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.     

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.     

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.     

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.     

Natural Convection Heat Transfer in an Enclosure Filled with an Ethylene Glycol—Copper Nanofluid Under Magnetic Fields

This article presents the results of a numerical study on natural convection in a square enclosure filled with ethylene glycol–copper nanofluid in the presence of magnetic fields. Two opposite horizontal walls of the enclosure are insulated and the two vertical walls are kept constant at different temperatures. A uniform horizontal magnetic field is externally imposed. The governing equations (mass, momentum, and energy) are formulated and solved numerically with a finite element using COMSOL Multiphysics. The effects of pertinent parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁷), Hartmann number (0 ≤ Ha ≤ 120), and solid volume fraction (0 ≤ φ ≤ 0.06) on the flow and the heat transfer performance of the enclosure are examined when the Prandtl number is assumed to be Pr = 151.     

Effect of nanofluid variable properties on natural convection in enclosures

In this work, the heat transfer enhancement in a differentially heated enclosure using variable thermal conductivity and variable viscosity of Al₂O₃–water and CuO–water nanofluids is investigated. The results are presented over a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 9%), and aspect ratios (½ ≤ A ≤ 2). For an enclosure with unity aspect ratio, the average Nusselt number of a Al₂O₃–water nanofluid at high Rayleigh numbers was reduced by increasing the volume fraction of nanoparticles above 5%. However, at low Rayleigh numbers, the average Nusselt number was slightly enhanced by increasing the volume fraction of nanoparticles. At high Rayleigh numbers, CuO–water nanofluids manifest a continuous decrease in Nusselt number as the volume fraction of nanoparticles is increased. However, the Nusselt number was not sensitive to the volume fraction at low Rayleigh numbers. The Nusselt number demonstrates to be sensitive to the aspect ratio. It was observed that enclosures, having high aspect ratios, experience more deterioration in the average Nusselt number when compared to enclosures having low aspect ratios. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett model and the Brinkman model. It was found that at high Rayleigh numbers the average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models.     

Natural Convection of Al2O3 Nanofluid Between Two Horizontal Cylinders Inside a Circular Enclosure

Natural convection heat transfer within horizontal annuli has many engineering applications such as heat exchangers like fire tube heaters. In this paper numerical methods were used for the computational analysis of heat transfer from the fire tube/hot tube to the gas tube/cold tube inside the water medium using alumina nanoparticles. Because of eccentricities of both hot and cold cylinders and different diameters, the geometry is asymmetric. The mathematical model is based on two-dimensional continuity, momentum, energy, and volume fraction equations, which are solved numerically. The simulation was done for different values of particle loading, 1%, 2%, and 5%, at Rayleigh numbers 10³, 10⁴, and 10⁵. The results show that nanoparticles enhance the heat transfer by increasing the volume concentrations of particles. It was observed that the maximum and minimum augmentation of the average Nusselt number are about 30% and 14% at the Ra = 10³ and Ra = 10⁵, respectively. Although the average Nusselt number rises by increasing the Rayleigh number, the ratio of heat transfer using nanofluid to that by pure fluid decreases. Using 5% volume fraction of alumina nanoparticles at Rayleigh number of 10³ increases the heat transfer to cold tube by about 23% compared to the pure water. The effect of nanolayer formation around particles was considered in a thermal conductivity model, which shows approximately 5% increase in the Nusselt number. To verify the solution results, comparisons with previously published work on the basis of special cases are performed.     

Simulation of heat transfer enhancement in nanofluids using dissipative particle dynamics

The current paper applied dissipative particle dynamics (DPD) approach to investigate heat transfer within nanofluids. The DPD approach was applied to study natural convection in a differential heated enclosure by considering the viscosity and the thermal conductivity of the nanofluid to be dual function of temperature and volume fraction of nanoparticles. Experimental data for viscosity and thermal conductivity are incorporated in the current DPD model to mimic energy transport within nanofluids. This incorporation is done through the modification of the dissipative weighting function that appears in the dissipative force vector and the dissipative heat flux. For the entire range of Rayleigh number considered in this study, it was found that the DPD results show a deterioration in heat transfer in the enclosure due to the presence of nanoparticles for φ > 4%. However, some slight enhancement is shown to take place for small volume fraction of nanoparticles, φ ≤ 4%. The DPD results experienced some degree of compressibility at high values of Rayleigh number Ra ≥ 10⁵.     

Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus

A numerical investigation on natural convective heat transfer of nanofluid (Al₂O₃+water) inside a partially heated vertical annulus of high aspect ratio (352) has been carried out. The computational fluid dynamics solver Ansys Fluent is used for simulation and results are presented for various volume fraction of nanoparticles (0‐0.04) at different heat flux values (3‐12 kW/m²). Two well‐known correlations for evaluating thermal conductivity and viscosity have been used. Thus different combinations of the available correlations have been set to form four models (I, II, III, and IV). Therefore, a detailed analysis has been executed to identify effects of thermophysical properties on heat transfer and fluid flow of nanofluids using different models. The results show enhancement in heat transfer coefficient with volume fraction of nanoparticles. Highest enhancement achieved is found to be 14.17% based on model III, while the minimum is around 7.27% based on model II. Dispersion of nanoparticles in base fluid declines the Nusselt number and Reynolds number with different rates depending on various models. A generalized correlation is proposed for Nusselt number of nanofluids in the annulus in terms of volume fraction of nanoparticles, Rayleigh number, Reynolds number, and Prandtl number.     

Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids

Heat transfer enhancement in horizontal annuli using nanofluids is investigated. Water-based nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂ nanoparticles is used. The addition of the different types and different volume fractions of nanoparticles were found to have adverse effects on heat transfer characteristics. For high values of Rayleigh number and high L/D ratio, nanoparticles with high thermal conductivity cause significant enhancement of heat transfer characteristics. On the other hand, for intermediate values of Rayleigh number, nanoparticles with low thermal conductivity cause a reduction in heat transfer. For Ra = 10³ and Ra = 10⁵ the addition of Al₂O₃ nanoparticles improves heat transfer. However, for Ra = 10⁴, the addition of nanoparticles has a very minor effect on heat transfer characteristics.     

Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid

In this study, natural convection in a concentric annulus between a cold outer square and heated inner circular cylinders in presence of static radial magnetic field is investigated numerically using the lattice Boltzmann method. The inner and outer cylinders are maintained at constant uniform temperatures and it is assumed that all walls are insulating the magnetic field. The numerical investigation is carried out for different governing parameters namely; the Hartmann number, nanoparticles volume fraction and Rayleigh number. The effective thermal conductivity and viscosity of nanofluids are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Also, the multi-distribution-function (MDF) model is used for simulating the effect of uniform magnetic field. The results reveal that the average Nusselt number is an increasing function of nanoparticle volume fraction as well as the Rayleigh number, while it is a decreasing function of the Hartmann number.     

Natural convection in a cavity with undulated walls filled with water-based non-Newtonian power-law CuO–water nanofluid under the influence of the external magnetic field

Natural convection heat transfer in a square cavity (with wavy or plane wall) filled with non-Newtonian power-law nanofluid has been elucidated for several input parameters like Ra spanning from 10⁵ to 10⁶, power-law index (n) from 0.6 to 1.4, and volume fraction of CuO nanoparticles (?) from to 0 to 0.12. Effect of external magnetic field on heat transfer has been illustrated by varying the Ha from 0 to 90. In the present study, our main objective is to explore the effect of nanoparticles on heat transfer enhancement in non-Newtonian power-law fluid. It is found that the addition of nanoparticles (?) to shear thinning fluid enhances the heat transfer approximately 15% when ? increases from 0 to 0.12 for Ha less than 60 at all Ra. For a shear thickening fluid, the same thing happens for all Ha at any Ra. The average surface Nusselt number for a cavity with wavy wall is less than that of a plane wall for all cases which is not true for the case of local Nusselt number.     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity

Transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity is investigated numerically. The effective thermal conductivity and dynamic viscosity of nanofluids are predicted by using the proposed models that take the contribution of Brownian motion of nanoparticles into account. Three different Rayleigh numbers and five different volume fractions of nanoparticles are considered. The development of natural convection is presented through the evolutions of the average Nusselt number along the cold side wall. The predicted flow development times and time-averaged Nusselt numbers are scaled with Rayleigh number. In addition, the time-averaged Nusselt numbers are presented in terms of volume fraction of nanoparticles. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is lowered with increasing volume fraction of nanoparticles.     

Convective heat transfer of ferrofluid in a lid-driven cavity with a heat-conducting solid backward step under the effect of a variable magnetic field

The effect of variable magnetic field on the mixed convective flow of a ferrofluid within a lid-driven cavity has been analyzed numerically. A heat-conducting solid block is located in the bottom part of the cavity. Governing partial differential equations have been formulated taking into account that the magnetic source is a point source located over the moving lid. Analysis has been performed for a wide range of Hartmann number, nanoparticles volume fraction, and magnetic number. It has been found that the growth of the magnetic number leads to the heat transfer enhancement.     

