Effect of uniform inclined magnetic field on natural convection and entropy generation in an open cavity having a horizontal porous layer saturated with a ferrofluid

Numerical analysis of natural convection combined with entropy generation in a square open cavity partially filled with a porous medium has been performed for a ferrofluid under the effect of inclined uniform magnetic field. Governing equations with corresponding boundary conditions formulated in dimensionless stream function and vorticity using Brinkman–extended Darcy model for porous layer have been solved numerically using finite difference method. An influence of key parameters on ferrofluid flow and heat transfer has been analyzed. It has been found that an inclusion of spherical ferric oxide nanoparticles can lead to a diminution of entropy generation in the case of similar flow and heat transfer structures.     

MHD heat transfer and entropy production of an Al2O3-water nanofluid in a horizontal cylinder

This paper deals with the effect of magnetic fields (B_r, B_θ, B_z) applied in r-, θ-, z-directions, respectively, on entropy production and heat transfer and in a horizontal cylinder filled with an Al₂O₃-water nanofluid. The results are verified using literature data. For different Richardson, Ri, and Hartmann numbers, Ha, the nanoparticles (NP) ϕ, and magnetic field orientation combined effect provide a better understanding of heat transfer and entropy optimization. The results indicate that entropy production and heat transfer and rates depend on magnetic field intensity and direction. Also, increasing Ri and NP increases entropy generation and heat transfer. Finally, applying a radial magnetic field promotes a better convective heat transfer and minimizes entropy production.     

Numerical investigation of nonuniform transverse magnetic field effects on the flow and heat transfer of magnetic nanofluid in a sintered porous channel

In this paper, fluid flow and convective heat transfer of a ferrofluid (water and 4 vol% Fe₃O₄) in sintered Aluminum porous channel, which is subjected to a nonuniform transverse magnetic field have been studied. The numerical simulations supposed an ordinary cubic and staggered arrangement organized by uniformly sized particles with a small contact area for the porous media and constant heat flux at the surface of the microchannel. A wire, in which the electric current passes creates a nonuniform magnetic field, which is perpendicular to the flow direction. To do this simulation, the control volume technique and the two‐phase mixture model have been employed. The results show that the obtained local heat transfer coefficient on the channel surface increased with increasing mass flow rate and decreased slightly along the axial direction. Moreover, exerting the above‐mentioned magnetic field increases the Nusselt number that enhances the heat transfer rate while it has no effect on the pressure drop along the channel.     

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.     

The Effects of Magnetization Saturation on Thermomagnetic Convection in a Locally Heated Square Enclosure

Steady-state simulation study of thermomagnetic convection is presented for a square cavity with localized heat-sources. The external magnetic field conforms to Maxwell's equations. Effects of magnetization saturation of the ferrofluid medium on heat transfer enhancement are studied by invoking Langevin's law. Thermal interactions between the heaters and the fluid at convection-dominated regimes are visualized through streamline, heatline, and isotherm plots. The variation of Nu_avg,heater is depicted for increasing dipole strength of the magnetic field sources. Fluid-magnetization contours explain the layout of the Kelvin force-field. The positions of the magnets for maximum value of Nu_avg,heater are determined. For the same heat generation rate, effects of enclosure dimensions on heat transfer augmentation are studied.     

Hydrothermal Behavior of a Ferrofluid in a Corrugated Channel in the Presence of a Magnetic Field

In this paper, results of applying a non‐uniform magnetic field on a dilute ferrofluid (water and 3% vol. Fe₃O₄) flow in a corrugated channel under a constant heat flux boundary condition have been reported. The thermal behavior of the flow is investigated numerically using a two‐phase mixture model and control volume technique. It is concluded that using a magnetic field with a negative gradient on a nanofluid flow in corrugated channels can be proposed as a suitable method to achieve higher heat transfer performance and augment the heat transfer coefficient and also reduces the wall temperature. This method can lead to the design of more compact heat exchangers. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 80–92, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21060     

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.     

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.     

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.     

Effect of magnetic field on two-layered natural/thermocapillary convection

Heat transfer in a two-layered fluid system is of great importance in a variety of applications. Control and optimization of convective heat transfer of the immiscible fluids needs complete understanding of all phenomena, especially those induced by surface tension at the fluid interface. The present work is focused on rather complex convective flow and heat transfer phenomena in a cavity, which can be subject to both buoyancy and thermocapillary effects in addition to the influence of magnetic field applied for flow control. With the encapsulant liquid posing magnetic properties, a magnetic force can arise to either enhance or counterbalance the gravity effect when the cavity is placed in a non-uniform magnetic field. In our study, the velocity and temperature distribution of the system can be significantly altered to change the heat transfer by varying intensity and gradient of the applied magnetic field. Preliminary results of numerical computation presented here are for a two-layered liquid cavity MnCl₂·4H₂O and Fluorinert FC40 under various magnetic fields intensities.     

