Symmetry

Research

Jump to: Review

14 pages, 3580 KiB

Open AccessArticle

Rotating 3D Flow of Hybrid Nanofluid on Exponentially Shrinking Sheet: Symmetrical Solution and Duality

by Liaquat Ali Lund, Zurni Omar, Sumera Dero, Dumitru Baleanu and Ilyas Khan

Symmetry 2020, 12(10), 1637; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101637 - 05 Oct 2020

Cited by 22 | Viewed by 2003

Abstract

This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (

A l_{2} O_{3}

), and copper [...] Read more.

This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (

A l_{2} O_{3}

), and copper (

C u

) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (

Ω

). Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

16 pages, 5781 KiB

Open AccessArticle

Magnetized Flow of Cu + Al₂O₃ + H₂O Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability

by Liaquat Ali Lund, Zurni Omar, Sumera Dero, Ilyas Khan, Dumitru Baleanu and Kottakkaran Sooppy Nisar

Symmetry 2020, 12(9), 1513; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091513 - 14 Sep 2020

Cited by 25 | Viewed by 2594

Abstract

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been [...] Read more.

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of

S_{c} \leq S and M_{c} \leq M

(

S_{c} > S and M_{c} > M

). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

18 pages, 1333 KiB

Open AccessArticle

Hybrid Nanofluid Flow Past a Shrinking Cylinder with Prescribed Surface Heat Flux

by Najiyah Safwa Khashi’ie, Iskandar Waini, Nurul Amira Zainal, Khairum Hamzah and Abdul Rahman Mohd Kasim

Symmetry 2020, 12(9), 1493; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091493 - 10 Sep 2020

Cited by 40 | Viewed by 2596

Abstract

This numerical study was devoted to examining the occurrence of non-unique solutions in boundary layer flow due to deformable surfaces (cylinder and flat plate) with the imposition of prescribed surface heat flux. The hybrid Al

_{2}

O

_{3}

-Cu/water nanofluid was formulated using [...] Read more.

This numerical study was devoted to examining the occurrence of non-unique solutions in boundary layer flow due to deformable surfaces (cylinder and flat plate) with the imposition of prescribed surface heat flux. The hybrid Al

_{2}

O

_{3}

-Cu/water nanofluid was formulated using the single phase model with respective correlations of hybrid nanofluids. The governing model was simplified by adopting a similarity transformation. The transformed differential equations were then numerically computed using the efficient bvp4c solver with the ranges of the control parameters

0.5 % \leq ϕ_{1}, ϕ_{2} \leq 1.5 %

(Al

_{2}

O

_{3}

and Cu volumetric concentration),

0 \leq K \leq 0.2

(curvature parameter),

2.6 < S \leq 3.2

(suction parameter) and

- 2.5 < λ \leq 0.5

(stretching/shrinking parameter). Dual steady solutions are presentable for both a cylinder

(K > 0)

and a flat plate

(K = 0)

with the inclusion of only the suction (transpiration) parameter. The real and stable solutions were mathematically validated through the stability analysis. The Al

_{2}

O

_{3}

-Cu/water nanofluid with

ϕ_{1} = 0.5 %

(alumina) and

ϕ_{2} = 1.5 %

(copper) has the highest skin friction coefficient and heat transfer rate, followed by the hybrid nanofluids with volumetric concentrations

(ϕ_{1} = 1 %, ϕ_{2} = 1 %)

and

(ϕ_{1} = 1.5 %, ϕ_{2} = 0.5 %)

, respectively. Surprisingly, the flat plate surface abates the separation of boundary layer while it enhances the heat transfer process. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

19 pages, 11081 KiB

Open AccessArticle

Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

by Liaquat Ali Lund, Zurni Omar, Ilyas Khan, El-Sayed M. Sherif and Hany S. Abdo

Symmetry 2020, 12(7), 1162; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071162 - 13 Jul 2020

Cited by 9 | Viewed by 2206

Abstract

In this research, we intend to develop a dynamical system for the magnetohydrodynamic (MHD) flow of an electrically conducting Casson nanofluid on exponentially shrinking and stretching surfaces, in the presence of a velocity and concertation slip effect, with convective boundary conditions. There are [...] Read more.

