Simulation of natural convection and entropy generation of MHD non-Newtonian nanofluid in a cavity using Buongiorno's mathematical model

In this paper, natural convection and entropy generation of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a cavity in the presence of a uniform magnetic field has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10⁴ and 10⁵), Hartmann number (Ha = 0, 15, 30), buoyancy ratio number (N_r = 0.1, 1, and 4), power-law index (n = 0.4–1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (N_t = 0.1, 0.5, 1), and Brownian motion parameter (N_b = 0.1, 1, 5). The Prandtl number is fixed at Pr = 1. The Results indicate that the augmentation of Hartmann number causes heat and mass transfer to drop. The increase in Rayleigh number enhances heat and mass transfer for various power-law indexes. The alteration of the power-law index changes heat and mass transfer. In addition, the rise of Hartmann number declines the shear-thinning behavior. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The augmentation of the power-law index declines various entropy generations in different Rayleigh numbers and Hartmann numbers. The increase in Hartmann number declines total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Hartmann number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility.     

Entropy Generation Due to Natural Convection in a Partially Open Cavity with a Thin Heat Source Subjected to a Nanofluid

This article presents a numerical study of natural convection cooling of a heat source mounted inside the cavity, with special attention being paid to entropy generation. The right vertical wall is partially open and is subjected to copper–water nanofluid at a constant low temperature and pressure, while the other boundaries are assumed to be 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 a Rayleigh number in the range 10³ < Ra < 10⁶, and for solid volume fraction 0 <? <0.05. In order to investigate the effect of the heat source and open boundary location, six different configurations are considered. The effects of Rayleigh numbers, heat source and open boundary locations on the streamlines, isotherms, local entropy generation, Nusselt number, and total entropy generation are investigated. The results indicate that when open boundary is located up, the fluid flow augments and hence the heat transfer and Nusselt number increase and total entropy generation decreases.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

MHD conjugate heat transfer and entropy generation analysis of MWCNT/water nanofluid in a partially heated divided medium

The aim of this article is to conduct the lattice Boltzmann simulation of the magnetohydrodynamic (MHD) natural conjugate heat transfer in an apportioned cavity loaded with a multiwalled carbon nanotube/water nanofluid. The divided cavity is, to some extent, heated and cooled at the upright walls, whereas the horizontal walls are adiabatic. The nanofluid properties are evaluated on the basis of experimental correlations. The parameters ranges in the study are as follows: nanoparticles' volume fraction (%): 0 ≤ ? ≤ 0.5, temperature (°C): T = 27, Rayleigh number (Ra): 10³ ≤ Ra ≤ 10⁵, Hartmann number (Ha): 0 ≤ Ha ≤ 90, and the magnetic field inclination angle (γ): 0 ≤ γ ≤ π/2. The current outcomes are observed to be in great concurrence with the numerical results introduced in the literature. The impacts of the aforesaid parameters on local and average heat transfer, entropy generation, and Bejan number (Be) are explored and discussed. Indeed, the transfer of heat increases linearly with ? for a low Ra. As Ra increases, the average Nusselt number decreases for a high value of ?. The increase of nanoparticles' volume fraction leads to a reduction in the entropy generation and an increase in the Bejan number for a high Ra, but at low Ra, these functions remain constant. As the Ha increases, the transfer of heat and the entropy generation decreases, whereas there is an increase in Be. The transfer of heat, total entropy generation, and the Be depends strongly on the direction of the magnetic field. The increase of heater and cooler size has a great influence on the transfer of heat, entropy generation, and Be.     

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.     

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.     

Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by Response Surface Methodology

The natural convection heat transfer and entropy generation of Al₂O₃-water nanofluid, in a square cavity with inclination angle θ and the presence of a constant axial magnetic field B₀ are examined in this paper. The governing equations are solved numerically by finite volume method. Also an effective parameters analysis was performed by using of the Response Surface Methodology (RSM). The effects of the Rayleigh number (10³, 10⁴, 10⁵ and 10⁶), Hartmann number (0, 10, 30 and 50) and also inclination angles (0°, 30°, 60° and 90°) are investigated. It is observed that the mean Nusselt number and the total entropy generation increase when the Rayleigh number increases. It is also found that, regardless of the Ha parameter, by increasing of the inclination angles, the mean Nusselt number and entropy generation rate increase until inclination angle 30° and then they decrease. Also, for low Ra numbers, by increasing the Ha parameter, the mean Nusselt number increases until Ha = 10 and then decreases. The analysis showed that the sensitivity of the Nusselt number and the entropy generation to Ha parameter was too small, and as a result it was negligible. Also, the sensitivity of the mean Nusselt number and the entropy generation to inclination angle, θ, increases by increasing of this angle. It is also observed that the mean Nusselt number and the entropy generation were more sensitive to the inclination angle θ than the Ha parameter.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

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     

Rayleigh–Benard convection in water-based alumina nanofluid: A numerical study

Rayleigh–Benard (R-B) convection in water-based alumina (Al₂O₃) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al₂O₃/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.     

