Special Issue "Symmetry and Fluid Mechanics"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 July 2019).

Special Issue Editor

Guest Editor
Prof. Rehmat Ellahi

1: Fulbright Fellow Department of Mechanical Engineering University of California Riverside, USA; 2: Chair Professor, Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; 3: Ex and founder Chairman, Department of Mathematics & Statistics IIUI, Islamabad Pakistan
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Interests: Nanofluid; non-Newtonian fluid; heat and mass transfer; porosity, MHD, Peristaltic, Blood flow

Special Issue Information

Dear Colleagues,

This Special Issue invites you to contribute your original research work and review articles on “Symmetry and Fluid Mechanics” that either advances the state-of-the-art of mathematical methods, theoretical, or experimental studies, or extends the bounds of existing methodologies to new contributions related to the symmetry, asymmetry, and lie symmetries of differential equations proposed as mathematical models in fluid mechanics to address current challenges. We hope that this Issue will provide an overall picture and up-to-date findings to readers of the scientific community that ultimately benefit the industrial sector regarding its specific market niches and end users.

Scope: Potential topics dealing with the following subheadings are deemed suitable for publication but are not limited to

  • The symmetry method, the lie group, homotopy perturbation, homotopy analysis, perturbative series, differential transform, integral transform, numerical simulations and approximate, finite element, volume and difference methods, and other new technologies;
  • Newtonian and non-Newtonian fluids;
  • Nanofluids and particle shape effects;
  • Convective heat and mass transfer;
  • Steady and unsteady flow problems;
  • Multiphase flow simulations;
  • Fractional order differential equations;
  • Thermodynamics;
  • Physiological fluid phenomena in biological systems.

Prof. Dr. Rehmat Ellahi
Guest Editor

Manuscript Submission Information

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Published Papers (24 papers)

