Solid Volume Fraction Of Nanofluid Research Articles

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

ABSTRACTClassical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.

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.

Unsteady MHD Mixed Convection inside L-shaped Enclosure in the Presence of Ferrofluid (Fe3O4)

Mixed convection has been one of the most interesting topics of research in the field of heat transfer for many years. In the present study, unsteady MHD mixed convection heat transfer inside a heated L-shaped enclosure filled with Fe3O4water has been investigated numerically. Lid-motion is introduced by the top wall to induce forced convection. For pure mixed convection (Ri = 1), Grashof number (Gr = 103 - 105) and time (τ) are varied, whereas the solid volume fraction of nanofluid (φ = 0.1) and Hartman number (Ha = 25) are kept constant. Results have been presented in terms of isotherm lines, streamlines, average Nusselt (Nu) number and average temperature (θay). The obtained results show that MHD causes significant effects on heat transfer rate. Interestingly, natural convection is more effective in this case of mixed convection as higher values of Nu are obtained for higher values of Gr.

Natural convection in T-shaped cavities filled with water-based suspensions of COOH-functionalized multi walled carbon nanotubes

In the present study, natural convection fluid flow and heat transfer inside a T-shaped cavity filled with water-based suspensions of COOH-functionalized multi walled carbon nanotube has been numerically investigated. The considered cavity is a T-shaped enclosure having six walls at high constant temperature (Th) and a horizontal top wall at low temperature (Tc) while the bottom wall is kept thermally insulated. To carry out the numerical simulations, the governing equations are discretized employing the finite volume method (FVM) while the SIMPLER algorithm is used to couple velocity and pressure fields to solve governing mass, momentum, and energy equations. The effects of solid volume fraction from 0.0% to 1.0%, the aspect ratio between 0.2 and 0.8 of the T-shaped cavity and Rayleigh number range of 103 and 105 on the fluid flow and heat transfer inside the cavity are examined in details. According to the predicted results, the average Nusselt number increases (to 124%) with increase in the solid volume fraction of nanofluid and Rayleigh number for different aspect ratios. Also, at low Rayleigh number, Ra=103 or 104, the conduction dominates the transport phenomenon in the T-shaped cavity. Therefore, the average Nusselt number decreases with an increase in aspect ratio.

Three dimensional simulation of natural convection and entropy generation in an air and MWCNT/water nanofluid filled cuboid as two immiscible fluids with emphasis on the nanofluid height ratio's effects

Abstract This paper reports a numerical study of the natural convection and entropy generation for a layered fluid system in a cuboid enclosure which is differentially heated from sides and filled by two immiscible gas/liquid fluids (air and MWCNTs-water nanofluid). This study emphasize on the effects of the liquid interface aspect ratio, solid volume fraction of nanofluid, and Rayleigh number on the fluid flow, heat transfer and entropy generation. The fluid flow streamlines, contours of local fluid friction irreversibility, temperature, and local heat transfer irreversibility in the 3D enclosure are obtained. The local and averaged Nusselt number and volumetric entropy generation are also discussed. The results show that the nanofluid interface aspect ratio has significant influences on the fluid flow, heat transfer performance and entropy generation. Moreover, it is shown that the total entropy generation and mean Nusselt number are reduced by increasing of nanofluid interface aspect ratio and are enhanced by increasing of Rayleigh number.

Combined effect of Reynolds and Grashof numbers on mixed convection in a lid-driven T-shaped cavity filled with water-Al2O3 nanofluid

Lid-driven mixed convection has been given immense importance due to its wide range of applications. A T-shaped cavity is introduced and pertinent parameters controlling mixed convection phenomenon are analyzed in this paper. Water-Al2O3 nanofluid is considered inside the cavity to augment heat transfer rate. Galerkin weighted residual method of finite element analysis is applied for the numerical simulations. Numerical solution is obtained for different solid volume fractions of nanofluid, (ϕ = 0-0.15), Grashof numbers (Gr = 0.1-5000) and Reynolds numbers (Re = 0.31-1000) in laminar flow regime. Special attention is given on the analysis of flow at the pure mixed convection regime. It is found that Grashof, Reynolds and Richardson numbers along with solid volume fraction of nanofluid have significant effect on heat transfer characteristics inside the cavity. Results are presented using streamline and isotherm contours along with related variation of average Nusselt numbers of the heated wall and average fluid temperature inside the cavity.

Unsteady MHD boundary-layer flow and heat transfer of nanofluid over a permeable shrinking sheet in the presence of thermal radiation

Forced convection in unsteady boundary layer flow of nanofluid over a permeable shrinking sheet in the presence of thermal radiation is studied. A variable magnetic field is applied normal to the sheet. The nanofluid model includes Brownian motion and thermophoresis effects. The governing momentum, energy and nanofluid solid volume fraction equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effects of various physical parameters on dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and local Sherwood numbers are analyzed. The numerical results indicate that dual solutions exist for certain values of the magnetic parameter (M), wall mass suction (s) and unsteadiness parameter (A). It is found that both magnetic field and wall mass suction widen the range of unsteadiness parameter for which the solution exists. The skin friction coefficient, local Nusselt and Sherwood numbers increase for the first solution and decrease for the second solution with the increase in M.

NUMERICAL SIMULATION OF MARANGONI MAGNETOHYDRODYNAMIC BIO-NANOFLUID CONVECTION FROM A NON-ISOTHERMAL SURFACE WITH MAGNETIC INDUCTION EFFECTS: A BIO-NANOMATERIAL MANUFACTURING TRANSPORT MODEL

Laminar magnetohydrodynamic Marangoni-forced convection boundary layer flow of a water-based biopolymer nanofluid containing nanoparticles from a non-isothermal plate is studied. Magnetic induction effects are incorporated. A variety of nanoparticles are studied, specifically, silver, copper, aluminium oxide and titanium oxide. The Tiwari–Das model is utilized for simulating nanofluid effects. The normalized ordinary differential boundary layer equations (mass, magnetic field continuity, momentum, induced magnetic field and energy conservation) are solved subject to appropriate boundary conditions using Maple shooting quadrature. The influence of Prandtl number (Pr), magnetohydrodynamic body force parameter (β), reciprocal of magnetic Prandtl number (α) and nanofluid solid volume fraction (φ) on velocity, temperature and magnetic stream function distributions is investigated in the presence of strong Marangoni effects (ξ i.e., Marangoni parameter is set as unity). Magnetic stream function is accentuated with body force parameter. The flow is considerably decelerated as is magnetic stream function gradient, with increasing nanofluid solid volume fraction, whereas temperatures are significantly enhanced. Interesting features in the flow regime are explored. The study finds applications in the fabrication of complex biomedical nanofluids, biopolymers, etc.

Forced convection boundary layer MHD flow of nanofluid over a permeable stretching plate with viscous dissipation

Forced convection boundary layer magneto-hydrodynamic (MHD) flow of a nanofluid over a permeable stretching plate is studied in this paper. The effects of suction-injection and viscous dissi1pation are taken into account. The nanofluid model includes Brownian motion and thermophoresis effects. The governing momentum, energy and nanofluid solid volume fraction equations are solved numerically using an implicit finite difference scheme known as Keller-box method and the results are compared with available numerical data. The results for the dimensionless velocity, dimensionless temperature, dimensionless nanofluid solid volume fraction, reduced Nusselt and reduced Sherwood numbers are presented illustrating the effects of magnetic parameter, suction-injection parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, Eckert number and Lewis number.

Buoyancy driven flow and heat transfer of nanofluids past a square cylinder in vertically upward flow