Three-dimensional numerical analysis of the natural convection and entropy generation of MWCNTs-H2O and air as two immiscible fluids in a rectangular cuboid with fillet corners

A numerical investigation has been carried out to study the natural convection and entropy generation within the three-dimensional enclosure with fillets. There are two immiscible fluids of Multi-Walled Carbon Nano-Tubes (MWCNTs)-water and air in the enclosure, which is simulated as two discrete phases. There are two heaters with constant heat flux at the sides, and the top and bottom walls are kept at cold constant temperature. The finite volume approach is applied to solve the governing equations. Moreover, a numerical method is developed based on the three-dimensional solution of Navier–Stokes equations. The fluid flow, heat transfer, and total volumetric entropy generation due to natural convection are studied carefully in a three-dimensional enclosure. The effects of the corner radius of fillets (r?=?0, 0.15, 0.2, and 0.25), Rayleigh number (10³?Ra?6), and solid volume fraction (φ?=?0.002 and 0.01) of the nanofluid have been investigated on both natural convection characteristic and volumetric entropy generation.* The results show that the curved corner can be an effective method to control fluid flow and energy consumption, and three dimensional solutions render more accurate results.     

Al2O3–Water nanofluid heat transfer and entropy generation in a ribbed channel with wavy wall in the presence of magnetic field

In this article, a parametric study is conducted to evaluate heat transfer enhancement in a ribbed channel containing Al₂O₃–Water nanofluid with wavy wall. The physical domain is under the influence of the magnetic field that creates a negative force against the working fluid to move. Nanofluid with higher temperature enters the cool ribbed duct and heat is exchanged along the walls of channel. The effects of the dominant parameters including number of the blocks, solid volume fractions of nanofluid, Hartmann number, Reynolds number, and different states of amplitude sine waves are numerically tested on the local and average Nusselt number, skin friction, and total entropy generation. Excellent agreement between present study and previous literature is observed. It is found that, an augmentation in magnetic field will result in higher values of both local and average Nusselt number accompanying with bigger values of skin friction and entropy generation. Computations illustrate that, increasing the solid volume fraction of the Al₂O₃ nanoparticles will raise the Nusselt number and total entropy generation rate but its effect on the skin friction is negligible. Also, numerical results imply that increasing amplitude sine waves of the geometry has incremental effect on the Nusselt number and skin friction but its effect on the total entropy generation rate is not so clear. Moreover, by adding number of the used blocks in the presence of magnetic field, the local Nusselt number experiences more jumps but it does not increase the average Nusselt number, necessarily. In addition, using more blocks increases skin friction but it has a reverse effect on the total entropy generation rate.     

Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water–Al2O3 nanofluid

This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al₂O₃ as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.     

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.     

Entropy generation in Poiseuille–Benard channel flow

The issue of entropy generation in Poiseuille–Benard channel flow is analyzed by solving numerically the mass, momentum and energy equations with the use of the classic Boussinesq incompressible approximation. The numerical scheme is based on Control Volume Finite Element Method with the SIMPLER algorithm for pressure–velocity coupling. Results are obtained for Rayleigh numbers Ra and irreversibility φ ranging from 10³ to 5×10⁴ and from 10⁻⁴ to 10 respectively. Variations of entropy generation and the Bejan number as a function of Ra and φ are studied. The limit value φ_l for which entropy generation due to heat transfer is equal to entropy due to fluid friction is evaluated. It has been found that φ_l is a decreasing function of the Rayleigh number Ra. φ_l varies from 0.0015 to 0.096 when Ra decrease from 5×10⁴ to 10³. Stream lines and entropy generation maps are plotted at six times over one period at Ra =10⁴ and φ=10⁻³. It has been found that the maximum entropy generation is localized at areas where heat exchanged between the walls and the flow is maximum. No significant entropy production is seen in the main flow.     

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.     

Numerical Investigation of the Entropy Generation Due to Natural Convection in a Partially Heated Square Cavity Filled With Nanofluids

A comprehensive numerical investigation has been carried out on the heat transfer performance and entropy generation within a rectangular cavity containing nanofluid. The cavity consists of two heat sources located on the bottom and a side wall. The effects of influential parameters including type and concentration of nanoparticles, radius of corner, width and thickness of heaters, heater distance from corners and aspect ratio of the enclosure were studied. The results showed that the Nusselt number enhanced by increasing the aspect ratio of the cavity, the distance of heaters from the corners, and concentration of nanoparticle and applying Cu as nanoparticle while it reduced by increasing the radius of the corner and the width and thickness of the heat sources. The entropy generation was found to be profoundly minimized by lowering the Rayleigh number. In addition, the entropy generation was attenuated by increasing the Eckert number, corner radius, the distance from the corner and concentration of nanoparticles and using Al₂O₃ as nanoparticle. On the other hand, increasing the aspect ratio of the cavity, width and thickness of the heaters augmented the entropy generation. Interestingly, the entropy generation of the system was lowered by just increasing the distance of one heater from the corner, whereas increasing the thickness and width of one heater resulted in larger entropy generation. This study provides valuable insight into the change in the amount of heat transfer and entropy by altering the geometry as well as fluid properties.     

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.     

Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid

Heat transfer enhancement has been investigated in a square cavity subject to different side wall temperatures using water/SiO₂ nanofluid. An experimental setup has been used to extract the conductivity value of nanofluid. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra_f = 10⁵–10⁷ and the volumetric fraction of nanoparticle between 0 and 4%. The comparisons show that the mean Nusselt number increases with volume fraction for the whole range of Rayleigh numbers. Although by using the theoretical formulations for conductivity no enhancement has been observed.