Entropy

23 pages, 5405 KiB

Open AccessArticle

Effects of Radiative Electro-Magnetohydrodynamics Diminishing Internal Energy of Pressure-Driven Flow of Titanium Dioxide-Water Nanofluid due to Entropy Generation

by Ahmed Zeeshan¹

, Nasir Shehzad¹, Tehseen Abbas² and Rahmat Ellahi^1,3,*

¹ Department of Mathematics & Statistics, FBAS, International Islamic University Islamabad, Islamabad 44000, Pakistan

² Department of Mathematics, University of Education Lahore, Faisalabad Campus, Faisalabad 38000, Pakistan

³ Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Entropy 2019, 21(3), 236; https://doi.org/10.3390/e21030236 - 1 Mar 2019

Cited by 100 | Viewed by 4229

Abstract

The internal average energy loss caused by entropy generation for steady mixed convective Poiseuille flow of a nanofluid, suspended with titanium dioxide (TiO₂) particles in water, and passed through a wavy channel, was investigated. The models of thermal conductivity and viscosity [...] Read more.

The internal average energy loss caused by entropy generation for steady mixed convective Poiseuille flow of a nanofluid, suspended with titanium dioxide (TiO₂) particles in water, and passed through a wavy channel, was investigated. The models of thermal conductivity and viscosity of titanium dioxide of 21 nm size particles with a volume concentration of temperature ranging from 15 °C to 35 °C were utilized. The characteristics of the working fluid were dependent on electro-magnetohydrodynamics (EMHD) and thermal radiation. The governing equations were first modified by taking long wavelength approximations, which were then solved by a homotopy technique, whereas for numerical computation, the software package BVPh 2.0 was utilized. The results for the leading parameters, such as the electric field, the volume fraction of nanoparticles and radiation parameters for three different temperatures scenarios were examined graphically. The minimum energy loss at the center of the wavy channel due to the increase in the electric field parameter was noted. However, a rise in entropy was observed due to the change in the pressure gradient from low to high. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows II)

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44 pages, 1531 KiB

Open AccessArticle

Entropy Generation in MHD Mixed Convection Non-Newtonian Second-Grade Nanoliquid Thin Film Flow through a Porous Medium with Chemical Reaction and Stratification

by Noor Saeed Khan¹

, Zahir Shah¹

, Saeed Islam¹

, Ilyas Khan^2,*

, Tawfeeq Abdullah Alkanhal³

and Iskander Tlili⁴

¹ Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan

² Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 736464, Vietnam

³ Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia

⁴ Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Entropy 2019, 21(2), 139; https://doi.org/10.3390/e21020139 - 1 Feb 2019

Cited by 60 | Viewed by 4756

Abstract

Chemical reaction in mixed convection magnetohydrodynamic second grade nanoliquid thin film flow through a porous medium containing nanoparticles and gyrotactic microorganisms is considered with entropy generation. The stratification phenomena, heat and mass transfer simultaneously take place within system. Microorganisms are utilized to stabilize [...] Read more.

Chemical reaction in mixed convection magnetohydrodynamic second grade nanoliquid thin film flow through a porous medium containing nanoparticles and gyrotactic microorganisms is considered with entropy generation. The stratification phenomena, heat and mass transfer simultaneously take place within system. Microorganisms are utilized to stabilize the suspended nanoparticles through bioconvection. For the chemical reaction of species, the mass transfer increases. The governing equations of the problem are transformed to nonlinear differential equations through similarity variables, which are solved through a well known scheme called homotopy analysis method. The solution is expressed through graphs and illustrations which show the influences of all the parameters. The residual error graphs elucidate the authentication of the present work. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows II)

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30 pages, 7390 KiB

Open AccessArticle

Entropy Generation of Carbon Nanotubes Flow in a Rotating Channel with Hall and Ion-Slip Effect Using Effective Thermal Conductivity Model

by Nosheen Feroz¹, Zahir Shah^1,*, Saeed Islam¹

, Ebraheem O. Alzahrani²

and Waris Khan³

¹ Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber, Pakhtunkhwa 23200, Pakistan

² Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

³ Department of Mathematics, Kohat University of Science and technology, Kohat 26000, Pakistan

Entropy 2019, 21(1), 52; https://doi.org/10.3390/e21010052 - 10 Jan 2019

Cited by 36 | Viewed by 5098

Abstract

This article examines the entropy analysis of magnetohydrodynamic (MHD) nanofluid flow of single and multiwall carbon nanotubes between two rotating parallel plates. The nanofluid flow is taken under the existence of Hall current and ion-slip effect. Carbon nanotubes (CNTs) are highly proficient heat [...] Read more.