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Research

Open AccessArticle
Peristaltic Pumping of Nanofluids through a Tapered Channel in a Porous Environment: Applications in Blood Flow
Symmetry 2019, 11(7), 868; https://doi.org/10.3390/sym11070868
Received: 22 May 2019 / Revised: 24 June 2019 / Accepted: 25 June 2019 / Published: 3 July 2019
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Abstract
In this study, we present an analytical study on blood flow analysis through with a tapered porous channel. The blood flow was driven by the peristaltic pumping. Thermal radiation effects were also taken into account. The convective and slip boundary conditions were also [...] Read more.
In this study, we present an analytical study on blood flow analysis through with a tapered porous channel. The blood flow was driven by the peristaltic pumping. Thermal radiation effects were also taken into account. The convective and slip boundary conditions were also applied in this formulation. These conditions are very helpful to carry out the behavior of particle movement which may be utilized for cardiac surgery. The tapered porous channel had an unvarying wave speed with dissimilar amplitudes and phase. The non-dimensional analysis was utilized for some approximations such as the proposed mathematical modelling equations were modified by using a lubrication approach and the analytical solutions for stream function, nanoparticle temperature and volumetric concentration profiles were obtained. The impacts of various emerging parameters on the thermal characteristics and nanoparticles concentration were analyzed with the help of computational results. The trapping phenomenon was also examined for relevant parameters. It was also observed that the geometric parameters, like amplitudes, non-uniform parameters and phase difference, play an important role in controlling the nanofluids transport phenomena. The outcomes of the present model may be applicable in the smart nanofluid peristaltic pump which may be utilized in hemodialysis. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Modified MHD Radiative Mixed Convective Nanofluid Flow Model with Consideration of the Impact of Freezing Temperature and Molecular Diameter
Symmetry 2019, 11(6), 833; https://doi.org/10.3390/sym11060833
Received: 13 March 2019 / Revised: 9 April 2019 / Accepted: 16 April 2019 / Published: 25 June 2019
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Abstract
Magnetohydrodynamics (MHD) deals with the analysis of electrically conducting fluids. The study of nanofluids by considering the influence of MHD phenomena is a topic of great interest from an industrial and technological point of view. Thus, the modified MHD mixed convective, nonlinear, radiative [...] Read more.
Magnetohydrodynamics (MHD) deals with the analysis of electrically conducting fluids. The study of nanofluids by considering the influence of MHD phenomena is a topic of great interest from an industrial and technological point of view. Thus, the modified MHD mixed convective, nonlinear, radiative and dissipative problem was modelled over an arc-shaped geometry for Al2O3 + H2O nanofluid at 310 K and the freezing temperature of 273.15 K. Firstly, the model was reduced into a coupled set of ordinary differential equations using similarity transformations. The impact of the freezing temperature and the molecular diameter were incorporated in the energy equation. Then, the Runge–Kutta scheme, along with the shooting technique, was adopted for the mathematical computations and code was written in Mathematica 10.0. Further, a comprehensive discussion of the flow characteristics is provided. The results for the dynamic viscosity, heat capacity and effective density of the nanoparticles were examined for various nanoparticle diameters and volume fractions. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel
Symmetry 2019, 11(6), 757; https://doi.org/10.3390/sym11060757
Received: 20 March 2019 / Revised: 23 May 2019 / Accepted: 27 May 2019 / Published: 4 June 2019
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Abstract
In the current study, laminar heat transfer and direct fluid jet injection of oil/MWCNT nanofluid were numerically investigated with a finite volume method. Both slip and no-slip boundary conditions on solid walls were used. The objective of this study was to increase the [...] Read more.
In the current study, laminar heat transfer and direct fluid jet injection of oil/MWCNT nanofluid were numerically investigated with a finite volume method. Both slip and no-slip boundary conditions on solid walls were used. The objective of this study was to increase the cooling performance of heated walls inside a rectangular microchannel. Reynolds numbers ranged from 10 to 50; slip coefficients were 0.0, 0.04, and 0.08; and nanoparticle volume fractions were 0–4%. The results showed that using techniques for improving heat transfer, such as fluid jet injection with low temperature and adding nanoparticles to the base fluid, allowed for good results to be obtained. By increasing jet injection, areas with eliminated boundary layers along the fluid direction spread in the domain. Dispersing solid nanoparticles in the base fluid with higher volume fractions resulted in better temperature distribution and Nusselt number. By increasing the nanoparticle volume fraction, the temperature of the heated surface penetrated to the flow centerline and the fluid temperature increased. Jet injection with higher velocity, due to its higher fluid momentum, resulted in higher Nusselt number and affected lateral areas. Fluid velocity was higher in jet areas, which diminished the effect of the boundary layer. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Numerical Solution of Non-Newtonian Fluid Flow Due to Rotatory Rigid Disk
