Three dimensional lattice Boltzmann simulation for mixed convection of nanofluids in the presence of magnetic field

In the present study, a three dimensional thermal lattice Boltzmann model was developed to investigate the flow dynamics and mixed convection heat transfer of Al₂O₃/water nanofluid in a cubic cavity in the presence of magnetic field. The model was first validated with previous numerical and experimental results. Satisfactory agreement was obtained. Then the effects of Rayleigh number, nanoparticle volume fraction, Hartmann number and Richardson number on nanofluid flow dynamics and heat transfer were examined. Numerical results indicate that adding nanoparticles to pure water leads to heat transfer enhancement for low Rayleigh numbers. However, this enhancement might be weakened and even reversed for high Rayleigh numbers. In addition, the results show the external applied magnetic field has an effect of suppressing the convective heat transfer in the cavity. Moreover, the results demonstrate that the Richardson number in mixed convection has significant influences on both streamlines and temperature field.     

Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall

ABSTRACT

Natural convection heat transfer of a nanofluid in the presence of an electric field is investigated. The control volume finite element method (CVFEM) is utilized to simulate this problem. A Fe₃O₄–ethylene glycol nanofluid is used as the working fluid. The effect of the electric field on nanofluid viscosity is taken into account. Numerical investigation is conducted for several values of Rayleigh number, nanoparticle volume fraction, and the voltage supplied. The numerical results show that the voltage used can change the flow shape. The Coulomb force causes the isotherms to become denser near the bottom wall. Heat transfer rises with increase in the voltage supplied and Rayleigh number. The effect of electric field on heat transfer is more pronounced at low Rayleigh numbers due to the predomination of the conduction mechanism.     

Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field

In this study natural convection heat transfer of Cu–water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of horizontal magnetic field is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Hartmann number, Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results indicate that in the absence of magnetic field, enhancement ratio decreases as Rayleigh number increases while an opposite trend is observed in the presence of magnetic field. Also it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction, the number of undulations and Rayleigh numbers while it is a decreasing function of Hartmann number.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

Three-dimensional tilted hydromagnetic natural double-diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

In this article, we use magnetic nanoparticles to explore the three-dimensional natural upward force flow within a quadrangular cuboid under the influence of a sloping magnetic flux. We consider three forms of thermic conditions on the bottom surface of the cavity, such as uniform surface temperature, constant heat flux, and temperature varied parabolically in space. The Galerkin-type finite element method is used to solve the unitless leading equations of implicit physical systems. Ferrite-water nanofluid is the default, used to study the flow field, thermal field, and concentration field other than the regular Nusselt number. We examined the influence of many model parameters, especially the thermal Rayleigh number, volumetric nanoparticles fraction, the Hartmann number, nanoparticles formation, and the predisposition of magnetic flux. The influence of the position of the thermal flux on the lower surface of the thermal field cavity is also studied. The heat transfer rate of various magnetic nanofluids is compared. Our simulated data echoed nicely with the available experimental one. The results show that Mn-Zn ferrite-kerosene nanofluid exhibits advanced heat transportation more than the other nanofluids studied. For lower dimensions of aspect ratio and nanoparticle diameter, higher heat transfer is obtained. Compared with other boundary conditions studied, the uniform temperature on the bottom surface of the cuboid provides a higher heat transfer rate.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

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 (1–5 vol.%), 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.     

Natural convection of water-CuO nanofluid in a cavity with two pairs of heat source-sink

Natural convection in a two-dimensional square cavity filled with a water-CuO nanofluid is numerically studied. Two pairs of heat source-sink are considered to cover the entire length of the bottom wall of the cavity while the other walls are thermally insulated. The nanofluid is assumed to be homogenous and Newtonian. The governing differential equations are discretised by the control volume approach and the coupling between velocity and pressure is solved using the SIMPLE algorithm. A comparison study is presented between two cases with different arrangements of the two pairs on the bottom wall. The effects of Rayleigh number and solid volume fraction of the nanofluid on the heat transfer rate have also been examined. The results show that regardless of the position of the pairs of source-sink, the heat transfer rate increases with an increase of the Rayleigh number and the solid volume fraction.     