This article examines the entropy analysis of magnetohydrodynamic (MHD) nanofluid flow of single and multiwall carbon nanotubes between two rotating parallel plates. The nanofluid flow is taken under the existence of Hall current and ion-slip effect. Carbon nanotubes (CNTs) are highly proficient heat transmission agents with bordering entropy generation and, thus, are considered to be a capable cooling medium. Entropy generation and Hall effect are mainly focused upon in this work. Using the appropriate similarity transformation, the central partial differential equations are changed to a system of ordinary differential equations, and an optimal approach is used for solution purposes. The resultant non-dimensional physical parameter appear in the velocity and temperature fields discussed using graphs. Also, the effect of skin fraction coefficient and Nusselt number of enclosed physical parameters are discussed using tables. It is observed that increased values of magnetic and ion-slip parameters reduce the velocity of the nanofluids and increase entropy generation. The results reveal that considering higher magnetic forces results in greater conduction mechanism. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows II)

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22 pages, 4281 KiB

Open AccessFeature PaperArticle

Modelling Study on Internal Energy Loss Due to Entropy Generation for Non-Darcy Poiseuille Flow of Silver-Water Nanofluid: An Application of Purification

by Nasir Shehzad¹, Ahmed Zeeshan¹

, Rahmat Ellahi^1,2

and Saman Rashidi^3,*

¹ Department of Mathematics & Statistics, FBAS, IIUI, Islamabad 44000, Pakistan

² Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

³ Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 91775-1111, Iran

Entropy 2018, 20(11), 851; https://doi.org/10.3390/e20110851 - 6 Nov 2018

Cited by 47 | Viewed by 3487

Abstract

In this paper, an analytical study of internal energy losses for the non-Darcy Poiseuille flow of silver-water nanofluid due to entropy generation in porous media is investigated. Spherical-shaped silver (Ag) nanosize particles with volume fraction 0.3%, 0.6%, and 0.9% are utilized. Four illustrative [...] Read more.

In this paper, an analytical study of internal energy losses for the non-Darcy Poiseuille flow of silver-water nanofluid due to entropy generation in porous media is investigated. Spherical-shaped silver (Ag) nanosize particles with volume fraction 0.3%, 0.6%, and 0.9% are utilized. Four illustrative models are considered: (i) heat transfer irreversibility (HTI), (ii) fluid friction irreversibility (FFI), (iii) Joule dissipation irreversibility (JDI), and (iv) non-Darcy porous media irreversibility (NDI). The governing equations of continuity, momentum, energy, and entropy generation are simplified by taking long wavelength approximations on the channel walls. The results represent highly nonlinear coupled ordinary differential equations that are solved analytically with the help of the homotopy analysis method. It is shown that for minimum and maximum averaged entropy generation, 0.3% by vol and 0.9% by vol of nanoparticles, respectively, are observed. Also, a rise in entropy is evident due to an increase in pressure gradient. The current analysis provides an adequate theoretical estimate for low-cost purification of drinking water by silver nanoparticles in an industrial process. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows II)

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10 pages, 2660 KiB

Open AccessArticle

Analysis of Entropy Generation in Flow of Methanol-Based Nanofluid in a Sinusoidal Wavy Channel

by Muhammad Qasim¹

, Zafar Hayat Khan², Ilyas Khan³

and Qasem M. Al-Mdallal^4,*

¹ Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, Pakistan

² Department of Mathematics, University of Malakand, Khyber Pakhtunktwo 18800, Pakistan

³ Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Majmaah 11592, Saudi Arabia

⁴ Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE

Entropy 2017, 19(10), 490; https://doi.org/10.3390/e19100490 - 8 Oct 2017

Cited by 48 | Viewed by 5271

Abstract

The entropy generation due to heat transfer and fluid friction in mixed convective peristaltic flow of methanol-Al₂O₃ nano fluid is examined. Maxwell’s thermal conductivity model is used in analysis. Velocity and temperature profiles are utilized in the computation of the [...] Read more.

The entropy generation due to heat transfer and fluid friction in mixed convective peristaltic flow of methanol-Al₂O₃ nano fluid is examined. Maxwell’s thermal conductivity model is used in analysis. Velocity and temperature profiles are utilized in the computation of the entropy generation number. The effects of involved physical parameters on velocity, temperature, entropy generation number, and Bejan number are discussed and explained graphically. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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15 pages, 5855 KiB

Open AccessArticle

Entropy Analysis on Electro-Kinetically Modulated Peristaltic Propulsion of Magnetized Nanofluid Flow through a Microchannel

by Muhammad Mubashir Bhatti¹, Mohsen Sheikholeslami^2,* and Ahmed Zeeshan³

¹ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

² Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol 47148-71167, Iran

³ Department of Mathematics, International Islamic university Islamabad, Islamabad 44000, Pakistan

Entropy 2017, 19(9), 481; https://doi.org/10.3390/e19090481 - 9 Sep 2017

Cited by 65 | Viewed by 5842

Abstract

A theoretical and a mathematical model is presented to determine the entropy generation on electro-kinetically modulated peristaltic propulsion on the magnetized nanofluid flow through a microchannel with joule heating. The mathematical modeling is based on the energy, momentum, continuity, and entropy equation in [...] Read more.

A theoretical and a mathematical model is presented to determine the entropy generation on electro-kinetically modulated peristaltic propulsion on the magnetized nanofluid flow through a microchannel with joule heating. The mathematical modeling is based on the energy, momentum, continuity, and entropy equation in the Cartesian coordinate system. The effects of viscous dissipation, heat absorption, magnetic field, and electrokinetic body force are also taken into account. The electric field terms are helpful to model the electrical potential terms by means of Poisson–Boltzmann equations, ionic Nernst–Planck equation, and Debye length approximation. A perturbation method has been applied to solve the coupled nonlinear partial differential equations and a series solution is obtained up to second order. The physical behavior of all the governing parameters is discussed for pressure rise, velocity profile, entropy profile, and temperature profile. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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15 pages, 6756 KiB

Open AccessArticle

Effect of Slip Conditions and Entropy Generation Analysis with an Effective Prandtl Number Model on a Nanofluid Flow through a Stretching Sheet

by Mohammad Mehdi Rashidi¹ and Munawwar Ali Abbas^2,*

¹ Department of Civil Engineering, University of Birmingham, Edjbaston, Birmingham B15 2TT, UK

² Department of Computer Science, Karakoram International University, Skardu Campus, Gilgit Baltistan 16100, Pakistan

Entropy 2017, 19(8), 414; https://doi.org/10.3390/e19080414 - 11 Aug 2017

Cited by 20 | Viewed by 4886

Abstract

This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum [...] Read more.

This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum boundary layers. For this purpose, we have considered a model for effective Prandtl number which is borrowed by means of experimental analysis on a nano boundary layer, steady, two-dimensional incompressible flow through a stretching sheet. We have considered γAl₂O₃-H₂O and Al₂O₃-C₂H₆O₂ nanoparticles for the governing flow problem. An entropy generation analysis is also presented with the help of the second law of thermodynamics. A numerical technique known as Successive Taylor Series Linearization Method (STSLM) is used to solve the obtained governing nonlinear boundary layer equations. The numerical and graphical results are discussed for two cases i.e., (i) effective Prandtl number and (ii) without effective Prandtl number. From graphical results, it is observed that the velocity profile and temperature profile increases in the absence of effective Prandtl number while both expressions become larger in the presence of Prandtl number. Further, numerical comparison has been presented with previously published results to validate the current methodology and results. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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16 pages, 363 KiB

Open AccessArticle

Investigation of Oriented Magnetic Field Effects on Entropy Generation in an Inclined Channel Filled with Ferrofluids

by Elgiz Baskaya¹, Guven Komurgoz^2,* and Ibrahim Ozkol³

¹ Ecole Nationale de l’Aviation Civile, Toulouse 31400, France

² Faculty of Electrics & Electronics, Istanbul Technical University, Istanbul 34469, Turkey

³ Faculty of Aeronautics & Astronautics, Istanbul Technical University, Istanbul 34469, Turkey

Entropy 2017, 19(7), 377; https://doi.org/10.3390/e19070377 - 23 Jul 2017

Cited by 12 | Viewed by 4757

Abstract

Dispersion of super-paramagnetic nanoparticles in nonmagnetic carrier fluids, known as ferrofluids, offers the advantages of tunable thermo-physical properties and eliminate the need for moving parts to induce flow. This study investigates ferrofluid flow characteristics in an inclined channel under inclined magnetic field and [...] Read more.

Dispersion of super-paramagnetic nanoparticles in nonmagnetic carrier fluids, known as ferrofluids, offers the advantages of tunable thermo-physical properties and eliminate the need for moving parts to induce flow. This study investigates ferrofluid flow characteristics in an inclined channel under inclined magnetic field and constant pressure gradient. The ferrofluid considered in this work is comprised of Cu particles as the nanoparticles and water as the base fluid. The governing differential equations including viscous dissipation are non-dimensionalised and discretized with Generalized Differential Quadrature Method. The resulting algebraic set of equations are solved via Newton-Raphson Method. The work done here contributes to the literature by searching the effects of magnetic field angle and channel inclination separately on the entropy generation of the ferrofluid filled inclined channel system in order to achieve best design parameter values so called entropy generation minimization is implemented. Furthermore, the effect of magnetic field, inclination angle of the channel and volume fraction of nanoparticles on velocity and temperature profiles are examined and represented by figures to give a thorough understanding of the system behavior. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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27 pages, 508 KiB

Open AccessArticle

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects on a Non-Linear Stretching Sheet

by Mohammed Almakki¹, Sharadia Dey^1,2,*, Sabyasachi Mondal¹ and Precious Sibanda¹

¹ School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, 3209 Pietermaritzburg, South Africa

² DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Private Bag 3, Wits, 2050 Johannesburg, South Africa

Entropy 2017, 19(7), 168; https://doi.org/10.3390/e19070168 - 12 Jul 2017

Cited by 21 | Viewed by 6034

Abstract

The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD) nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the [...] Read more.

The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD) nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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16 pages, 14331 KiB

Open AccessArticle

Natural Convection and Entropy Generation in a Square Cavity with Variable Temperature Side Walls Filled with a Nanofluid: Buongiorno’s Mathematical Model

by Mikhail A. Sheremet^1,2, Teodor Grosan³ and Ioan Pop^3,*

¹ Department of Theoretical Mechanics, Tomsk State University, Tomsk 634050, Russia

² Department of Nuclear and Thermal Power Plants, Tomsk Polytechnic University, Tomsk 634050, Russia

³ Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania

Entropy 2017, 19(7), 337; https://doi.org/10.3390/e19070337 - 5 Jul 2017

Cited by 46 | Viewed by 5860

Abstract

Natural convection heat transfer combined with entropy generation in a square cavity filled with a nanofluid under the effect of variable temperature distribution along left vertical wall has been studied numerically. Governing equations formulated in dimensionless non-primitive variables with corresponding boundary conditions taking [...] Read more.

Natural convection heat transfer combined with entropy generation in a square cavity filled with a nanofluid under the effect of variable temperature distribution along left vertical wall has been studied numerically. Governing equations formulated in dimensionless non-primitive variables with corresponding boundary conditions taking into account the Brownian diffusion and thermophoresis effects have been solved by finite difference method. Distribution of streamlines, isotherms, local entropy generation as well as Nusselt number has been obtained for different values of key parameters. It has been found that a growth of the amplitude of the temperature distribution along the left wall and an increase of the wave number lead to an increase in the average entropy generation. While an increase in abovementioned parameters for low Rayleigh number illustrates a decrease in average Bejan number. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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17 pages, 8165 KiB

Open AccessArticle

Effects of Movable-Baffle on Heat Transfer and Entropy Generation in a Cavity Saturated by CNT Suspensions: Three-Dimensional Modeling

by Abdullah A.A.A. Al-Rashed¹, Walid Aich^2,3

, Lioua Kolsi^2,4

, Omid Mahian^5,*, Ahmed Kadhim Hussein⁶ and Mohamed Naceur Borjini⁴

¹ Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority of Applied Education and Training, 13092 Kuwait City, Kuwait

² College of Engineering, Mechanical Engineering Department, Haïl University, 2440 Haïl City, Saudi Arabia

³ Unité de Recherche Matériaux, Energie et Energies Renouvelables MEER, Faculté des Sciences de Gafsa, Sidi Ahmed Zarroug, 2112 Gafsa, Tunisia

⁴ Unité de Recherche de Métrologie et des Systèmes Energétiques, Ecole Nationale d’Ingénieurs, University of Monastir, 5000 Monastir, Tunisia

⁵ Renewable Energies, Magnetism and Nanotechnology Lab, Faculty of Science, Ferdowsi University of Mashhad, 9187147578 Mashhad, Iran

⁶ Mechanical Engineering Department, College of Engineering, Babylon University, 51002 Babylon City, Iraq

Entropy 2017, 19(5), 200; https://doi.org/10.3390/e19050200 - 29 Apr 2017

Cited by 54 | Viewed by 5831

Abstract

Convective heat transfer and entropy generation in a 3D closed cavity, equipped with adiabatic-driven baffle and filled with CNT (carbon nanotube)-water nanofluid, are numerically investigated for a range of Rayleigh numbers from 10³ to 10⁵. This research is conducted for [...] Read more.

Convective heat transfer and entropy generation in a 3D closed cavity, equipped with adiabatic-driven baffle and filled with CNT (carbon nanotube)-water nanofluid, are numerically investigated for a range of Rayleigh numbers from 10³ to 10⁵. This research is conducted for three configurations; fixed baffle (V = 0), rotating baffle clockwise (V+) and rotating baffle counterclockwise (V−) and a range of CNT concentrations from 0 to 15%. Governing equations are formulated using potential vector vorticity formulation in its three-dimensional form, then solved by the finite volume method. The effects of motion direction of the inserted driven baffle and CNT concentration on heat transfer and entropy generation are studied. It was observed that for low Rayleigh numbers, the motion of the driven baffle enhances heat transfer regardless of its direction and the CNT concentration effect is negligible. However, with an increasing Rayleigh number, adding driven baffle increases the heat transfer only when it moves in the direction of the decreasing temperature gradient; elsewhere, convective heat transfer cannot be enhanced due to flow blockage at the corners of the baffle. Full article

(This article belongs to the Special Issue Entropy Generation in Nanofluid Flows)

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17 pages, 9468 KiB

Open AccessArticle

3D Buoyancy-Induced Flow and Entropy Generation of Nanofluid-Filled Open Cavities Having Adiabatic Diamond Shaped Obstacles

by Lioua Kolsi^1,2

, Omid Mahian^3,*, Hakan F. Öztop^4,5, Walid Aich^1,6

, Mohamed Naceur Borjini², Nidal Abu-Hamdeh⁵ and Habib Ben Aissia²

¹ College of Engineering, Mechanical Engineering Department, Haïl University, Haïl City 2240, Saudi Arabia

