleigh numbers. It is indicated that average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models. A deterioration of the mean Nusselt number was also observed with increasing volume fraction of the nanoparticles for the whole range of Rayleigh number.

MIXED CONVECTION BOUNDARY LAYER FLOW ON A VERTICAL SURFACE IN A POROUS MEDIUM SATURATED BY A NANOFLUID WITH SUCTION OR INJECTION

An analysis of the steady mixed convection boundary layer flow past a vertical permeable surface embedded in a porous medium saturated by a nanofluid is performed in this study. Numerical solutions of the similarity equations are obtained using the shooting method. Three types of metallic or nonmetallic nanoparticles, namely Copper (Cu), Alumina (Al2O3) and Titania (TiO2) are considered by using a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter ψ of the nanofluid. The numerical results of the skin friction coefficient and the velocity profiles are presented and discussed. It is found that the imposition of suction is to increase the velocity profiles and to delay the separation of boundary layer, while the injection parameter decreases the velocity profiles. On the other hand, the range of solutions for the injection case is largest for Al2O3 nanoparticles and smallest for Cu nanoparticles.

Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate

We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w), Biot number (Bi), and slip parameter (β), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

Natural Convection of Water-Based Nanofluids in a Square Enclosure with Non-Uniform Heating of the Bottom Wall

In this paper, a numerical study of natural convection in a square enclosure with non-uniform temperature distribution maintained at the bottom wall and filled with nanofluids is carried out using different types of nanoparticles. The remaining walls of the enclosure are kept at a lower temperature. Calculations are performed for Rayleigh numbers in the range 5 × 103 ≤ Ra ≤ 106 and different solid volume fraction of nanoparticles 0 ≤ χ ≤ 0.2. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction for the whole range of Rayleigh numbers. It is also observed that the heat transfer enhancement strongly depends on the type of nanofluids. For Ra = 106, the pure water flow becomes unsteady. It is observed that the increase of the volume fraction of nanoparticles makes the flow return to steady state.

NUMERICAL SIMULATION OF NATURAL CONVECTION AROUND AN OBSTACLE PLACED IN AN ENCLOSURE FILLED WITH DIFFERENT TYPE OF NANOFLUID

The present numerical study deals with natural convection in an enclosure with a heated cylindrical block fi lled with nanofl uid. The governing equations have been discretized using the finite volume method, and the SIMPLE algorithm has been used to couple velocity and pressure fields. The eff ect of the Rayleigh number, type, solid volume fraction of nanoparticles, radius, and position of the hot body is studied, and obtained results are presented in the form of streamline and isotherm plots, a Nusselt diagram, and comparative tables. Water, Cu–water, and Al2O3–water have been utilized as working fl uids. In this study, the particle diameters of Cu and Al2O3 nanoparticles are 90 and 47 nm, respectively. On the basis of the results, increasing solid volume fraction and Ra number causes a noticeable enhancement in the rate of heat transfer. Also, increasing the radius of the hot circular cylinder, diff erences in values of Nusselt number between base fl uid and nanofl uid signifi cantly increase.

Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case

An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.