In this research, we intend to develop a dynamical system for the magnetohydrodynamic (MHD) flow of an electrically conducting Casson nanofluid on exponentially shrinking and stretching surfaces, in the presence of a velocity and concertation slip effect, with convective boundary conditions. There are three main objectives of this article, specifically, to discuss the heat characteristics of flow, to find multiple solutions on both surfaces, and to do stability analyses. The main equations of flow are governed by the Brownian motion, the Prandtl number, and the thermophoresis parameters, the Schmid and Biot numbers. The shooting method and three-stage Lobatto IIIa formula have been employed to solve the equations. The ranges of the dual solutions are

f_{w c 1} \leq f_{w}

and

λ_{c} \leq λ

, while the no solution ranges are

f_{w c 1} > f_{w}

and

λ_{c} > λ

. The results reveal that the temperature of the fluid increases with the extended values of the thermophoresis parameter, the Brownian motion parameter, and the Hartmann and Biot numbers, for both solutions. The presence of dual solutions depends on the suction parameter. In order to indicate that the first solution is physically relevant and stable, a stability analysis has been performed. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

31 pages, 7466 KiB

Open AccessArticle

Effect of Zinc Oxide Nano-Additives and Soybean Biodiesel at Varying Loads and Compression Ratios on VCR Diesel Engine Characteristics

by Rakhamaji S. Gavhane, Ajit M. Kate, Abhay Pawar, Mohammad Reza Safaei, Manzoore Elahi M. Soudagar, Muhammad Mujtaba Abbas, Hafiz Muhammad Ali, Nagaraj R Banapurmath, Marjan Goodarzi, Irfan Anjum Badruddin, Waqar Ahmed and Kiran Shahapurkar

Symmetry 2020, 12(6), 1042; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12061042 - 22 Jun 2020

Cited by 77 | Viewed by 5917

Abstract

The present investigation is directed towards synthesis of zinc oxide (ZnO) nanoparticles and steady blending with soybean biodiesel (SBME25) to improve the fuel properties of SBME25 and enhance the overall characteristics of a variable compression ratio diesel engine. The soybean biodiesel (SBME) was [...] Read more.

The present investigation is directed towards synthesis of zinc oxide (ZnO) nanoparticles and steady blending with soybean biodiesel (SBME25) to improve the fuel properties of SBME25 and enhance the overall characteristics of a variable compression ratio diesel engine. The soybean biodiesel (SBME) was prepared using the transesterification reaction. Numerous characterization tests were carried out to ascertain the shape and size of zinc oxide nanoparticles. The synthesized asymmetric ZnO nanoparticles were dispersed in SBME25 at three dosage levels (25, 50, and 75 ppm) with sodium dodecyl benzene sulphonate (SDBS) surfactant using the ultrasonication process. The quantified physicochemical properties of all the fuels blends were in symmetry with the American society for testing and materials (ASTM) standards. Nanofuel blends demonstrated enhanced fuel properties compared with SBME25. The engine was operated at two different compression ratios (18.5 and 21.5) and a comparison was made, and best fuel blend and compression ratio (CR) were selected. Fuel blend SBME25ZnO50 and compression ratio (CR) of 21.5 illustrated an overall enhancement in engine characteristics. For SBME25ZnO50 and CR 21.5 fuel blend, brake thermal efficiency (BTE) increased by 23.2%, brake specific fuel consumption (BSFC) were reduced by 26.66%, and hydrocarbon (HC), CO, smoke, and CO₂ emissions were reduced by 32.234%, 28.21% 22.55% and 21.66%, respectively; in addition, the heat release rate (HRR) and mean gas temperature (MGT) improved, and ignition delay (ID) was reduced. In contrast, the NOx emissions increased for all the nanofuel blends due to greater supply of oxygen and increase in the temperature of the combustion chamber. At a CR of 18.5, a similar trend was observed, while the values of engine characteristics were lower compared with CR of 21.5. The properties of nanofuel blend SBME25ZnO50 were in symmetry and comparable to the diesel fuel. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

13 pages, 11841 KiB

Open AccessArticle

Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body

by Mikhail A. Sheremet, Dalia Sabina Cimpean and Ioan Pop

Symmetry 2020, 12(4), 593; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040593 - 08 Apr 2020

Cited by 29 | Viewed by 2783

Abstract

A problem with the thermogravitational energy transference of a hybrid nanofluid (Al₂O₃-SiO₂/H₂O) in a porous space with a central heat-conducting body has been presented and numerical analysis has been performed. Governing equations, transformed in terms [...] Read more.

A problem with the thermogravitational energy transference of a hybrid nanofluid (Al₂O₃-SiO₂/H₂O) in a porous space with a central heat-conducting body has been presented and numerical analysis has been performed. Governing equations, transformed in terms of non-dimensional parameters, have been solved by a developed numerical algorithm based on the finite difference technique. The behavior of streamlines and isotherms was investigated, and the impact of various important characteristics is discussed. The variation in the average and local Nusselt numbers was studied; by selecting various appropriate nano-sized particle combinations in hybrid nanosuspension, the desired energy transport strength could be obtained. The results were compared and successfully validated with previous reported numerical and experimental data from the literature. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

18 pages, 3151 KiB

Open AccessArticle

Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance

by Hassan Waqas, Sami Ullah Khan, Iskander Tlili, Muhammad Awais and Mostafa S. Shadloo

Symmetry 2020, 12(2), 214; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020214 - 02 Feb 2020

Cited by 44 | Viewed by 2561

Abstract

The analysis of bioconvection flow nanofluids is the topic of concern in recent decades as it involves a variety of physical significance in biotechnology. Bioconvection has many applications in the interdisciplinary field of sciences such as in biomedical science, biofuel biotechnology, and enzyme-based [...] Read more.