Symmetry 2019, 11(5), 699; https://doi.org/10.3390/sym11050699
Received: 12 March 2019 / Revised: 7 April 2019 / Accepted: 16 April 2019 / Published: 22 May 2019
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Abstract
In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced [...] Read more.
In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced above the rotating disk. The magnetized flow field is framed with Navier’s slip assumption. The Von Karman scheme is adopted to transform flow narrating equations in terms of reduced system. For better depiction a self-coded computational algorithm is executed rather than to move-on with build-in array. Numerical observations via magnetic, Lewis numbers, Casson, slip, Brownian motion, and thermophoresis parameters subject to radial, tangential velocities, temperature, and nanoparticles concentration are reported. The validation of numerical method being used is given through comparison with existing work. Comparative values of local Nusselt number and local Sherwood number are provided for involved flow controlling parameters. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Significance of Velocity Slip in Convective Flow of Carbon Nanotubes
Symmetry 2019, 11(5), 679; https://doi.org/10.3390/sym11050679
Received: 7 April 2019 / Revised: 16 April 2019 / Accepted: 18 April 2019 / Published: 17 May 2019
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Abstract
The present article inspects velocity slip impacts in three-dimensional flow of water based carbon nanotubes because of a stretchable rotating disk. Nanoparticles like single and multi walled carbon nanotubes (CNTs) are utilized. Graphical outcomes have been acquired for both single-walled carbon nanotubes (SWCNTs) [...] Read more.
The present article inspects velocity slip impacts in three-dimensional flow of water based carbon nanotubes because of a stretchable rotating disk. Nanoparticles like single and multi walled carbon nanotubes (CNTs) are utilized. Graphical outcomes have been acquired for both single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). The heat transport system is examined in the presence of thermal convective condition. Proper variables lead to a strong nonlinear standard differential framework. The associated nonlinear framework has been tackled by an optimal homotopic strategy. Diagrams have been plotted so as to examine how the temperature and velocities are influenced by different physical variables. The coefficients of skin friction and Nusselt number have been exhibited graphically. Our results indicate that the skin friction coefficient and Nusselt number are enhanced for larger values of nanoparticle volume fraction. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Boundary Layer Flow through Darcy–Brinkman Porous Medium in the Presence of Slip Effects and Porous Dissipation
Symmetry 2019, 11(5), 659; https://doi.org/10.3390/sym11050659
Received: 20 March 2019 / Revised: 22 April 2019 / Accepted: 6 May 2019 / Published: 11 May 2019
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Abstract
This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate [...] Read more.
This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Two-Phase Couette Flow of Couple Stress Fluid with Temperature Dependent Viscosity Thermally Affected by Magnetized Moving Surface
Symmetry 2019, 11(5), 647; https://doi.org/10.3390/sym11050647
Received: 19 March 2019 / Revised: 1 May 2019 / Accepted: 5 May 2019 / Published: 8 May 2019
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Abstract
The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of [...] Read more.
The Couette–Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds’ model was utilized. The Runge–Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Integer and Non-Integer Order Study of the GO-W/GO-EG Nanofluids Flow by Means of Marangoni Convection
Symmetry 2019, 11(5), 640; https://doi.org/10.3390/sym11050640
Received: 7 February 2019 / Revised: 14 March 2019 / Accepted: 22 March 2019 / Published: 7 May 2019
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Abstract
Characteristically, most fluids are not linear in their natural deeds and therefore fractional order models are very appropriate to handle these kinds of marvels. In this article, we studied the base solvents of water and ethylene glycol for the stable dispersion of graphene [...] Read more.
Characteristically, most fluids are not linear in their natural deeds and therefore fractional order models are very appropriate to handle these kinds of marvels. In this article, we studied the base solvents of water and ethylene glycol for the stable dispersion of graphene oxide to prepare graphene oxide-water (GO-W) and graphene oxide-ethylene glycol (GO-EG) nanofluids. The stable dispersion of the graphene oxide in the water and ethylene glycol was taken from the experimental results. The combined efforts of the classical and fractional order models were imposed and compared under the effect of the Marangoni convection. The numerical method for the non-integer derivative that was used in this research is known as a predictor corrector technique of the Adams–Bashforth–Moulton method (Fractional Differential Equation-12) or shortly (FDE-12). The impact of the modeled parameters were analyzed and compared for both GO-W and GO-EG nanofluids. The diverse effects of the parameters were observed through a fractional model rather than the traditional approach. Furthermore, it was observed that GO-EG nanofluids are more efficient due to their high thermal properties compared with GO-W nanofluids. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