² Unité de Recherche de Métrologie et des Systèmes Energétique, Ecole Nationale d’Ingénieurs, University of Monastir, Monastir City 5000, Tunisia

³ Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad 9187147578, Iran

⁴ Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig 23119, Turkey

⁵ Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

⁶ Unité de Recherche Matériaux, Énergie et Énergies Renouvelables, Faculté des Sciences de Gafsa, Gafsa 2100, Tunisia

Entropy 2016, 18(6), 232; https://doi.org/10.3390/e18060232 - 21 Jun 2016

Cited by 54 | Viewed by 5925

Abstract

A three dimensional computational solution has been obtained to investigate the natural convection and entropy generation of nanofluid-filled open cavities with an adiabatic diamond shaped obstacle. In the model, the finite volume technique was used to solve the governing equations. Based on the [...] Read more.

A three dimensional computational solution has been obtained to investigate the natural convection and entropy generation of nanofluid-filled open cavities with an adiabatic diamond shaped obstacle. In the model, the finite volume technique was used to solve the governing equations. Based on the configuration, the cavity is heated from the left vertical wall and the diamond shape was chosen as adiabatic. Effects of nanoparticle volume fraction, Rayleigh number (10³ ≤ Ra ≤ 10⁶) and width of diamond shape were studied as governing parameters. It was found that the geometry of the partition is a control parameter for heat and fluid flow inside the open enclosure. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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14 pages, 4008 KiB

Open AccessArticle

Entropy Generation on MHD Eyring–Powell Nanofluid through a Permeable Stretching Surface

by Muhammad Mubashir Bhatti¹, Tehseen Abbas², Mohammad Mehdi Rashidi^3,4

, Mohamed El-Sayed Ali^5,* and Zhigang Yang³

¹ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

² Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan

³ Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

⁴ ENN-Tongji Clean Energy Institute of Advanced Studies, Tongji University, Shanghai 200072, China

⁵ Mechanical Engineering Department, College of Engineering, King Saud University, P. O. Box 800, Riyadh 11421, Saudi Arabia

Entropy 2016, 18(6), 224; https://doi.org/10.3390/e18060224 - 8 Jun 2016

Cited by 139 | Viewed by 8503

Abstract

In this article, entropy generation of an Eyring–Powell nanofluid through a permeable stretching surface has been investigated. The impact of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also taken into account. The governing flow problem is modeled with the help of similarity transformation [...] Read more.

In this article, entropy generation of an Eyring–Powell nanofluid through a permeable stretching surface has been investigated. The impact of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also taken into account. The governing flow problem is modeled with the help of similarity transformation variables. The resulting nonlinear ordinary differential equations are solved numerically with the combination of the Successive linearization method and Chebyshev spectral collocation method. The impact of all the emerging parameters such as Hartmann number, Prandtl number, radiation parameter, Lewis number, thermophoresis parameter, Brownian motion parameter, Reynolds number, fluid parameter, and Brinkmann number are discussed with the help of graphs and tables. It is observed that the influence of the magnetic field opposes the flow. Moreover, entropy generation profile behaves as an increasing function of all the physical parameters. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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14 pages, 3877 KiB

Open AccessArticle

Numerical Simulation of Entropy Generation with Thermal Radiation on MHD Carreau Nanofluid towards a Shrinking Sheet

by Muhammad Mubashir Bhatti¹, Tehseen Abbas², Mohammad Mehdi Rashidi^3,4

and Mohamed El-Sayed Ali^5,*

¹ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

² Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan

³ Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

⁴ ENN-Tongji Clean Energy Institute of advanced studies, Shanghai 200072, Tongji University, China

⁵ Mechanical Engineering Department, College of Engineering, King Saud University, P. O. Box 800, Riyadh 11421, Saudi Arabia

Entropy 2016, 18(6), 200; https://doi.org/10.3390/e18060200 - 24 May 2016

Cited by 106 | Viewed by 7601

Abstract

In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD) are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations [...] Read more.

In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD) are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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19 pages, 3877 KiB

Open AccessArticle

Analytical Modeling of MHD Flow over a Permeable Rotating Disk in the Presence of Soret and Dufour Effects: Entropy Analysis

by Navid Freidoonimehr¹, Mohammad Mehdi Rashidi^2,3, Shirley Abelman^4,*

and Giulio Lorenzini⁵

¹ Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, 65181-15743, Hamedan, Iran

² Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

³ ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai 201804, China

⁴ DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa

⁵ Department of Industrial Engineering, University of Parma, Parma 43124, Italy

Entropy 2016, 18(5), 131; https://doi.org/10.3390/e18050131 - 26 Apr 2016

Cited by 23 | Viewed by 8137

Abstract

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with [...] Read more.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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15 pages, 4193 KiB

Open AccessArticle

Heat Transfer Enhancement and Entropy Generation of Nanofluids Laminar Convection in Microchannels with Flow Control Devices

by Ping Li¹, Yonghui Xie², Di Zhang^1,* and Gongnan Xie³

¹ Key Laboratory of Thermal Fluid Science and Engineering of Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China

² School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

³ Department of Mechanical and Power Engineering, School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Entropy 2016, 18(4), 134; https://doi.org/10.3390/e18040134 - 21 Apr 2016

Cited by 45 | Viewed by 6017

Abstract

The heat transfer enhancement and entropy generation of Al₂O₃-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel, [...] Read more.