The analysis of bioconvection flow nanofluids is the topic of concern in recent decades as it involves a variety of physical significance in biotechnology. Bioconvection has many applications in the interdisciplinary field of sciences such as in biomedical science, biofuel biotechnology, and enzyme-based biosensors, among others. The aim of the current work is to analyze the bioconvection phenomenon in the two-dimensional steady flow of viscoelastic nanofluid over a vertical surface. Here, the effects of activation energy, second-order slip, and nanoparticles zero mass flux conditions are considered to investigate the flow problem. Based on dimensionless variables, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) which are further solved numerically by using a built-in BVP4C approach in MATLAB software. Various controlling parameters like Hartman number, viscoelastic parameter, first and second-order slip factors, buoyancy ratio parameter, thermophoresis parameter, Brownian motion constant, bioconvection Lewis number and Peclet number are graphically illustrated for the distributions of velocity, temperature, concentration, and motile microorganism. Moreover, the variation of local Nusselt number, local Sherwood number, and motile density number are numerically investigated for the involved parameters. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

17 pages, 2029 KiB

Open AccessArticle

Thermal Conductivity Modeling of Nanofluids Contain MgO Particles by Employing Different Approaches

by Na Wang, Akbar Maleki, Mohammad Alhuyi Nazari, Iskander Tlili and Mostafa Safdari Shadloo

Symmetry 2020, 12(2), 206; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12020206 - 01 Feb 2020

Cited by 59 | Viewed by 3059

Abstract

The existence of solid-phase nanoparticles remarkably improves the thermal conductivity of the fluids. The enhancement in this property of the nanofluids is affected by different items such as the solid-phase volume fraction and dimensions, temperature, etc. In the current paper, three different mathematical [...] Read more.

The existence of solid-phase nanoparticles remarkably improves the thermal conductivity of the fluids. The enhancement in this property of the nanofluids is affected by different items such as the solid-phase volume fraction and dimensions, temperature, etc. In the current paper, three different mathematical models, including polynomial correlation, Multivariate Adaptive Regression Spline (MARS), and Group Method of Data Handling (GMDH), are applied to forecast the thermal conductivity of nanofluids containing MgO particles. The inputs of the model are the base fluid thermal conductivity, volume concentration, and average dimension of solid-phase, and nanofluids’ temperature. Comparing the proposed models revealed higher confidence of GMDH in estimating the thermal conductivity, which is attributed to its complicated structure and more appropriate consideration of the input’s interaction. The values of R-squared for the correlation, MARS, and GMDH are 0.9949, 0.9952, and 0.9991, respectively. In addition, based on the sensitivity analysis, the effect of thermal conductivity of the base fluid on the overall thermal conductivity of nanofluids is more remarkable compared with the other inputs such as volume fraction, temperature, and dimensions of the particles which are used as the inputs of the models. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

Review

Jump to: Research

24 pages, 4221 KiB

Open AccessReview

A Comprehensive Review on Theoretical Aspects of Nanofluids: Exact Solutions and Analysis

by Nadeem Ahmad Sheikh, Dennis Ling Chuan Ching and Ilyas Khan

Symmetry 2020, 12(5), 725; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050725 - 03 May 2020

Cited by 18 | Viewed by 4346

Abstract

In the present era, nanofluids are one of the most important and hot issue for scientists, physicists, and mathematicians. Nanofluids have many important and updated characteristics compared to conventional fluids. The thermal conductivity, thermal expansion, and the heat transfer rate of conventional fluids [...] Read more.

In the present era, nanofluids are one of the most important and hot issue for scientists, physicists, and mathematicians. Nanofluids have many important and updated characteristics compared to conventional fluids. The thermal conductivity, thermal expansion, and the heat transfer rate of conventional fluids are not up to the mark for industrial and experimental uses. To overcome these deficiencies, nanoparticles have been dispersed into base fluids to make them more efficient. The heat transfer characteristics through symmetry trapezoidal-corrugated channels can be enhanced using nanofluids. In the present article, a literature survey has been presented for different models of nanofluids and their solutions—particularly, exact solutions. The models for hybrid nanofluids were also mentioned in the present study. Furthermore, some important and most used models for the viscosity, density, coefficient of thermal expansion, coefficient of mass expansion, heat capacitance, electrical conductivity, and thermal conductivity are also presented in tabular form. Moreover, some future suggestions are also provided in this article. Full article

(This article belongs to the Special Issue Nanofluids in Advanced Symmetric Systems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Nanofluids in Advanced Symmetric Systems

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (9 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI