Symmetrical Mathematical Computation in Fluid Dynamics

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

Deadline for manuscript submissions: 30 April 2024 | Viewed by 8027

Special Issue Editors

Department of Mechanical Engineering, Rice University, Houston, TX 77005, USA
Interests: fluid mechanics; electro-hydrodynamics; combustion
Heilongjiang Key Laboratory of Micro- and Nanoscale Fluid Flow and Heat Transfer, School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
Interests: electrohydrodynamics; heat and mass transfer; fluid–structure interaction problems; computational fluid dynamics

Special Issue Information

Dear Colleagues,

Symmetry is a ubiquitous phenomenon in natural and engineered complex systems. This phenomenon emerges from the physical laws of nature and serves as an important mathematical tool for understanding the properties of physics-based dynamical systems, such as fluid mechanics.

Computational fluid dynamics has in recent years experienced extensive progress due to the rapid growth of computational power and the fast-changing development of mathematical algorithms. Leveraging high-fidelity models and fine resolution, symmetric evolutions can be observed in flow simulations. In return, symmetry-preserving and symmetry-constrained models provide extra guarantees in accurate and effective reduced-order modelings.

The present Special Issue emphasizes phenomena based on the combinatory concepts of symmetry and the mathematical computation of fluid dynamics. For example, the manifestation of symmetries and symmetry breaking in the route to the turbulence of convective flows have driven the study of flow stability and bifurcation. On the other hand, symmetry constraints added to reduced-order models enhance the predictive capabilities of large-scale coherent structures in complex flows.

We are soliciting contributions (research and review articles) covering a broad range of topics on symmetry and mathematical computations in fluid dynamics, including (and not limited to) the following:

Transition between regular and chaotic dynamics in fluid mechanics;

  • Manifestation of symmetry in chaotic or turbulent flows;
  • Local symmetry breaking;
  • Possible coexistence of different types of symmetry breaking;
  • Symmetries in multiphase flows;
  • Symmetries of coherent structures in turbulence;
  • Symmetry-constrained or symmetry-preserving computational models;
  • Symmetry constraints in reduced-order modeling;
  • Symmetry constraints in data-driven models of fluid systems.

Dr. Yifei Guan
Prof. Dr. Jian Wu 
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

  • symmetry
  • mathematical computation of fluid dynamics
  • symmetry constraints
  • symmetry breaking
  • transitional flow
  • reduced-order modeling
  • data-driven models

Published Papers (7 papers)

