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Special Issue "Symmetry in Fluid Dynamics"

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 31 January 2024 | Viewed by 8011

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Special Issue Editors

Dr. Aamir Hamid

E-Mail Website
Guest Editor

ITU School of Mechanical Engineering, Istanbul Techjnical University, 34437 Gümüşsuyu, İstanbul, Turkey
Interests: computational fluid dynamics; heat transfer enhancement in two phase flow; Reactive transport in porous media; dynamics of natural CO₂ reservoirs; thermodynamics; analytical methods for nonlinear differential equations; mathematical physics; numerical solutions of the ordinary and partial differential equations and computer programming

Prof. Dr. Hasan Bulut
E-Mail Website
Co-Guest Editor

Department of Mathematics, Faculty of Science, Firat University, 23000 Elazig, Turkey
Interests: ordinary and partial differential equations

Special Issue Information

Dear Colleagues,

The literature review shows that Newtonian and non-Newtonian fluids with their valuable importance in industrial applications have been a source of inspiration to the researchers during past years. The research interest and practical applications have produced a considerable interest in obtaining analytical or numerical solutions to the fluid equations that govern Newtonian and non-Newtonian fluid flows. Some of their known applications are biological fluid movements, wire coating, food processing, plastic manufacturing, and so forth. In recent years, numerous researchers have been working on the flow and heat transfer characteristics of Newtonian and non-Newtonian fluids. However, many theoretical analyses, experimental studies, and practical applications remain to be further explored.

The aim of this Special Issue is to collect contributions of the recent developments regarding fluid flows and Lie symmetry methods in all fields of physical sciences and engineering.

The Special Issue welcomes papers on computational fluid dynamics, Lie symmetry methods, thermodynamics, analytical methods for non-linear differential equations, mathematical physics, and their applications on modeling psychical, chemical, biological, biomedical, social, and economical systems together with engineering applications. Theoretical and experimental studies, numerical solutions of the ordinary and partial differential equations and computer programming are also welcomed.

Please kindly note that all submitted papers should be within the scope of the journal where symmetry, or the deliberate lack of symmetry, is present.

Dr. Aamir Hamid
Prof. Dr. Hasan Bulut
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

newtonian and non-newtonian fluids
hybrid nanofluids and particle shape effects
mathematica physics
fluid-structure-interaction
multiphase flow simulations
applied mathematical modeling
thermodynamics and heat transfer
reactive transport in porous media
symmetric flow
anti-symmetric flow
rotational symmetry
planar symmetry
point symmetry
symmetry breaking
symmetric boundary conditions
symmetric vortex
symmetric wake
symmetric streamlines
symmetric turbulence
symmetric flow control
symmetry analysis in fluid dynamics
symmetric navier-stokes equations
symmetric stokes flow

Published Papers (7 papers)

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Research

Open AccessArticle

Brinkman–Bénard Convection with Rough Boundaries and Third-Type Thermal Boundary Conditions

Pradeep G. Siddheshwar

Mahesha Narayana

David Laroze

and

C. Kanchana

Symmetry 2023, 15(8), 1506; https://doi.org/10.3390/sym15081506 - 28 Jul 2023

Viewed by 697

Abstract

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number,

R a_{c}

, and the wave number,

a_{c}

, are obtained in closed form. An asymptotic analysis is performed, to obtain

R a_{c}

for the case of adiabatic boundaries, for which

a_{c} ≃ 0

. A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

Semi-Analytical Approach in BiER4BP for Exploring the Stable Positioning of the Elements of a Dyson Sphere

Sergey Ershkov

Dmytro Leshchenko

and

Evgeniy Yu. Prosviryakov

Symmetry 2023, 15(2), 326; https://doi.org/10.3390/sym15020326 - 24 Jan 2023

Cited by 3 | Viewed by 982

Abstract

In this study, we present a new approach with semi-analytical and numerical findings for solving equations of motion of small orbiter m, which is moving under the combined gravitational attraction of three primaries,

M_{1}

M_{2}

, and

M_{3}

[...] Read more.

M_{1}

M_{2}

, and

M_{3}

, in case of the bi-elliptic restricted problem of four bodies (BiER4BP), where three such primaries,

M_{1}

M_{2}

, and

M_{3}

, are moving on elliptic orbits with hierarchical configuration

M_{3}

M_{2}

M_{1}

within one plane as follows: third primary body

M_{3}

is moving on elliptical orbit around second

M_{2}

, and second primary

M_{2}

is moving on elliptical orbit around first

M_{1}

. Our aim for constructing the aforementioned quasi-planar motion of planetoid m is obtaining its coordinates supporting its orbit in a regime of close motion to the plane of orbiting the main bodies

M_{1}

M_{2}

, and

M_{3}

. Meanwhile, the system of equations of motion was successfully numerically explored with respect to the existence and stable positioning of approximate solution for a Dyson sphere. As a result, the concept of the Dyson sphere for possible orbiting variety of solar energy absorbers was transformed to the elongated Dyson space net with respect to their trajectories for the successful process of absorbing the energy from the Sun; this can be recognized as symmetry reduction. We obtain the following: (1) the solution for coordinates {x, y} is described by the simplified system of two nonlinear ordinary differential equations of second order, depending on true anomaly f; (2) the expression for coordinate z is given by an equation of Riccati-type where small orbiter that quasi-oscillates close to the fixed plane

