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Mathematics
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Numerical Model and Methods for Magnetic Fluids
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Numerical Model and Methods for Magnetic Fluids

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 9941

Special Issue Editors

Dr. Marko Jesenik

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Guest Editor
Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia
Interests: engineering; mathematics; medicine; chemistry
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Mladen Trlep

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Guest Editor
Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia
Interests: Electromagnetics; electric machines; numerical methods; finite elements method

Special Issue Information

Dear Colleagues,

Magnetic Fluids are an area of broad interest in the last decades since these are new materials that open possibilities for use in different areas. Magnetic fluid is a multi-disciplinary topic covering physical and colloidal chemistry, magnetism, hydro- and thermomechanics, physics of fluids, disperses systems, and engineering science. It is essential to know their magnetic and thermal properties and their behavior in case of exposure to external magnetic fields and exposure to different ambient temperatures. For this purpose, various theoretical and numerical models are used along with different numerical methods such as Finite Element Method, Boundary Element Method and also optimization methods, neural networks etc.

We are searching for papers on original approaches based on modern numerical and optimization techniques to make magnetic fluids models as realistic as possible. Experimental support is desirable but not necessary. Also, magnetic fluid models and their applications in engineering, medicine, etc., where the fusion of mathematics (numerical models) and computation (numerical methods) stimulate progress in magnetic fluid research are welcome as well.

Prof. Dr. Marko Jesenik
Prof. Dr. Mladen Trlep
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Magnetism 
  • Physical and colloidal chemistry Hydro- and thermomechanics
  • Numerical models
  • Numerical methods
  • Optimization methods
  • Hyperthermia
  • Measurement methods

Published Papers (6 papers)