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 Study and POD-Based Prediction of Natural Convection in a Ferrofluids–Filled Triangular Cavity with Generalized Neural Networks

The effects of a magnetic dipole source on the natural convection of ferrofluids in a triangular cavity are studied. A partial heater is added to the left vertical wall of the cavity while the right vertical wall is kept at the constant temperature. A magnetic dipole source is placed outside the cavity close to the heater. The governing equations of a coupled multi-physics system are solved with a commercial solver using the finite element method. Computations are performed for different ranges of parameters: Rayleigh number (10⁴  ≤ Ra ≤ 10⁶ ), strength of the magnetic dipole (0 ≤ γ ≤ 8), horizontal and vertical location of the magnetic dipole (?2.5H ≤ a ≤ ?0.5H, 0.2H ≤ b ≤ 0.8H). It is observed that the interaction between natural convection and ferrofluid convection under the influence of magnetic dipole affects the flow and thermal field in such the triangular enclosure. The external magnetic field acts in such a way to decrease local heat transfer in some locations and increase it in others for certain combinations of flow parameters and therefore it can be used as a control parameter for fluid flow and heat transfer. Furthermore, an interpolation method based on Proper Orthogonal Decomposition and Generalized Neural Networks is proposed to predict the thermal performance of the system. This approach gives satisfactory results in terms of local and averaged heat transfer values.     

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.     

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.     

NUMERICAL MODELING OF ELECTROHYDRODYNAMIC (EHD) EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE

Mathematical and numerical modeling of electrohydrodynamic (EHD) enhancement of natural convection in enclosures is carried out. An electric current in dielectric liquid is modeled as a directed motion of electrically charged particles injected into a neutral fluid; the electric body force and Joule heat are added to the momentum and energy equations, respectively. Based on this, numerical studies are carried out for EHD effects on natural convection in enclosures. It is found that, at the same electric field intensity, the EHD enhancement of heat transfer is different for different electric density injections; applying a nonuniform electric field offers better EHD enhancement of heat transfer than applying a uniform electric field.     

Experimental study on the influence of the aspect ratio of square cavity on natural convection heat transfer with Al2O3/Water nanofluids

Cavity design is an important aspect in thermal systems, and proper cavity design saves plenty of energy as losses are minimised through better design. In this work, the influence that the Aspect Ratio (AR) of a rectangular cavity filled with nanofluids has on the natural convection process is studied experimentally. Three different cavities with the AR of 1, 2 and 4 are fabricated, and the heat transfer performance is studied using two different fluids namely de-ionised water and Al₂O₃/Water nanofluids. It is found that the AR of the cavity has a significant effect on the heat transfer coefficient and Nusselt number. More importantly, the optimum nanofluid concentration for maximum heat transfer varies with the AR of the cavity. It also found that the Rayleigh number has a strong effect on the Nusselt number as well as nanofluid buoyancy.     

A magnetic vortex generator for simultaneous heat transfer enhancement and pressure drop reduction in a mini channel

An active vortex generator is proposed for heat transfer enhancement in heat sinks and heat exchangers and removal of highly concentrated heat fluxes. It is based on applying a uniform magnetic field of permanent magnets to a magnetic fluid (ferrofluid) flowing in a heated channel. Numerical simulations are carried out for a 2 Vol% ferrofluid at different Reynolds numbers (150‐210) and magnetic field intensities (0‐1400 G) to investigate the possibility of simultaneous heat transfer enhancement and pressure drop reduction by the proposed method. Comparisons are also made with the other conventional vortex generators. Results indicate that the external magnetic field acts as a vortex generator that changes the velocity distribution, improves the flow mixing, and thereby increases the convective heat transfer. Surprisingly, the heat transfer enhancement is accompanied by a decrease of the friction coefficient due to the flow separation and decrease of the flow contact with the surface. It is also concluded that increasing the magnetic field intensity, decreasing the flow rate, and adding a second identical magnetic vortex generator have favorable effects on both pressure drop and heat transfer. A maximum of 37.8% enhancement of heat transfer with a 29.18% reduction of pressure drop has been achieved at the optimum condition.     

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 magnetic field on the thermal performance of a ferrofluid-based solar flat plate collector

In this paper, the effectiveness of ferrofluid as a working fluid for solar flat plate collectors (FPCs) is studied. A mini-ferrofluid-based solar FPC is designed and tested under laboratory conditions. The thermal performance of the designed solar FPC is evaluated under different conditions and it is observed that it provides higher efficiency for the case of ferrofluid in the presence of a magnetic field. The thermal efficiency is observed to increase by 54% for ferrofluid in presence of a magnetic field as compared to no magnetic field. The thermal efficiency is observed to increase further with the increase in the magnetic field. The increase in thermal efficiency is attributed to the combined effects of higher thermal conductivity and magnetohydrodynamics of ferrofluid, which result in higher convective heat transfer from the riser tube walls into ferrofluid. The higher heat transfer for ferrofluid with a magnetic field is established by calculating the Nusselt number numerically using COMSOL. Simulation results show an increase in Nusselt number for ferrofluid with magnetic field and hence higher thermal efficiency for the solar FPC. The designed FPC provides simple modifications to conventional FPCs to use ferrofluid with magnetic field for higher thermal efficiencies.     

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.