{x, y, 0}

. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

Flow of a Viscous Incompressible Fluid from a Moving Point Source

Sergey V. Ershkov

Evgeniy Yu. Prosviryakov

and

Dmytro D. Leshchenko

Symmetry 2022, 14(10), 2156; https://doi.org/10.3390/sym14102156 - 14 Oct 2022

Cited by 1 | Viewed by 840

Abstract

The flow of a viscous incompressible fluid outflowing from a uniformly moving point source is considered. An exact solution to the problem is found in the way that the velocity decreases inversely with the radial coordinate. It is shown that a spherical volume of fluid is carried away by the source, the radius of which is inversely proportional with respect to the velocity of motion. In this case, a cylindrical discontinuity arises in the region of forming a wake behind the body, the dimensions of which are determined by the magnitude of the external pressure and do not depend on the velocity of the source. The obtained solutions are governed by hydrodynamical fields of flows which can be recognized as special invariants at symmetry reduction. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

Magneto-Hydrodynamic Flow above Exponentially Stretchable Surface with Chemical Reaction

Mohamed Abdelghany Elkotb

and

Fahad M. Alharbi

Symmetry 2022, 14(8), 1688; https://doi.org/10.3390/sym14081688 - 15 Aug 2022

Cited by 7 | Viewed by 919

Abstract

This article is focused on investigating the convective magneto-hydrodynamic single-phase flow for comparative analysis of two different base fluids above an exponentially stretchable porous surface under the effect of the chemical reaction. The Buongiorno fluid model is incorporated to observe the Thermophoresis and Brownian diffusion in this study. Boussinesq approximation for temperature and concentration are accounted for flow to be naturally convective. In this study, water and ethanol are assumed for comparative analysis. Additionally, to achieve the outcomes of the designed three-dimensional flow boundary value, problem technique is employed to simulate the problem in MATLAB. Increase in the magnetic field, thermophoresis diffusion, temperature exponent, and Prandtl number expand thermal boundary, whereas contraction is observed with an increase in porosity. Shear stress rates in respective directions have decreased with an increase in the stretching ratio of the surface. Moreover, through comparison, reasonably enhanced Nusselt number is observed for water under influence of study parameters while the Nusselt number abruptly decreases for ethanol. High mass coefficients are observed for both examined fluids. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

Capture in Regime of a Trapped Motion with Further Inelastic Collision for Finite-Sized Asteroid in ER3BP

Sergey Ershkov

Dmytro Leshchenko

and

Alla Rachinskaya

Symmetry 2022, 14(8), 1548; https://doi.org/10.3390/sym14081548 - 28 Jul 2022

Cited by 7 | Viewed by 929

Abstract

The application of a modern solving algorithm or method of resolving dynamical equations for small projectile of finite sizes orbiting to be captured in a trapped zigzaging oscillations on orbit around the another large asteroid and in a further inelastic colliding scenario with him (using a formulation of the elliptic restricted three-body problem, ER3BP) is studied semi-analytically. Herein, two primaries M_Sun and m_p (m_p < M_Sun) revolve around their barycenter on Keplerian orbits with low eccentricities. A smaller body (projectile for attacking a large asteroid) is supposed to be a solid, almost symmetric ellipsoid, having the gravitational potential of the MacCullagh type. Our aim is to develop a previously introduced solving procedure and to investigate the updated dynamics of the projectile captured to a trapped dynamical resonance, thereby having the inelastic collision of a small projectile orbiting on quasi-stable elliptic orbits around the large asteroid, m_p. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

The Fate of Molecular Species in Water Layers in the Light of Power-Law Time-Dependent Diffusion Coefficient

Mohamed Mokhtar Hefny

and

Ashraf M. Tawfik

Symmetry 2022, 14(6), 1146; https://doi.org/10.3390/sym14061146 - 02 Jun 2022

Cited by 2 | Viewed by 966

Abstract

In the present paper, we propose two methods for tracking molecular species in water layers via two approaches of the diffusion equation with a power-law time-dependent diffusion coefficient. The first approach shows the species densities and the growth of different species via numerical simulation. At the same time, the second approach is built on the fractional diffusion equation with a time-dependent diffusion coefficient in the sense of regularised Caputo fractional derivative. As an illustration, we present here the species densities profiles and track the normal and anomalous growth of five molecular species OH, H₂O₂, HO₂, NO₃^-, and NO₂^- via the calculation of the mean square displacement using the two methods. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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Open AccessArticle

Combined Pressure-Driven and Electroosmotic Slip Flow through Elliptic Cylindrical Microchannels: The Effect of the Eccentricity of the Channel Cross-Section

Pearanat Chuchard

and

Nattakarn Numpanviwat

Symmetry 2022, 14(5), 999; https://doi.org/10.3390/sym14050999 - 13 May 2022

Cited by 1 | Viewed by 1086

Abstract

Electroosmotic force has been used extensively to manipulate fluid flow in a microfluidic system with various channel shapes, especially an elliptic cylinder. However, developing a computational domain and simulating fluid flow for a system involving an elliptic channel consumes a large amount of time. Moreover, the mathematical expression for the fluid velocity of electroosmotic flow in an elliptic channel may be given in the form of the Mathieu functions that have difficulty in achieving the numerical result. In addition, there is clear scientific evidence that confirms the slippage of fluid at the solid-fluid interface in a microscale system. In this study, we present the mathematical model of combined pressure-driven and electroosmotic flow through elliptic microchannels under the slip-fluid condition. From the practical point of view in fluidics, the effect of the eccentricity of the channel cross-section is investigated on the volumetric flow rate to overcome the difficulty. The results show that the substitution of the equivalent circular channel for an elliptic channel provides a valid flow rate under the situation that the areas of both channel cross-sections are equal and the eccentricity of the elliptic cross-section is less than 0.5. Additionally, the flow rate obtained from the substitution is more accurate when the slip length increases or the pressure-gradient-to-external-electric-field ratio decreases. Full article

(This article belongs to the Special Issue Symmetry in Fluid Dynamics)

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