The heat transfer enhancement and entropy generation of Al₂O₃-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel, nanofluids concentration φ(0%–3%), and Reynolds number Re (50–300) were comparatively studied by means of performance parameters, as well as the limiting streamlines and temperature contours on the modified heated surfaces. The results reveal that the relative Fanning frictional factor f/f₀ of the microchannel with rectangle and protrusion devices are much larger and smaller than others, respectively. As the nanofluids concentration increases, f/f₀ increases accordingly. For the microchannel with rectangle ribs, there is a transition Re for obtaining the largest heat transfer. The relative Nusselt number Nu/Nu₀ of the cases with larger nanofluids concentration are greater. The microchannels with cylinder and v-groove profiles have better heat transfer performance, especially at larger Re cases, while, the microchannel with the protrusion devices is better from an entropy generation minimization perspective. Furthermore, the variation of the relative entropy generation S′/S′₀ are influenced by not only the change of Nu/Nu₀ and f/f₀, but also the physical parameters of working substances. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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19 pages, 4032 KiB

Open AccessArticle

Entropy Generation and Heat Transfer Performances of Al₂O₃-Water Nanofluid Transitional Flow in Rectangular Channels with Dimples and Protrusions

by Yonghui Xie^1,*, Lu Zheng¹, Di Zhang² and Gongnan Xie³

¹ School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

² Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

³ Department of Mechanical and Power Engineering, School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Entropy 2016, 18(4), 148; https://doi.org/10.3390/e18040148 - 19 Apr 2016

Cited by 19 | Viewed by 6144

Abstract

Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al₂O₃-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this [...] Read more.

Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al₂O₃-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this study. Four different volume fractions are considered and the boundary condition with a constant heat flux is adopted. The flow Reynolds number covers laminar flow, transitional flow and turbulent flow. The influences of the flow regime and nanofluid volume fraction are examined. Furthermore, dimples and protrusions are employed, and the impacts on heat transfer characteristic and entropy generation are acquired. It is found that the average heat transfer entropy generation rate descends and the average friction entropy generation rate rises with an increasing nanofluid volume fraction. The effect of nanofluid on average heat transfer entropy generation rate declines when Reynolds number ascends, which is inverse for average friction entropy generation rate. The average wall temperature and temperature uniformity both drop accompanied with increasing pumping power with the growth in nanofluid volume fraction. The employment of dimples and protrusions significantly decreases the average entropy generation rate and improve the heat transfer performance. The effect of dimple-case shows great difference with that of protrusion-case. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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14 pages, 2899 KiB

Open AccessArticle

Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface

by Jia Qing¹, Muhammad Mubashir Bhatti², Munawwar Ali Abbas³, Mohammad Mehdi Rashidi^1,4 and Mohamed El-Sayed Ali^5,*

¹ Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

² Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

³ Department of Mathematics, Shanghai University, Shanghai 201804, China

⁴ ENN-Tongji Clean Energy Institute of Advanced Studies, Tongji University, Shanghai 200072, China

⁵ Mechanical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Entropy 2016, 18(4), 123; https://doi.org/10.3390/e18040123 - 6 Apr 2016

Cited by 216 | Viewed by 9414

Abstract

In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation [...] Read more.

In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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16 pages, 5104 KiB

Open AccessArticle

Entropy Generation on MHD Blood Flow of Nanofluid Due to Peristaltic Waves

by Mohammad Mehdi Rashidi^1,2

, Muhammad Mubashir Bhatti³, Munawwar Ali Abbas⁴ and Mohamed El-Sayed Ali^5,*

¹ Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

² ENN-Tongji Clean Energy Institute of Advanced Studies, Tongji University, Shanghai 200072, China

³ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

⁴ Department of Mathematics, Shanghai University, Shanghai 200444, China

⁵ Mechanical Engineering Department, College of Engineering, King Saud University, P. O. Box 800, Riyadh 11421, Saudi Arabia

Entropy 2016, 18(4), 117; https://doi.org/10.3390/e18040117 - 1 Apr 2016

Cited by 110 | Viewed by 7485

Abstract

This present study describes the entropy generation on magnetohydrodynamic (MHD) blood flow of a nanofluid induced by peristaltic waves. The governing equation of continuity, equation of motion, nano-particle and entropy equations are solved by neglecting the inertial forces and taking long wavelength approximation. [...] Read more.

