Entropy

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9468 KiB

Open AccessArticle

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

by Lioua Kolsi, Omid Mahian, Hakan F. Öztop, Walid Aich, Mohamed Naceur Borjini, Nidal Abu-Hamdeh and Habib Ben Aissia

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

Cited by 52 | Viewed by 5741

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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4008 KiB

Open AccessArticle

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

by Muhammad Mubashir Bhatti, Tehseen Abbas, Mohammad Mehdi Rashidi, Mohamed El-Sayed Ali and Zhigang Yang

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

Cited by 135 | Viewed by 8244

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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3877 KiB

Open AccessArticle

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

by Muhammad Mubashir Bhatti, Tehseen Abbas, Mohammad Mehdi Rashidi and Mohamed El-Sayed Ali

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

Cited by 105 | Viewed by 7344

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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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 Freidoonimehr, Mohammad Mehdi Rashidi, Shirley Abelman and Giulio Lorenzini

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

Cited by 23 | Viewed by 7936

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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4193 KiB

Open AccessArticle

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

by Ping Li, Yonghui Xie, Di Zhang and Gongnan Xie

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

Cited by 45 | Viewed by 5757

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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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, Lu Zheng, Di Zhang and Gongnan Xie

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

Cited by 17 | Viewed by 5889

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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2899 KiB

Open AccessArticle

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

by Jia Qing, Muhammad Mubashir Bhatti, Munawwar Ali Abbas, Mohammad Mehdi Rashidi and Mohamed El-Sayed Ali

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

Cited by 209 | Viewed by 9058

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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5104 KiB

Open AccessArticle

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

by Mohammad Mehdi Rashidi, Muhammad Mubashir Bhatti, Munawwar Ali Abbas and Mohamed El-Sayed Ali

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

Cited by 104 | Viewed by 7196

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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2518 KiB

Open AccessArticle

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

by Munawwar Ali Abbas, Yanqin Bai, Mohammad Mehdi Rashidi and Muhammad Mubashir Bhatti

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

Cited by 79 | Viewed by 6130

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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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

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

Cited by 69 | Viewed by 5833

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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3608 KiB

Open AccessArticle

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

by Ali Chamkha, Muneer Ismael, Abbas Kasaeipoor and Taher Armaghani

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

Cited by 141 | Viewed by 7800

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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3518 KiB

Open AccessArticle

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

by Fatih Selimefendigil, Hakan F. Öztop and Nidal Abu-Hamdeh

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

Cited by 70 | Viewed by 6437

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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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, Hakan F. Oztop, Ioan Pop and Nidal Abu-Hamdeh

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

Cited by 116 | Viewed by 7872

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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1106 KiB

Open AccessArticle

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

by Mohammad Nasiri, Mohammad Mehdi Rashidi and Giulio Lorenzini

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

Cited by 18 | Viewed by 6892

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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