Thermal Enhancement of Triangular Ducts Using Compound of Vortex Generators and Nanofluids

Laminar flow and heat transfer of three different types of nanofluids; Al₂O₃, CuO, and SiO₂ suspended in ethylene glycol, in a triangular duct using delta-winglet pair of vortex generator are numerically simulated in three dimensions. The governing equations of mass, momentum and energy are solved using the finite volume method. The effects of types, concentrations, and diameter of solid nanoparticles and Reynolds number on thermal and hydraulic performance of triangular duct are examined. The range of Reynolds number, volume fraction and nanoparticles diameters is 100–1200, 1–4%, and 25–85 nm, respectively. The results indicate that the average Nusselt number increases with the particles volume fraction and Reynolds number associated with an increase in the pressure drop. The heat transfer enhancement and pressure drop penalty reduce with increasing the particles diameters. However, a reduction in the pumping power required is observed to force the nanofluids when the volume fraction increases, assuming the heat transfer coefficient remains constant.     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Numerical simulation of turbulent natural convection of nanofluid with thermal radiation inside a tall enclosure under the influence of magnetohydrodynamic

In the present study, the natural convective heat transfer in the turbulent flow of water/CuO nanofluid with volumetric radiation and magnetic field inside a tall enclosure has been numerically investigated. The thermophysical properties of nanofluid have been considered variable with temperature and the effects of Brownian motion of nanoparticles have been considered. The main objective of this work is an investigation of the effect of using water/CuO nanofluid and presence of magnetic field on turbulent natural convection in three types of enclosures (vertical, inclined, and horizontal) by considering the volumetric radiation. The governing equations on turbulent flow domain under the influence of the magnetic field and by considering the combination of volumetric radiation and natural convection have been solved by a coupled algorithm. For validating the present research, a comparison has been carried out with the laminar natural convection flow under the influence of the magnetic field and radiation effects and also, the natural turbulent convection flow of previous studies and a proper coincidence has been achieved. The results indicated that by increasing volume fraction and Hartmann number the average Nusselt number enhances and reduces, respectively. By adding 1% CuO nanoparticles to the base fluid, heat transfer improves from 10.59% to 17.05%. However, by increasing the volume fraction from 1% to 4%, heat transfer improves from 1.35% to 4.90%. By increasing Hartmann number from 0 to 600, heat transfer reduces from 9.29% to 22.07%. Also, the results show that the ratio of deviation angle of the enclosure to the horizontal surface has considerable effects on heat transfer performance. Therefore, in similar conditions, the inclined enclosure with a deviation angle of 45° compared to the vertical and horizontal enclosure has better thermal performance.     

Numerical study of MHD natural convection in a rectangular enclosure with an insulated block

The present study numerically investigates the two-dimensional laminar natural convection in a differently heated rectangular enclosure with an insulated square block, in the presence of a uniform magnetic field applied in the horizontal direction. Numerical simulations were performed for the conditions of different Rayleigh and Hartmann numbers with a fixed Prandtl number. The heat transfer rate decreases with the increase in the intensity of the magnetic field. It was found that the insertion of an insulated block contributes to the enhancement of the heat transfer rate in certain ranges of the block size and the Hartmann number.     

Effects of Magnetic Field and Inclination on Natural Convection in a Cavity Filled with Nanofluids by a Double Multiple-Relaxation-Time Thermal Lattice Boltzmann Method

Abstract

The present study numerically investigates the magneto-hydrodynamic flow and heat transfer of copper (Cu)-water nanofluids in an inclined cavity with one heat and one cold source. Simulations have been done via double multiple-relaxation-time thermal lattice Boltzmann method. Impacts of Hartmann number, Rayleigh number, inclination angle and the volume fraction of nanoparticles on the fluid flow and heat transfer performance are illustrated in terms of streamlines, isotherms, local, and average Nusselt numbers. Outputs demonstrate that the average Nusselt number decreases remarkably first as the inclination angle increases and then the average Nusselt number increases continuously and approaches a maximum value at a certain inclination angle for high Rayleigh numbers. In addition, the position where the average Nusselt number is maximized moves toward the lower inclination angle with increasing the Hartmann number for high Rayleigh numbers.