This present study describes the entropy generation on magnetohydrodynamic (MHD) blood flow of a nanofluid induced by peristaltic waves. The governing equation of continuity, equation of motion, nano-particle and entropy equations are solved by neglecting the inertial forces and taking long wavelength approximation. The resulting highly non-linear coupled partial differential equation has been solved analytically with the help of perturbation method. Mathematical and graphical results of all the physical parameters for velocity, concentration, temperature, and entropy are also presented. Numerical computation has been used to evaluate the expression for the pressure rise and friction forces. Currently, magnetohydrodynamics is applicable in pumping the fluids for pulsating and non-pulsating continuous flows in different microchannel designs and it also very helpful to control the flow. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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13 pages, 2518 KiB

Open AccessArticle

Analysis of Entropy Generation in the Flow of Peristaltic Nanofluids in Channels With Compliant Walls

by Munawwar Ali Abbas¹, Yanqin Bai^1,*, Mohammad Mehdi Rashidi^2,3

and Muhammad Mubashir Bhatti⁴

¹ Department of Mathematics, Shanghai University, Shanghai 200444, China

² Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

³ ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai 200072, China

⁴ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Entropy 2016, 18(3), 90; https://doi.org/10.3390/e18030090 - 11 Mar 2016

Cited by 85 | Viewed by 6381

Abstract

Entropy generation during peristaltic flow of nanofluids in a non-uniform two dimensional channel with compliant walls has been studied. The mathematical modelling of the governing flow problem is obtained under the approximation of long wavelength and zero Reynolds number (creeping flow regime). The [...] Read more.

Entropy generation during peristaltic flow of nanofluids in a non-uniform two dimensional channel with compliant walls has been studied. The mathematical modelling of the governing flow problem is obtained under the approximation of long wavelength and zero Reynolds number (creeping flow regime). The resulting non-linear partial differential equations are solved with the help of a perturbation method. The analytic and numerical results of different parameters are demonstrated mathematically and graphically. The present analysis provides a theoretical model to estimate the characteristics of several Newtonian and non-Newtonian fluid flows, such as peristaltic transport of blood. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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16 pages, 2504 KiB

Open AccessArticle

Sensitivity Analysis of Entropy Generation in Nanofluid Flow inside a Channel by Response Surface Methodology

by Bijan Darbari, Saman Rashidi and Javad Abolfazli Esfahani^*

Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 91775-1111, Iran

Entropy 2016, 18(2), 52; https://doi.org/10.3390/e18020052 - 5 Feb 2016

Cited by 75 | Viewed by 6094

Abstract

Nanofluids can afford excellent thermal performance and have a major role in energy conservation aspect. In this paper, a sensitivity analysis has been performed by using response surface methodology to calculate the effects of nanoparticles on the entropy generation. For this purpose, the [...] Read more.

Nanofluids can afford excellent thermal performance and have a major role in energy conservation aspect. In this paper, a sensitivity analysis has been performed by using response surface methodology to calculate the effects of nanoparticles on the entropy generation. For this purpose, the laminar forced convection of Al₂O₃-water nanofluid flow inside a channel is considered. The total entropy generation rates consist of the entropy generation rates due to heat transfer and friction loss are calculated by using velocity and temperature gradients. The continuity, momentum and energy equations have been solved numerically using a finite volume method. The sensitivity of the entropy generation rate to different parameters such as the solid volume fraction, the particle diameter, and the Reynolds number is studied in detail. Series of simulations were performed for a range of solid volume fraction 0 ≤ ϕ ≤ 0.05 , particle diameter 30 nm ≤ d p ≤ 90 nm , and the Reynolds number 200 ≤ Re ≤ 800. The results showed that the total entropy generation is more sensitive to the Reynolds number rather than the nanoparticles diameter or solid volume fraction. Also, the magnitude of total entropy generation, which increases with increase in the Reynolds number, is much higher for the pure fluid rather than the nanofluid. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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18 pages, 3608 KiB

Open AccessArticle

Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field

by Ali Chamkha^1,*

, Muneer Ismael²

, Abbas Kasaeipoor³

and Taher Armaghani³

¹ Mechanical Engineering Department, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi Arabia

² Mechanical Engineering Department, College of Engineering, University of Basrah, Basrah 61004, Iraq

³ Department of Engineering, Mahdishahr Branch, Islamic Azad University, Mahdishahr 75915-35618, Iran

Entropy 2016, 18(2), 50; https://doi.org/10.3390/e18020050 - 5 Feb 2016

Cited by 146 | Viewed by 8120

Abstract

This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite [...] Read more.

This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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22 pages, 3518 KiB

Open AccessArticle

Natural Convection and Entropy Generation in Nanofluid Filled Entrapped Trapezoidal Cavities under the Influence of Magnetic Field

by Fatih Selimefendigil^1,*,†, Hakan F. Öztop^2,3,† and Nidal Abu-Hamdeh^3,†

¹ Department of Mechanical Engineering, Celal Bayar University, 45140 Manisa, Turkey

² Department of Mechanical Engineering, Technology Faculty, Fırat University, 23119 Elazığ, Turkey

³ Department of Mechanical Engineering, King Abdulaziz University, 21589 Jeddah, Saudi Arabia

^† These authors contributed equally to this work.

Entropy 2016, 18(2), 43; https://doi.org/10.3390/e18020043 - 28 Jan 2016

Cited by 71 | Viewed by 6696

Abstract

In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al₂O₃-water) nanofluid. The top and bottom [...] Read more.

In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al₂O₃-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined walls of the enclosures are at constant cold temperature. Different combinations of Hartmann numbers are imposed on the upper and lower trapezoidal cavities. Numerical simulations are conducted for different values of Rayleigh numbers, Hartmann number and solid volume fraction of the nanofluid by using the finite element method. In the upper and lower trapezoidal cavities magnetic fields with different combinations of Hartmann numbers are imposed. It is observed that the averaged heat transfer reduction with magnetic field is more pronounced at the highest value of the Rayleigh number. When there is no magnetic field in the lower cavity, the averaged Nusselt number enhances as the value of the Hartmann number of the upper cavity increases. The heat transfer enhancement rates with nanofluids which are in the range of 10% and 12% are not affected by the presence of the magnetic field. Second law analysis of the system for various values of Hartmann number and nanoparticle volume fractions of upper and lower trapezoidal domains is performed. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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15 pages, 3951 KiB

Open AccessArticle

Analysis of Entropy Generation in Natural Convection of Nanofluid inside a Square Cavity Having Hot Solid Block: Tiwari and Das’ Model

by Mikhail A. Sheremet^1,2, Hakan F. Oztop^3,4, Ioan Pop^5,* and Nidal Abu-Hamdeh⁴

¹ Department of Theoretical Mechanics, Faculty of Mechanics and Mathematics, Tomsk State University, 634050 Tomsk, Russia

² Institute of Power Engineering, Tomsk Polytechnic University, 634050 Tomsk, Russia

³ Department of Mechanical Engineering, Technology Faculty, Fırat University, 23100 Elazig, Turkey

⁴ Department of Mechanical Engineering, Engineering Faculty, King Abdulaziz University, 21589 Jeddah, Saudi Arabia

⁵ Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Entropy 2016, 18(1), 9; https://doi.org/10.3390/e18010009 - 31 Dec 2015

Cited by 118 | Viewed by 8235

Abstract

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume [...] Read more.

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume method. The study is performed for different geometrical ratio of solid inserted block and corner isothermal cooler, Rayleigh number and solid volume fraction parameter of nanoparticles. It is observed that an insertion of nanoparticles leads to enhancement of heat transfer and attenuation of convective flow inside the cavity. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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12 pages, 1106 KiB

Open AccessArticle

Effect of Magnetic Field on Entropy Generation in a Microchannel Heat Sink with Offset Fan Shaped

by Mohammad Nasiri¹, Mohammad Mehdi Rashidi^2,3,* and Giulio Lorenzini⁴

¹ Department Mechanical Engineering, Faculty of Mechanical Engineering, University of Tabriz, Tabriz 5166616471, Iran

² Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China

³ ENN-Tongji Clean Energy Institute of Advanced Studies, Tongji University, Shanghai 201804, China

⁴ Department of Industrial Engineering, University of Parma, Parma 43124, Italy

Entropy 2016, 18(1), 10; https://doi.org/10.3390/e18010010 - 29 Dec 2015

Cited by 21 | Viewed by 7153

Abstract

In this study, convection flow in microchannel heat sink with offset fan-shaped reentrant cavities in sidewall filled with Fe₃O₄-water is numerically investigated. The effects of changing some parameters such as Reynolds number and magnetic field are considered. The nanofluid [...] Read more.

In this study, convection flow in microchannel heat sink with offset fan-shaped reentrant cavities in sidewall filled with Fe₃O₄-water is numerically investigated. The effects of changing some parameters such as Reynolds number and magnetic field are considered. The nanofluid flow is laminar, steady and incompressible, while the thermo-physical properties of nanoparticles were assumed constant. A finite volume method and two phase mixture models were used to simulate the flow. The obtained results show that the frictional entropy generation increases as Reynolds number increases, while a reverse trend is observed for thermal entropy generation. By applying a non-uniform magnetic field, the entropy generation due to heat transfer decreases at first and then increases. When using the uniform magnetic field, the frictional entropy generation and thermal entropy generation is negligible. For all studied cases, the total entropy generation decreases using non-uniform magnetic fields. The results indicate that by increasing the magnetic field power, the total entropy generation decreases. Full article

(This article belongs to the Special Issue Entropy in Nanofluids)

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