MHD Boundary Layer Flow of Carreau Fluid over a Convectively Heated Bidirectional Sheet with Non-Fourier Heat Flux and Variable Thermal Conductivity
Symmetry 2019, 11(5), 618; https://doi.org/10.3390/sym11050618
Received: 1 April 2019 / Revised: 18 April 2019 / Accepted: 23 April 2019 / Published: 2 May 2019
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Abstract
In the present exploration, instead of the more customary parabolic Fourier law, we have adopted the hyperbolic Cattaneo–Christov (C–C) heat flux model to jump over the major hurdle of “parabolic energy equation”. The more realistic three-dimensional Carreau fluid flow analysis is conducted in [...] Read more.
In the present exploration, instead of the more customary parabolic Fourier law, we have adopted the hyperbolic Cattaneo–Christov (C–C) heat flux model to jump over the major hurdle of “parabolic energy equation”. The more realistic three-dimensional Carreau fluid flow analysis is conducted in attendance of temperature-dependent thermal conductivity. The other salient impacts affecting the considered model are the homogeneous-heterogeneous (h-h) reactions and magnetohydrodynamic (MHD). The boundary conditions supporting the problem are convective heat and of h-h reactions. The considered boundary layer problem is addressed via similarity transformations to obtain the system of coupled differential equations. The numerical solutions are attained by undertaking the MATLAB built-in function bvp4c. To comprehend the consequences of assorted parameters on involved distributions, different graphs are plotted and are accompanied by requisite discussions in the light of their physical significance. To substantiate the presented results, a comparison to the already conducted problem is also given. It is envisaged that there is a close correlation between the two results. This shows that dependable results are being submitted. It is noticed that h-h reactions depict an opposite behavior versus concentration profile. Moreover, the temperature of the fluid augments for higher values of thermal conductivity parameters. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
MHD Slip Flow of Casson Fluid along a Nonlinear Permeable Stretching Cylinder Saturated in a Porous Medium with Chemical Reaction, Viscous Dissipation, and Heat Generation/Absorption
Symmetry 2019, 11(4), 531; https://doi.org/10.3390/sym11040531
Received: 13 February 2019 / Revised: 7 March 2019 / Accepted: 8 March 2019 / Published: 12 April 2019
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Abstract
The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous [...] Read more.
The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous dissipation, and heat generation/absorption on flow fields is also investigated. Similarity transformations are employed to convert the nonlinear governing equations to nonlinear ordinary differential equations, and then solved via the Keller box method. Findings demonstrate that the magnitude of the friction factor and mass transfer rate are suppressed with increment in Casson parameter, whereas heat transfer rate is found to be intensified. Increase in the curvature parameter enhanced the flow field distributions. The magnitude of wall shear stress is noticed to be higher with an increase in porosity and suction/blowing parameters. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Modeling and Optimization of Gaseous Thermal Slip Flow in Rectangular Microducts Using a Particle Swarm Optimization Algorithm
Symmetry 2019, 11(4), 488; https://doi.org/10.3390/sym11040488
Received: 17 January 2019 / Revised: 31 March 2019 / Accepted: 2 April 2019 / Published: 4 April 2019
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Abstract
In this study, pressure-driven flow in the slip regime is investigated in rectangular microducts. In this regime, the Knudsen number lies between 0.001 and 0.1. The duct aspect ratio is taken as 0ε1. Rarefaction effects are introduced through [...] Read more.
In this study, pressure-driven flow in the slip regime is investigated in rectangular microducts. In this regime, the Knudsen number lies between 0.001 and 0.1. The duct aspect ratio is taken as 0 ε 1 . Rarefaction effects are introduced through the boundary conditions. The dimensionless governing equations are solved numerically using MAPLE and MATLAB is used for artificial neural network modeling. Using a MAPLE numerical solution, the shear stress and heat transfer rate are obtained. The numerical solution can be validated for the special cases when there is no slip (continuum flow), ε = 0 (parallel plates) and ε = 1 (square microducts). An artificial neural network is used to develop separate models for the shear stress and heat transfer rate. Both physical quantities are optimized using a particle swarm optimization algorithm. Using these results, the optimum values of both physical quantities are obtained in the slip regime. It is shown that the optimal values ensue for the square microducts at the beginning of the slip regime. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative
Symmetry 2019, 11(4), 449; https://doi.org/10.3390/sym11040449
Received: 3 January 2019 / Revised: 15 March 2019 / Accepted: 17 March 2019 / Published: 1 April 2019
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Abstract