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Research

16 pages, 6171 KiB  
Article
Numerical Study of the Flow and Thermomagnetic Convection Heat Transfer of a Power Law Non-Newtonian Ferrofluid within a Circular Cavity with a Permanent Magnet
by Nidhal Ben Khedher, Mohammad Shahabadi, Abed Saif Alghawli, Christopher Neil Hulme and Seyed Abdollah Mansouri Mehryan
Mathematics 2022, 10(15), 2612; https://doi.org/10.3390/math10152612 - 26 Jul 2022
Cited by 1 | Viewed by 1129
Abstract
The aim of this study is to analyze the thermo-magnetic-gravitational convection of a non-Newtonian power law ferrofluid within a circular cavity. The ferrofluid is exposed to the magnetic field of a permanent magnet. The finite element method is employed to solve the non-dimensional [...] Read more.
The aim of this study is to analyze the thermo-magnetic-gravitational convection of a non-Newtonian power law ferrofluid within a circular cavity. The ferrofluid is exposed to the magnetic field of a permanent magnet. The finite element method is employed to solve the non-dimensional controlling equations. A grid sensitivity analysis and the validation of the used method are conducted. The effect of alterable parameters, including the power law index, 0.7 ≤ n ≤ 1.3, gravitational Rayleigh number, 104 ≤ RaT ≤ 106, magnetic Rayleigh number, 105 ≤ RaM ≤ 108, the location of the hot and cold surfaces, 0 ≤ λ ≤ π/2, and the length of the magnet normalized with respect to the diameter of the cavity, 0.1 ≤ L ≤ 0.65, on the flow and heat transfer characteristics are explored. The results show that the heat transfer rate increases at the end of both arcs compared to the central region because of buoyancy effects, and it is greater close to the hot arc. The location of the arcs does not affect the heat transfer rate considerably. An increase in the magnetic Rayleigh number contributes to stronger circulation of the flow inside and higher heat transfer. When the Kelvin force is the only one imposed on the flow, it enhances the heat transfer for magnets of length 0.2 ≤ L ≤ 0.3. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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15 pages, 687 KiB  
Article
Computer Simulations of Dynamic Response of Ferrofluids on an Alternating Magnetic Field with High Amplitude
by Vladimir Zverev, Alla Dobroserdova, Andrey Kuznetsov, Alexey Ivanov and Ekaterina Elfimova
Mathematics 2021, 9(20), 2581; https://doi.org/10.3390/math9202581 - 14 Oct 2021
Cited by 3 | Viewed by 1385
Abstract
The response of ferrofluids to a high-amplitude AC magnetic field is important for several applications including magnetic hyperthermia and biodetection. In computer simulations of the dynamic susceptibility of a ferrofluid outside the linear response region, there are several problems associated with the fact [...] Read more.
The response of ferrofluids to a high-amplitude AC magnetic field is important for several applications including magnetic hyperthermia and biodetection. In computer simulations of the dynamic susceptibility of a ferrofluid outside the linear response region, there are several problems associated with the fact that an increase in the frequency of the AC field leads to the appearance of additional computational errors, which can even lead to unphysical results. In this article, we study the dependence of the computational error arising in the computer simulation of the dynamic susceptibility on the input parameters of the numerical algorithm: the length of the time step, the total number of computer simulation periods, and averaging period. Computer simulation is carried out using the Langevin dynamics method and takes Brownian rotational relaxation of magnetic particles and interparticle interactions into account. The reference theory [Yoshida T.; Enpuku K. Jap. J. Ap. Phys. 2009] is used to estimate computational error. As a result, we give practical recommendations for choosing the optimal input parameters of the numerical algorithm, which make it possible to obtain reliable results of the dynamic susceptibility of a ferrofluid in a high-amplitude AC field in a wide frequency range. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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25 pages, 31243 KiB  
Article
Energy Based Calculation of the Second-Order Levitation in Magnetic Fluid
by Mislav Trbušić, Marko Jesenik, Mladen Trlep and Anton Hamler
Mathematics 2021, 9(19), 2507; https://doi.org/10.3390/math9192507 - 07 Oct 2021
Cited by 3 | Viewed by 1334
Abstract
A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. [...] Read more.
A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. Various authors have proposed different computational methods, but all of them rely on force formulation. This paper presents an alternative energy approach in the equilibrium height calculation, which was settled on the minimum energy principle. The problem, involving a cylindrical magnet suspended in a closed cylindrical container full of magnetic fluid, was considered in the study. The results accomplished by the proposed method were compared with those of the well-established surface integral method already verified by experiments. The difference in the results gained by both methods appears to be under 2.5%. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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11 pages, 335 KiB  
Article
Dynamic Susceptibility of Ferrofluids: The Numerical Algorithm for the Inverse Problem of Magnetic Granulometry
by Alexey O. Ivanov and Vladimir S. Zverev
Mathematics 2021, 9(19), 2450; https://doi.org/10.3390/math9192450 - 02 Oct 2021
Cited by 2 | Viewed by 1435
Abstract
The size-dependent properties of magnetic nanoparticles (MNP) are the major characteristics, determining MNP application in modern technologies and bio-medical techniques. Direct measurements of the nanosized particles, involved in intensive Brownian motion, are very complicated; so the correct mathematical methods for the experimental data [...] Read more.
The size-dependent properties of magnetic nanoparticles (MNP) are the major characteristics, determining MNP application in modern technologies and bio-medical techniques. Direct measurements of the nanosized particles, involved in intensive Brownian motion, are very complicated; so the correct mathematical methods for the experimental data processing enable to successfully predict the properties of MNP suspensions. In the present paper, we describe the fast numerical algorithm allowing to get the distribution over the relaxation time of MNP magnetic moments in ferrofluids. The algorithm is based on numerical fitting of the experimentally measured frequency spectra of the initial dynamic magnetic susceptibility. The efficiency of the algorithm in the solution of the inverse problem of magnetic granulometry is substantiated by the computer experiments for mono- and bi-fractional ferrofluids. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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22 pages, 830 KiB  
Article
Flow Dynamics of the Homogeneous and Heterogeneous Reactions with an Internal Heat Generation and Thermal Radiation between Two Squeezing Plates
by Wajid Ullah Jan, Muhammad Farooq, Rehan Ali Shah, Aamir Khan, M S Zobaer and Rashid Jan
Mathematics 2021, 9(18), 2309; https://doi.org/10.3390/math9182309 - 18 Sep 2021
Cited by 2 | Viewed by 1744
Abstract
This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate [...] Read more.
This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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20 pages, 2174 KiB  
Article
Analytical Solution for Wave Diffraction by a Concentric Three-Cylinder System near a Vertical Wall
by Zhenfeng Zhai, Weifeng Ye, Fei Xia and Lele Yang
Mathematics 2021, 9(16), 1876; https://doi.org/10.3390/math9161876 - 07 Aug 2021
Viewed by 1831
Abstract
In this study, a semi-analytical model was developed to study wave diffraction around a concentric three-cylinder system near a wall based on linear potential theory. As a critical element, the target problem is transformed into bidirectional incident wave diffraction around two concentric structures [...] Read more.
In this study, a semi-analytical model was developed to study wave diffraction around a concentric three-cylinder system near a wall based on linear potential theory. As a critical element, the target problem is transformed into bidirectional incident wave diffraction around two concentric structures based on the image principle and an analytical solution is obtained through eigenfunction expansion combined with a matching technique and Graf’s addition theorem. The validity of the proposed model was verified by comparing its results to known values. Parametric studies on porosity, annular spacing, incident angle, space between the structure and wall, and water depth were performed. The hydrodynamic loads and free-surface elevations in the system were calculated and compared to those reported in existing works on impermeable and permeable cylinders near a wall. The results indicate that the wave loads and run-ups on the exterior cylinder increase significantly based on the existence of the wall. However, based on the presence of an exterior porous protective structure, a significantly reduced influence of the wall on the interior cylinder can be observed. Considering the widespread use of concentric circular structures in ocean engineering, it is essential to conduct study on the hydrodynamic performance of concentric systems near walls, which can provide useful information for the design of marine structures. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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