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Research

14 pages, 2009 KiB  
Article
Permanent Solutions for MHD Motions of Generalized Burgers’ Fluids Adjacent to an Unbounded Plate Subjected to Oscillatory Shear Stresses
by Constantin Fetecau, Shehraz Akhtar and Costică Moroşanu
Symmetry 2023, 15(9), 1683; https://doi.org/10.3390/sym15091683 - 01 Sep 2023
Cited by 1 | Viewed by 489
Abstract
Closed-form expressions have been obtained to characterize the non-dimensional velocity and corresponding non-trivial shear stress in the context of two magnetohydrodynamic (MHD) motions exhibited by incompressible generalized Burgers’ fluids. These motions occur over an infinite plate, which subjects the fluid to oscillatory shear [...] Read more.
Closed-form expressions have been obtained to characterize the non-dimensional velocity and corresponding non-trivial shear stress in the context of two magnetohydrodynamic (MHD) motions exhibited by incompressible generalized Burgers’ fluids. These motions occur over an infinite plate, which subjects the fluid to oscillatory shear stresses. The obtained solutions represent the first exact analytical solutions for MHD motions of such fluids under the condition of shear stress prescribed along the boundary. The establishment of these solutions relies upon the utilization of a perfect symmetry existing between the governing equations of fluid velocity and shear stress. To validate the results, a comprehensive analysis has been undertaken using two distinct methods. This validation process is further substantiated through graphical representation, demonstrating the congruence between the obtained solutions. Additionally, the convergence of the initial solutions, obtained through numerical techniques, towards their corresponding permanent counterparts has been visually established. This graphical depiction not only substantiates the accuracy of the solutions but also provides insights into the temporal evolution of the system toward its permanent state. An insight to characterize the non-dimensional shear stresses in the context of two values of the magnetic parameter is to identify that the permanent state is reached at an earlier time and the absolute magnitude of fluid velocity is reduced in the presence of an applied magnetic field. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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21 pages, 8587 KiB  
Article
Analysis of Heat Transfer Behavior of Porous Wavy Fin with Radiation and Convection by Using a Machine Learning Technique
by Chandan Kumar, P. Nimmy, Kallur Venkat Nagaraja, R. S. Varun Kumar, Amit Verma, Shalan Alkarni and Nehad Ali Shah
Symmetry 2023, 15(8), 1601; https://doi.org/10.3390/sym15081601 - 18 Aug 2023
Cited by 9 | Viewed by 1180
Abstract
The impact of convection and radiation on the thermal distribution of the wavy porous fin is examined in the present study. A hybrid model that combines the differential evolution (DE) algorithm with an artificial neural network (ANN) is proposed for predicting the heat [...] Read more.
The impact of convection and radiation on the thermal distribution of the wavy porous fin is examined in the present study. A hybrid model that combines the differential evolution (DE) algorithm with an artificial neural network (ANN) is proposed for predicting the heat transfer of the wavy porous fin. The equation representing the thermal variation in the wavy porous fin is reduced to its dimensionless arrangement and is numerically solved using Rung, e-Kutta-Fehlberg’s fourth-fifth order method (RKF-45). The study demonstrates the effectiveness of this hybrid model, and the results indicate that the proposed approach outperforms the ANN model with parameters obtained through grid search (GS), showcasing the superiority of the hybrid DE-ANN model in terms of accuracy and performance. This research highlights the potential of utilizing DE with ANN for improved predictive modeling in the heat transfer sector. The originality of this study is that it addresses the heat transfer problem by optimizing the selection of parameters for the ANN model using the DE algorithm. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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9 pages, 247 KiB  
Article
A Note on Incompressible Vector Fields
by Nasser Bin Turki
Symmetry 2023, 15(8), 1479; https://doi.org/10.3390/sym15081479 - 26 Jul 2023
Cited by 2 | Viewed by 577
Abstract
In this paper, we use incompressible vector fields for characterizing Killing vector fields. We show that on a compact Riemannian manifold, a nontrivial incompressible vector field has a certain lower bound on the integral of the Ricci curvature in the direction of the [...] Read more.
In this paper, we use incompressible vector fields for characterizing Killing vector fields. We show that on a compact Riemannian manifold, a nontrivial incompressible vector field has a certain lower bound on the integral of the Ricci curvature in the direction of the incompressible vector field if, and only if, the vector field ξ is Killing. We also show that a nontrivial incompressible vector field ξ on a compact Riemannian manifold is a Jacobi-type vector field if, and only if, ξ is Killing. Finally, we show that a nontrivial incompressible vector field ξ on a connected Riemannian manifold has a certain lower bound on the Ricci curvature in the direction of ξ, and if ξ is also a geodesic vector field, it necessarily implies that ξ is Killing. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
18 pages, 4098 KiB  
Article
Nonlinear Radiative Nanofluidic Hydrothermal Unsteady Bidirectional Transport with Thermal/Mass Convection Aspects
by Muhammad Faisal, Kanayo Kenneth Asogwa, Nazek Alessa and Karuppusamy Loganathan
Symmetry 2022, 14(12), 2609; https://doi.org/10.3390/sym14122609 - 09 Dec 2022
Cited by 7 | Viewed by 1008
Abstract
The collective effect of thermal and mass convection along with the significance of thermal radiation, heat source/sink, and magneto-nanofluid are considered. A bi-directional stretching device is used to generate the symmetry of the flowing structure. Nonlinear behavior of thermal radiation is considered here. [...] Read more.
The collective effect of thermal and mass convection along with the significance of thermal radiation, heat source/sink, and magneto-nanofluid are considered. A bi-directional stretching device is used to generate the symmetry of the flowing structure. Nonlinear behavior of thermal radiation is considered here. The magnetic field is considered non-uniform and vertically upward. Significances of pedesis motion and Ludwig–Soret are also revealed in an innovative way with heat source/sink effects. The concept of symmetry is used to transmute the transport equations from PDE type to nonlinear ODE type. We solved the transformed setup numerically by adopting Keller-box method criteria with the targeted accuracy rate. Graphical interpretations are explored with code verification. It is important to conclude that friction coefficients decline for incremental values of stretching parameter (0.1α0.9), magnetic field (0.3M0.9), and unsteady parameter (0.2Λ0.9) along with the bidirectional velocity components, and the rate of heat transmission rises with temperature ratio (1.3Γ1.7) and temperature Biot number (0.3BiT0.9) amplification. Moreso, the rate of mass transfer is enhanced with growing values of pedesis motion (0.2Nb0.6), unsteady parameter and concentration Biot number (0.3BiC0.9) with opposite effect when the Ludwig–Soret parameter (0.3Nt0.6) is boosted. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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22 pages, 7314 KiB  