In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive [...] Read more.
In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Influence of Cattaneo–Christov Heat Flux on MHD Jeffrey, Maxwell, and Oldroyd-B Nanofluids with Homogeneous-Heterogeneous Reaction
Symmetry 2019, 11(3), 439; https://doi.org/10.3390/sym11030439
Received: 4 March 2019 / Revised: 17 March 2019 / Accepted: 19 March 2019 / Published: 25 March 2019
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Abstract
This research article deals with the determination of magnetohydrodynamic steady flow of three combile nanofluids (Jefferey, Maxwell, and Oldroyd-B) over a stretched surface. The surface is considered to be linear. The Cattaneo–Christov heat flux model was considered necessary to study the relaxation properties [...] Read more.
This research article deals with the determination of magnetohydrodynamic steady flow of three combile nanofluids (Jefferey, Maxwell, and Oldroyd-B) over a stretched surface. The surface is considered to be linear. The Cattaneo–Christov heat flux model was considered necessary to study the relaxation properties of the fluid flow. The influence of homogeneous-heterogeneous reactions (active for auto catalysts and reactants) has been taken in account. The modeled problem is solved analytically. The impressions of the magnetic field, Prandtl number, thermal relaxation time, Schmidt number, homogeneous–heterogeneous reactions strength are considered through graphs. The velocity field diminished with an increasing magnetic field. The temperature field diminished with an increasing Prandtl number and thermal relaxation time. The concentration field upsurged with the increasing Schmidt number which decreased with increasing homogeneous-heterogeneous reactions strength. Furthermore, the impact of these parameters on skin fraction, Nusselt number, and Sherwood number were also accessible through tables. A comparison between analytical and numerical methods has been presented both graphically and numerically. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet
Symmetry 2019, 11(3), 438; https://doi.org/10.3390/sym11030438
Received: 14 March 2019 / Revised: 20 March 2019 / Accepted: 22 March 2019 / Published: 25 March 2019
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Abstract
In this paper, Jeffrey fluid is studied in a microgravity environment. Unsteady two-dimensional incompressible and laminar g-Jitter mixed convective boundary layer flow over an inclined stretching sheet is examined. Heat generation and Magnetohydrodynamic MHD effects are also considered. The governing boundary layer equations [...] Read more.
In this paper, Jeffrey fluid is studied in a microgravity environment. Unsteady two-dimensional incompressible and laminar g-Jitter mixed convective boundary layer flow over an inclined stretching sheet is examined. Heat generation and Magnetohydrodynamic MHD effects are also considered. The governing boundary layer equations together with boundary conditions are converted into a non-similar arrangement using appropriate similarity conversions. The transformed system of equations is resolved mathematically by employing an implicit finite difference pattern through quasi-linearization method. Numerical results of temperature, velocity, local heat transfer, and local skin friction coefficient are computed and plotted graphically. It is found that local skin friction and local heat transfer coefficients increased for increasing Deborah number when the magnitude of the gravity modulation is unity. Assessment with previously published results showed an excellent agreement. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points
Symmetry 2019, 11(3), 412; https://doi.org/10.3390/sym11030412
Received: 31 December 2018 / Revised: 6 March 2019 / Accepted: 8 March 2019 / Published: 20 March 2019
Cited by 1 | PDF Full-text (8429 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, steady two-dimensional laminar incompressible magnetohydrodynamic flow over an exponentially shrinking sheet with the effects of slip conditions and viscous dissipation is examined. An extended Darcy Forchheimer model was considered to observe the porous medium embedded in a non-Newtonian-Casson-type nanofluid. The [...] Read more.
In this paper, steady two-dimensional laminar incompressible magnetohydrodynamic flow over an exponentially shrinking sheet with the effects of slip conditions and viscous dissipation is examined. An extended Darcy Forchheimer model was considered to observe the porous medium embedded in a non-Newtonian-Casson-type nanofluid. The governing equations were converted into nonlinear ordinary differential equations using an exponential similarity transformation. The resultant equations for the boundary values problem (BVPs) were reduced to initial values problems (IVPs) and then shooting and Fourth Order Runge-Kutta method (RK-4th method) were applied to obtain numerical solutions. The results reveal that multiple solutions occur only for the high suction case. The results of the stability analysis showed that the first (second) solution is physically reliable (unreliable) and stable (unstable). Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
MHD Nanofluids in a Permeable Channel with Porosity
Symmetry 2019, 11(3), 378; https://doi.org/10.3390/sym11030378
Received: 19 January 2019 / Revised: 25 February 2019 / Accepted: 8 March 2019 / Published: 14 March 2019
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Abstract
This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely [...] Read more.
