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Applications of Partial Differential Equations in Engineering, 2nd Edition
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Applications of Partial Differential Equations in Engineering, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (20 April 2023) | Viewed by 5231

Special Issue Editors

Prof. Dr. Francisco Ureña

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Guest Editor
Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
Interests: partial differential equations; applied mathematics; computational mathematics; numerical analysis; discrete math; mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Antonio Manuel Vargas

E-Mail Website
Guest Editor
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Interests: partial differential equations; applied mathematics; computational mathematics; numerical analysis
Dr. Ángel García Gómez

E-Mail Website
Guest Editor
Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
Interests: partial differential equations; applied mathematics; computational mathematics; numerical analysis; mechanics

Special Issue Information

Dear Colleagues,

Partial differential equations have become an extensive topic in mathematics, physics and engineering due to the novel techniques recently developed and great achievements in computational sciences. Both theoretical and applied viewpoints have gained great attention from many different natural sciences.

A partial list of topics includes modeling, solution techniques and applications of computational methods in a variety of areas (e.g., liquid and gas dynamics, solid and structural mechanics, and bio-mechanics), variational formulations and numerical algorithms related to implementation of the finite and boundary element methods, finite difference and finite volume methods, and other basic computational methodologies.

Prof. Dr. Francisco Ureña
Dr. Antonio Manuel Vargas
Dr. Ángel García Gómez
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

  • applied mathematics
  • modeling
  • fluid mechanics
  • computational methods
  • finite elements
  • finite differences
  • solution techniques
  • mesh generation
  • computational engineering

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Published Papers (3 papers)

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Research

16 pages, 6213 KiB  
Article
Three-Dimensional Swirling Flow of Nanofluid with Nanoparticle Aggregation Kinematics Using Modified Krieger–Dougherty and Maxwell–Bruggeman Models: A Finite Element Solution
by M. D. Alsulami, Amal Abdulrahman, R. Naveen Kumar, R. J. Punith Gowda and B. C. Prasannakumara
Mathematics 2023, 11(9), 2081; https://doi.org/10.3390/math11092081 - 27 Apr 2023
Cited by 40 | Viewed by 1765
Abstract
The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified [...] Read more.
The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified Krieger–Dougherty models for viscosity are employed to scrutinize the impact of nanoparticle aggregation. A mathematical model based on partial differential equations (PDEs) is developed to solve the flow problem. Following that, a similarity transformation is performed to reduce the equations to ordinary differential equations (ODEs), which are then solved using the finite element method. It has been proven that nanoparticle aggregation significantly increases the temperature field. The results reveal that the rise in Reynolds number improves the heat transport rate, whereas an increase in the heat source/sink parameter value declines the heat transport rate. Swirling flows are commonly found in many industrial processes such as combustion, mixing, and fluidized bed reactors. Studying the behavior of nanofluids in these flows can lead to the development of more efficient and effective industrial processes. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering, 2nd Edition)
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16 pages, 19213 KiB  
Article
Application of Finite Element Method to Create a Digital Elevation Model
by Eduardo Conde López, Eduardo Salete Casino, Jesús Flores Escribano and Antonio Vargas Ureña
Mathematics 2023, 11(6), 1522; https://doi.org/10.3390/math11061522 - 21 Mar 2023
Cited by 5 | Viewed by 1428
Abstract
The generation of a topographical surface or digital elevation model for a given set of points in space is a known problem in civil engineering and topography. In this article, we propose a simple and efficient way to obtain the terrain surface by [...] Read more.
The generation of a topographical surface or digital elevation model for a given set of points in space is a known problem in civil engineering and topography. In this article, we propose a simple and efficient way to obtain the terrain surface by using a structural shell finite element model, giving advice on how to implement it. The proposed methodology does not need a large number of points to define the terrain, so it is especially suitable to be used with data provided by manual topographical tools. Several examples are developed to demonstrate the easiness and accuracy of the methodology. The digital terrain model of a real landscape is modeled by using different numbers of points (from 49 to 400) using a regular mesh or a randomly generated cloud of points. The results are compared, showing how the proposed methodology creates a sufficiently accurate model, even with a low number of points (compared with the thousands of points handled in a LiDAR representation). A real case application is also shown. As an appendix, the sample code to generate the examples is provided. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering, 2nd Edition)
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11 pages, 290 KiB  
Article
Symmetries and Solutions for a Class of Advective Reaction-Diffusion Systems with a Special Reaction Term
by Mariano Torrisi and Rita Tracinà
Mathematics 2023, 11(1), 160; https://doi.org/10.3390/math11010160 - 28 Dec 2022
Cited by 2 | Viewed by 1564
Abstract
This paper is devoted to apply the Lie methods to a class of reaction diffusion advection systems of two interacting species u and v with two arbitrary constitutive functions f and g. The reaction term appearing in the equation for the species [...] Read more.
This paper is devoted to apply the Lie methods to a class of reaction diffusion advection systems of two interacting species u and v with two arbitrary constitutive functions f and g. The reaction term appearing in the equation for the species v is a logistic function of Lotka-Volterra type. Once obtained the Lie algebra for any form of f and g a Lie classification is carried out. Interesting reduced systems are derived admitting wide classes of exact solutions. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering, 2nd Edition)
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