Article
Numerical and Computational Analysis of Magnetohydrodynamics over an Inclined Plate Induced by Nanofluid with Newtonian Heating via Fractional Approach
by Ali Raza, Umair Khan, Zehba Raizah, Sayed M. Eldin, Abeer M. Alotaibi, Samia Elattar and Ahmed M. Abed
Symmetry 2022, 14(11), 2412; https://doi.org/10.3390/sym14112412 - 14 Nov 2022
Cited by 5 | Viewed by 1387
Abstract
This study examines a viscous, incompressible, free-convective Casson fluid flow over an inclined plate, which characterizes an asymmetrical nanofluid flow and heat transfer behavior. Here, the two different nanofluids are basically made of molybdenum disulfide (MoS2) with CMC-based fluid [...] Read more.
This study examines a viscous, incompressible, free-convective Casson fluid flow over an inclined plate, which characterizes an asymmetrical nanofluid flow and heat transfer behavior. Here, the two different nanofluids are basically made of molybdenum disulfide (MoS2) with CMC-based fluid and graphene oxide (GO) nanoparticles with CMC-based fluid to form a particular (CMC/MoS2) nanofluid and (CMC/GO) nanofluid. The Newtonian heating effect, slip boundary, porosity, and inclined magnetic effects are also considered. When memory effects are present, conventional PDEs are unable to investigate and evaluate the physical behavior of various flow parameters. We employed the Prabhakar fractional derivative, the best and most current fractional mathematical operator, to tackle the considered nanofluid problem. Using the integral transform approach, Laplace transforms, the non-dimensional governed model is converted into a fractional model and solved. The graphical analysis examines the influence and symmetrical behavior of significant physical and fractional parameters. The numerical effects of the Nusselt number, Sherwood number, and skin friction are also looked at, at various sundry values of the time. As a result, we conclude that increasing Prabhakar fractional constraints causes the thermal and momentum profiles to decelerate down. In addition, for two distinct values of time, 0.8 and 1.8, improvements of 3.823% and 5.042%, respectively, are observed in the mass transfer rate for the higher impacts of the Prabhakar fractional parameter, α, while the heat transfer rate declines by 10.065% and 15.908%, respectively. Also, the shear stress upsurges by 0.881% and 2.482%, respectively, for the change values of time 0.8 and 1.8 with higher values of Prabhakar fractional parameter α. Furthermore, with varying time, the accompanying criteria are satisfied, and the velocity and temperature fields both expand asymptotically in the y-direction and decline away from the plate. When comparing the two nanofluids, the (CMC/MoS2) nanofluid has a somewhat higher thermal and flow rate than the (CMC/GO) nanofluid. The studies indicated that increasing the volume percentage of nanoparticles causes heat transmission to be enriched. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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17 pages, 2770 KiB  
Article
A Model of Water Treatment by Nanoparticles in a Channel with Adjustable Width under a Magnetic Field
by Sergei Zuev, Petr Kabalyants and Zakir Hussain
Symmetry 2022, 14(8), 1728; https://doi.org/10.3390/sym14081728 - 18 Aug 2022
Viewed by 1056
Abstract
The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry, and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a channel with mixing of [...] Read more.
The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry, and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a channel with mixing of water, nanoparticles, and contaminants. It is assumed that fluid is homogeneous at the starting moment, the parameters of the nanoparticles and contaminants are known, and there is a constant non-homogeneous magnetic field applied to the system. The flow starts moving when the walls of the channel shift to each other. Exact and numerical solutions of the system of ordinary differential equations are used to obtain the results. The article gives an answer to the question about stability of the flow and proposes the technique to evaluate the essential characteristics of the system to achieve the treatment process efficiency. The main result is that the considered system shows excellent properties concerning purification of water on the selected part of the squeezing stage. This effect does not appear without a magnetic field. The mentioned properties are: decreasing of nanoparticle concentration to zero inside of the unsteady layer under magnetic field close to 1 T and this effect stays until the channel become about 10% of initial width as a result of the squeezing. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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14 pages, 2474 KiB  
Article
Theoretical Survey of Time-Dependent Micropolar Nanofluid Flow over a Linear Curved Stretching Surface
by Nadeem Abbas and Wasfi Shatanawi
Symmetry 2022, 14(8), 1629; https://doi.org/10.3390/sym14081629 - 08 Aug 2022
Cited by 18 | Viewed by 1259
Abstract
The heat and mass transfer of the unsteady flow of a micropolar fluid over a curved stretching surface was considered in this study. The Brownian motion and thermophoresis effects were explored in this analysis. The effects of suction/injection cases on the curved surface [...] Read more.
The heat and mass transfer of the unsteady flow of a micropolar fluid over a curved stretching surface was considered in this study. The Brownian motion and thermophoresis effects were explored in this analysis. The effects of suction/injection cases on the curved surface were discussed. Under flow assumptions, a mathematical model was designed employing boundary layer approximations using partial differential equations. A suitable transformation was developed using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique, namely bvp4c. The involved physical parameters’ influences are described in the form of graphs as well as numerical results in the form of tables. Our current work is helpful in the engineering and industrial fields. The unsteadiness parameter increases which Nusselt number at increased but concentrations declined. The thermophoresis parameter increases when increasing the Nusselt number because the small number of nanoparticles enhances the heat transfer rate. The temperature profile declined due to increasing values of unsteadiness parameter for both cases of suction and injection cases. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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