This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely to the flow direction. The walls of the channel are permeable. The flow is due to convection combined with uniform suction/injection at the boundary. The model is formulated in terms of unsteady, one-dimensional partial differential equations (PDEs) with imposed physical conditions. The cluster effect of nanoparticles is demonstrated in the C 2 H 6 O 2 , and H 2 O base fluids. The perturbation technique is used to obtain a closed-form solution for the velocity and temperature distributions. Based on numerical experiments, it is concluded that both the velocity and temperature profiles are significantly affected by ϕ . Moreover, the magnetic parameter retards the nanofluid motion whereas porosity accelerates it. Each H 2 O -based and C 2 H 6 O 2 -based nanofluid in the suction case have a higher magnitude of velocity as compared to the injections case. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current
Symmetry 2019, 11(3), 333; https://doi.org/10.3390/sym11030333
Received: 7 January 2019 / Revised: 24 February 2019 / Accepted: 1 March 2019 / Published: 6 March 2019
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Abstract
The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The [...] Read more.
The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Cattaneo–Christov Heat Flux Model for Three-Dimensional Rotating Flow of SWCNT and MWCNT Nanofluid with Darcy–Forchheimer Porous Medium Induced by a Linearly Stretchable Surface
Symmetry 2019, 11(3), 331; https://doi.org/10.3390/sym11030331
Received: 2 January 2019 / Revised: 14 February 2019 / Accepted: 14 February 2019 / Published: 6 March 2019
Cited by 4 | PDF Full-text (2502 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we investigated the 3-D Magnetohydrodynamic (MHD) rotational nanofluid flow through a stretching surface. Carbon nanotubes (SWCNTs and MWCNTs) were used as nano-sized constituents, and water was used as a base fluid. The Cattaneo–Christov heat flux model was used for heat [...] Read more.
In this paper we investigated the 3-D Magnetohydrodynamic (MHD) rotational nanofluid flow through a stretching surface. Carbon nanotubes (SWCNTs and MWCNTs) were used as nano-sized constituents, and water was used as a base fluid. The Cattaneo–Christov heat flux model was used for heat transport phenomenon. This arrangement had remarkable visual and electronic properties, such as strong elasticity, high updraft stability, and natural durability. The heat interchanging phenomenon was affected by updraft emission. The effects of nanoparticles such as Brownian motion and thermophoresis were also included in the study. By considering the conservation of mass, motion quantity, heat transfer, and nanoparticles concentration the whole phenomenon was modeled. The modeled equations were highly non-linear and were solved using homotopy analysis method (HAM). The effects of different parameters are described in tables and their impact on different state variables are displayed in graphs. Physical quantities like Sherwood number, Nusselt number, and skin friction are presented through tables with the variations of different physical parameters. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle
Symmetry 2019, 11(3), 312; https://doi.org/10.3390/sym11030312
Received: 7 January 2019 / Revised: 31 January 2019 / Accepted: 2 February 2019 / Published: 2 March 2019
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Abstract
In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer [...] Read more.
In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer flow comprising single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with variable wall temperatures passing over a needle was examined. The numerical solutions for the similarity equations were obtained for the integer and fractional values by applying the Adams-type predictor corrector method. A comparison of the SWCNTs and MWCNTs for the classical and fractional schemes was investigated. The classical and fractional order impact of the physical parameters such as skin fraction and Nusselt number are presented physically and numerically. It was observed that the impact of the physical parameters over the momentum and thermal boundary layers in the classical model were limited; however, while utilizing the fractional model, the impact of the parameters varied at different intervals. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect
Symmetry 2019, 11(3), 297; https://doi.org/10.3390/sym11030297
Received: 4 January 2019 / Revised: 13 February 2019 / Accepted: 15 February 2019 / Published: 26 February 2019
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Abstract
A steady laminar flow over a vertical stretching sheet with the existence of viscous dissipation, heat source/sink, and magnetic fields has been numerically inspected through a shooting scheme based Runge—Kutta–Fehlberg-integration algorithm. The governing equation and boundary layer balance are expressed and then converted [...] Read more.
A steady laminar flow over a vertical stretching sheet with the existence of viscous dissipation, heat source/sink, and magnetic fields has been numerically inspected through a shooting scheme based Runge—Kutta–Fehlberg-integration algorithm. The governing equation and boundary layer balance are expressed and then converted into a nonlinear normal system of differential equations using suitable transformations. The impact of the physical parameters on the dimensionless velocity, temperature, the local Nusselt, and skin friction coefficient are described. Results show good agreement with recent researches. Findings reveal that the Nusselt number at the sheet surface augments, since the Hartmann number, stretching velocity ratio A, and Hartmann number Ha increase. Nevertheless, it reduces with respect to the heat generation/absorption coefficient δ. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