Field-Synergy and Figure-of-Merit Analysis of Two Oxide–Water-Based Nanofluids' Flow in Heated Tubes

Field-synergy analysis is performed on the water–oxide nanofluid flow in circular heat sinks to examine the synergetic relation between the flow and temperature fields for heating processes. By varying the Reynolds number and the nanoparticle volume fraction, the convective heat transfer of nanofluid is investigated based on the field synergy number. For heating, the degree of synergy between the velocity and temperature fields of nanofluid flow deteriorates with the Reynolds number increase, leading to a decreased heat transfer performance of the nanofluid. By increasing the particle volume fraction, the degree of synergy between the velocity and temperature fields of the nanofluid flow can be intensified, thus going to convection heat transfer enhancement. After generating results, one can notice that the heat transfer enhancement is strongly dependent on nanoparticle type, Reynolds number, and volume fraction. The results are similar, even if the thermal conductivity of the two considered oxide nanoparticles are quite different. Additionally, a convenient figure of merit that is known as the Mouromtseff number was used as base of comparison, and the results indicated that the considered nanofluids can successfully replace water in specific applications for single-phase forced convection flow in a tube.     

Impact of volume fraction and fluid layer thickness on heat transfer effectiveness of water-based nanofluids

The heat transfer effectiveness of nanofluids is adversely affected by the delay in convection onset. The lesser effectiveness, when compared to that of base fluid, is observed in a range of nanofluid layer thickness. The heat transfer coefficient of water–Al₂O₃ nanofluid can be enhanced by sustaining the equilibrium between Rayleigh number, temperature, particle volume fraction, and enclosure aspect ratio. In this paper, the specific correlation of fluid layer thickness and the onset of convection, which can significantly dominate the heat transfer characteristics of nanofluids are investigated using the concept of critical Rayleigh number. The water layer thickness for convection onset is first experimentally assessed for different real-life heat flux densities. It is then performed for Al₂O₃–water nanofluid for varying volume fractions. With the increase in volume fraction even though thermal conductivity increases, the overall heat transfer enhancement of the nanofluid is reduced. Temperature involved (heat flux density), the volume fraction of the nanofluid used, nanofluid layer thickness (space availability for the cooling system), and mass of the nanoparticle influence heat transfer enhancement. A higher volume fraction may not always result in enhancement of heat transfer as far as nanofluids are concerned.     

Natural convection of nanofluids in enclosures with low aspect ratios

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO-water nanofluid heated from one side and cooled from the ceiling. The transport equations for the flow are solved numerically by the finite volume element method using the SIMPLER algorithm Based on numerical predictions. The effects of Rayleigh number and aspect ratio on flow pattern and energy transport are investigated for Rayleigh numbers ranging from 10⁴ to 10⁷ volume fraction of solid varied to 0%–4% and for five different aspect ratios of 0.08, 0.1, 0.125, 0.25 and 0.5. It is found that the effect of Rayleigh number on heat transfer is less significant when the enclosure is shallow (AR = 0.5) and the influence of aspect ratio is stronger when the enclosure is tall and the Rayleigh number is high.     

Natural convection heat transfer in horizontal concentric annulus between outer cylinder and inner flat tube using nanofluid

Natural convection heat transfer in two-dimensional region formed by constant heat flux horizontal flat tube concentrically located in cooled horizontal cylinder was studied numerically by using nanofluid. The model solved using the FLUENT CFD package. The numerical simulations covered a range of hydraulic radius ratio (5, 7.5, and 10) at orientation angles from 0° up to 90°.The results showed that the average Nusselt number increases with hydraulic radius ratio, orientation angles and Rayleigh number, as well as enhancement ratio for Nusselt number at orientation angle 90° and hydraulic radius ratio 7.5 is equal to 24.87%. Both the nanofluid flow and heat transfer characteristics for different cases are illustrated that obtained from the CFD code. The results for the average Nusselt numbers are compared with previous works and show good agreement.     

Natural convection heat transfer in a nanofluid filled semi-annulus enclosure

To investigate natural convection heat transfer in a semi-annulus enclosure filled with nanofluid, the Control Volume based Finite Element Method (CVFEM) is used. The fluid in the enclosure is Cu–water nanofluid. The inner and outer semi circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern and isotherms. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and the angle of turn for the enclosure. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The results reveal that there is an optimum angle of turn in which the average Nusselt number is maximum for each Rayleigh number. Moreover, the angle of turn has an important effect on the streamlines, isotherms and maximum or minimum values of local Nusselt number.     

Prandtl number effect on cooling performance of a heated cylinder in an enclosure filled with nanofluid

Natural convection heat transfer from a heated cylinder contained in a square enclosure filled with water–Cu nanofluid is investigated numerically. The main objective of this study is to explore the influence of pertinent parameters such as Prandtl number (Pr) and diameter (D) of the heated body on the flow and heat transfer performance of nanofluids while Rayleigh number (Ra) and the solid particle volume fraction (?) of nanoparticle are considered fixed. The results obtained from finite element method clearly indicate that heat transfer augmentation is possible using highly viscous nanofluid resulting in the compactness of many industrial devices.     

Brownian motion of nanoparticles in a triangular enclosure with natural convection

This paper presents the results of a numerical study on the natural convection in a right triangular enclosure, with a heat source on its vertical wall and filled with a water–CuO nanofluid. The effects of parameters such as Rayleigh number, solid volume fraction, heat source location, enclosure aspect ratio and Brownian motion on the flow and temperature fields as well as the heat transfer rate, are examined. The results show that when Brownian motion is considered in the analysis, the solid volume fraction, the heat source location and the enclosure aspect ratio affect the heat transfer performance differently at low and high Rayleigh numbers. At high Rayleigh numbers, an optimum value for the solid volume fraction is found which results in the maximum heat transfer rate. This is in contradiction to the results of the analysis in which Brownian motion is neglected.     

Combined Effect of Magnetic Field and Nanofluid Variable Properties on Heat Transfer Enhancement in Natural Convection

The current work investigated, numerically, enhancement of heat transfer in natural convection using CuO-water nanofluid in the presence of a magnetic field. The governing equations were discretized using the control volume method and solved numerically via the SIMPLE algorithm. For the case of absence of a magnetic field and for low Rayleigh number, the heat transfer was almost insensitive to the presence of nanoparticles. For moderate and high Rayleigh numbers, the presence of nanoparticles had an adverse effect on heat transfer at high volume fraction of nanoparticles. The highest reduction in heat transfer was registered for the case of Ra = 10⁵. Contour maps are generated for the normalized Nusselt number (Nu*) to determine the optimum selection of volume fraction of nanoparticles and magnetic field that gives maximum heat transfer enhancement. The results demonstrated the effectiveness and practicality of using high values of magnetic field in enhancing heat transfer using nanofluids.     

The Effect of Alumina–Water Nanofluid on Natural Convection Heat Transfer Inside Vertical Circular Enclosures Heated from Above

Experimental investigation on natural convection heat transfer is carried out inside vertical circular enclosures filled with Al₂O₃–water nanofluid with different concentrations; 0.0%, 0.85% (0.21%), 1.98 (0.51%), and 2.95% (0.75%) by mass (volume). Two enclosures are used with 0.20 m inside diameter and with two different aspect ratios. The top surface of the enclosure is heated using a constant-heat-flux flexible foil heater while the bottom surface is subject to cooling using an ambient air stream. Various heat fluxes are used to generate heat transfer through the nanofluid. The average Nusselt number is obtained for each enclosure and correlated with the modified Rayleigh number using the concentration ratio as a parameter. A general correlation for the average Nusselt number with the modified Rayleigh number is obtained using the volume fraction and the aspect ratio as parameters to cover both enclosures. The results show that the Nusselt number for the alumina–water nanofluid is less than that of the base fluid. This means that using the alumina–water nanofluids adversely affects the heat transfer coefficient compared to using pure water. It is also found that the degree of deterioration depends on the concentration ratio as well as the aspect ratio of the enclosure.     

Hydromagnetic natural cooling of a triangular heat source in a triangular cavity with water–CuO nanofluid

This paper presents a numerical analysis of natural cooling of a right triangular heat source by a water–CuO nanofluid in a right triangular cavity that is under the influence of a horizontal magnetic field. A computational domain is defined and a numerical scheme based on the control volume formulation using the SIMPLE algorithm is developed. The convection–diffusion terms are discretised using a power-law scheme. The effects of the Rayleigh number, the solid volume fraction, the Hartmann number and the heat source position in the cavity on the heat transfer performance of the cavity are examined. The thermal performance of the cavity is enhanced as the Rayleigh number increases, the Hartmann number decreases and the distance of the heat source with the cold walls decreases. An optimum solid volume fraction is found that maximises the heat transfer at high Rayleigh numbers.     

Heat transfer enhancement for combined convection flow of nanofluids in a vertical rectangular duct considering radiation effects

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 10⁶ ≤ Ra ≤ 2 × 10⁷ and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO₂ with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO₂ nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20354     

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 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 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.