The present work simulates the buoyancy driven mixed convective flow and heat transfer characteristics of water-based nanofluid past a square cylinder in vertically upward flow using a SUPG (Streamline Upwind Petrov–Galerkin) based finite element method. Nano sized copper (Cu) and alumina (Al2O3) particles suspended in water are used with Prandtl number (Pr)=6.9. The range of nanoparticle volume fractions (ϕ) considered is 0⩽ϕ⩽20%. Computations are carried out at a representative Reynolds number (Re) of 100. Effect of aiding and opposing buoyancy is brought about by considering the Richardson number (Ri) range −0.5⩽Ri⩽0.5. Al2O3–water and Cu–water nanofluids show suppression of vortex shedding at Ri⩾0.15. Vortex shedding process is initiated and a completely new phenomenon is discovered when the nanofluid solid volume fraction,ϕ, is increased. For Al2O3–water nanofluids, at Ri=0.15, completely periodic vortex shedding is found for ϕ⩾10%. For Cu–water nanofluid, shedding is observed for both Ri=0.15 and Ri=0.5. At Ri=0.15 shedding is found at ϕ⩾5%, whereas at Ri=0.5 it is at ϕ⩾15%. A new expression for convective instability of nanofluids is derived to calculate critical nanofluid solid volume fraction. The local Nusselt number increases with increasing ϕ. At a fixed ϕ, the time averaged local Nusselt number is higher for Cu–water nanofluids, as compared to Al2O3–water nanofluids. The average Nusselt number (Nuavg) increases with the concentration of ϕ. Cu–water based nanofluids show higher magnitudes of Nuavg compared to Al2O3–water nanofluids.

Numerical Simulation of Mixed Convection Flows in a Square Double Lid-Driven Cavity Partially Heated Using Nanofluid

A numerical study has been done through an Al2O3–water in a double lid-driven square cavity with various inclination angles and discrete heat sources. The top and right moving walls are at low temperature. Half of the left and bottom walls are insulated and the temperatures of the other half are kept at high. A large number of simulations for a wide range of Richardson number of 0.1 to 10, Reynolds number from 1 to 100, inclination angle of cavity from -90 o to 90 o and solid volume fraction between 0 and 0.06 are performed. The results are presented in the form of streamline, isotherm and Nusselt number plots. The influence of solid volume fraction of nanofluids and angle of inclination on hydrodynamic and thermal characteristics have been analyzed and discussed. As a result, it was found that the heat transfer increases with increase in solid volume fraction for a constant Reynolds number, heat transfer also increases with increase in Richardson and Reynolds for a particular volume fraction.

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.

Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model

Mixed convection of a nanofluid consisting of water and SiO2 in an inclined enclosure cavity has been studied numerically. The left and right walls are maintained at different constant temperatures while upper and bottom insulated walls are moving lids. Two-phase mixture model has been used to investigate the thermal behaviors of the nanofluid for various inclination angles of enclosure ranging from θ = − 60° to θ = 60°, volume fraction from 0% to 8 %, Richardson numbers varying from 0.01 to 100 and constant Grashof number 10 4. The governing equations are solved numerically using the finite-volume approach. Results are presented in the form of streamlines, isotherms, distribution of nanoparticles and average Nusselt number. In addition, effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated. The results reveal that addition of nanoparticles enhances heat transfer in the cavity remarkably and causes significant changes in the flow pattern. Besides, effect of inclination angle is more pronounced at higher Richardson numbers.

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper–water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective–conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10 5 ≤ Ra ≤ 10 8, and for the solid volume fraction at 0 ≤ ϕ ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.

Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid

In this paper, mixed convection flow and temperature fields in a vented square cavity subjected to an external copper–water nanofluid are studied numerically. The natural convection effect is attained by heating from the constant flux heat source on the bottom wall and cooling from the injected flow. In order to investigate the effect of inlet and outlet location, four different placement configurations of the inlet and outlet ports are considered. In each of them, both the inlet and outlet ports are alternatively located either on the top or the bottom of the sides and external flow enters in to the cavity through an inlet opening in the left vertical wall and exits from another opening in the opposite wall. The remaining boundaries are considered adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range of 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ϕ ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.

Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid

Abstract A numerical investigation of mixed convection flows through a copper–water nanofluid in a square cavity with inlet and outlet ports has been executed. The natural convection effect is attained by heating from the constant flux heat source which is symmetrical located at the bottom wall and cooling from the injected flow. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ϕ ≤ 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. Results are presented in the form of streamlines, isotherms, average Nusselt number and average bulk temperature. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The results indicate that increase in solid concentration leads to increase in the average Nusselt number at the heat source surface and decrease in the average bulk temperature.

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10 4 to 10 6, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.