A Numerical Simulation of Silver–Water Nanofluid Flow with Impacts of Newtonian Heating and Homogeneous–Heterogeneous Reactions Past a Nonlinear Stretched Cylinder
Symmetry 2019, 11(2), 295; https://doi.org/10.3390/sym11020295
Received: 29 December 2018 / Revised: 28 January 2019 / Accepted: 29 January 2019 / Published: 24 February 2019
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Abstract
The aim of the present study is to address the impacts of Newtonian heating and homogeneous–heterogeneous (h-h) reactions on the flow of Ag–H2O nanofluid over a cylinder which is stretched in a nonlinear way. The additional effects of magnetohydrodynamics (MHD) and nonlinear thermal [...] Read more.
The aim of the present study is to address the impacts of Newtonian heating and homogeneous–heterogeneous (h-h) reactions on the flow of Ag–H2O nanofluid over a cylinder which is stretched in a nonlinear way. The additional effects of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also added features of the problem under consideration. The Shooting technique is betrothed to obtain the numerical solution of the problem which is comprised of highly nonlinear system ordinary differential equations. The sketches of different parameters versus the involved distributions are given with requisite deliberations. The obtained numerical results are matched with an earlier published work and an excellent agreement exists between both. From our obtained results, it is gathered that the temperature profile is enriched with augmented values radiation and curvature parameters. Additionally, the concentration field is a declining function of the strength of h-h reactions. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Peristaltic Blood Flow of Couple Stress Fluid Suspended with Nanoparticles under the Influence of Chemical Reaction and Activation Energy
Symmetry 2019, 11(2), 276; https://doi.org/10.3390/sym11020276
Received: 28 January 2019 / Revised: 18 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
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Abstract
The present study gives a remedy for the malign tissues, cells, or clogged arteries of the heart by means of permeating a slim tube (i.e., catheter) in the body. The tiny size gold particles drift in free space of catheters having flexible walls [...] Read more.
The present study gives a remedy for the malign tissues, cells, or clogged arteries of the heart by means of permeating a slim tube (i.e., catheter) in the body. The tiny size gold particles drift in free space of catheters having flexible walls with couple stress fluid. To improve the efficiency of curing and speed up the process, activation energy has been added to the process. The modified Arrhenius function and Buongiorno model, respectively, moderate the inclusion of activation energy and nanoparticles of gold. The effects of chemical reaction and activation energy on peristaltic transport of nanofluids are also taken into account. It is found that the golden particles encapsulate large molecules to transport essential drugs efficiently to the effected part of the organ. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
Impact of Nonlinear Thermal Radiation and the Viscous Dissipation Effect on the Unsteady Three-Dimensional Rotating Flow of Single-Wall Carbon Nanotubes with Aqueous Suspensions
Symmetry 2019, 11(2), 207; https://doi.org/10.3390/sym11020207
Received: 30 December 2018 / Revised: 27 January 2019 / Accepted: 31 January 2019 / Published: 12 February 2019
Cited by 7 | PDF Full-text (3036 KB) | HTML Full-text | XML Full-text
Abstract
The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, [...] Read more.
The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of ϕ augments the strength of frictional force within a liquid motion. For greater R and θ w ; the heat transfer rate rises. Temperature profile reduces by rising values of Pr . Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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Open AccessArticle
MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip
Symmetry 2019, 11(2), 132; https://doi.org/10.3390/sym11020132
Received: 1 January 2019 / Revised: 20 January 2019 / Accepted: 22 January 2019 / Published: 24 January 2019
Cited by 4 | PDF Full-text (629 KB) | HTML Full-text | XML Full-text
Abstract
In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of [...] Read more.
In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of the stagnation point flow. The governing Naiver–Stokes equation, along with the equations of nanofluid for three-dimensional flow, are modified using similarity transform, and reduced nonlinear coupled ordinary differential equations are solved numerically. It is observed that magnetic field M and slip parameter λ 1 increase the velocity and decrease the boundary layer thickness near the stagnation point. Also, a thermal boundary layer is achieved earlier than the momentum boundary layer, with the increase in thermophoresis parameter N t and Brownian motion parameter N b . Important physical quantities, such as skin friction, and Nusselt and Sherwood numbers, are also computed and discussed through graphs and tables. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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