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Numerical Methods for Problems Arising in Mechanics
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Numerical Methods for Problems Arising in Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 8073

Special Issue Editors

Prof. Dr. Muhammad Hamid

E-Mail Website
Guest Editor
1. School of Mathematical Sciences, Peking University, Beijing 100871, China
2. Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China
Interests: applied mathematics; fractional calculus; fluids mechanics and heat transfer; geometry and topology; manifolds
Prof. Dr. Wei Wang

E-Mail Website
Guest Editor
School of Mathematical Sciences, Peking University, Beijing 100871, China
Interests: nonlinear analysis

Special Issue Information

Dear Colleagues,

Thermal control and flow analysis using the concept of fluids are considerably significant due to several applications in engineering sciences. The potential applications are avionics, automotive, cooling/heating systems in buildings, furnaces, electronic equipment, tanks containing cold/hot water, phase change materials (PCMs), petrochemical, and textile sectors. Several studies examine such mechanisms experimentally or through mathematical modeling governed by nonlinear equations in the last few eras. Mathematical techniques are pretty representative and practical as they save time and money. The development or extension of mathematical algorithms requires current research that could validate the experimental data.

However, the advancement in fluid mechanics and investigation using mathematical algorithms has been deemed to be critical. The area needs to be studied through different aspects and various geometries, while developing mathematical methods for such models will be challenging.

This Special Issue will provide a platform for researchers to present their substantial, novel, and unpublished work that will contribute positively to the scientific community and the journal. Moreover, it will provide sufficient knowledge to researchers working on the numerical treatment of fluid models.

Prof. Dr. Muhammad Hamid
Prof. Dr. Wei Wang
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

  • Newtonian and non-Newtonian fluids
  • thermal analysis
  • MHD
  • numerical methods

Published Papers (5 papers)

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Research

26 pages, 8859 KiB  
Article
Numerical Scrutinization of Ternary Nanofluid Flow over an Exponentially Stretching Sheet with Gyrotactic Microorganisms
by Basma Souayeh and Katta Ramesh
Mathematics 2023, 11(4), 981; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040981 - 14 Feb 2023
Cited by 14 | Viewed by 1671
Abstract
In the modern age, the study of nanofluids over the stretching sheet has received much attention from researchers due to its significant role in the polymer industry, for instance in the production of fibre sheets and the extrusion of molten polymers through a [...] Read more.
In the modern age, the study of nanofluids over the stretching sheet has received much attention from researchers due to its significant role in the polymer industry, for instance in the production of fibre sheets and the extrusion of molten polymers through a slit die. Due to these affordable applications, the current study focusses on the motion of metallic ternary nanofluids (Ag-Au-Cu/H2O) past an exponential stretching sheet, taking diverse effects such as gyrotactic microorganisms, activation energy, buoyancy forces and thermal radiation into consideration. The model was created with the complex system of partial differential equations. Suitable similarity transformations and non-dimensional quantities were utilized to transform the complex system of partial differential equations to a set of ordinary differential equations. The resultant system is solved with the help of Matlab software. The computational outcomes are presented through the tables and pictorial notations. It is observed from the current analysis that the nanoparticle temperature of the ternary nanofluid enhances with the enhancement of activation energy and Brownian motion parameters. For the rising values of Lewis and thermophoresis numbers there is a declination in the nanoparticle concentration distribution. The Brownian motion and radiation effects increase the microorganism profile. Full article
(This article belongs to the Special Issue Numerical Methods for Problems Arising in Mechanics)
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17 pages, 1831 KiB  
Article
Hybrid Nano-Jet Impingement Cooling of Double Rotating Cylinders Immersed in Porous Medium
by Fatih Selimefendigil, Mondher Hamzaoui, Abdelkarim Aydi, Badr M. Alshammari and Lioua Kolsi
Mathematics 2023, 11(1), 51; https://0-doi-org.brum.beds.ac.uk/10.3390/math11010051 - 23 Dec 2022
Cited by 1 | Viewed by 1395
Abstract
A cooling system with impinging jets is used extensively in diverse engineering applications, such as solar panels, electronic equipments, battery thermal management, textiles and drying applications. Over the years many methods have been offered to increase the effectiveness of the cooling system design [...] Read more.
A cooling system with impinging jets is used extensively in diverse engineering applications, such as solar panels, electronic equipments, battery thermal management, textiles and drying applications. Over the years many methods have been offered to increase the effectiveness of the cooling system design by different techniques. In one of the available methods, nano-jets are used to achieve a higher local and average heat transfer coefficient. In this study, convective cooling of double rotating cylinders embedded in a porous medium is analyzed by using hybrid nano-jets. A finite element formulation of the thermo-fluid system is considered, while impacts of Reynolds number, rotational speed of the double cylinders, permeability of the porous medium and distance between the cylinders on the cooling performance are numerically assessed. Hybrid and pure fluid performances in the jet cooling system are compared. It is observed that the cooling performance improves when the rotating speed of the cylinder, permeability of the medium and jet Reynolds number are increased. The heat transfer behavior when varying the distance between the cylinders is different for the first and second cylinder. Higher thermal performances are achieved when hybrid nanofluid with higher nanoparticle loading is used. An optimization algorithm is used for finding the optimum distance and rotational speeds of the cylinders for obtaining an improved cooling performance, while results show higher effectiveness as compared to a parametric study. The outcomes of the present work are useful for the thermal design and optimization of the cooling system design for configurations encountered in electronic cooling, energy extraction and waste heat recovery. Full article
(This article belongs to the Special Issue Numerical Methods for Problems Arising in Mechanics)
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21 pages, 2969 KiB  
Article
Application and CFD-Based Optimization of a Novel Porous Object for Confined Slot Jet Impingement Cooling Systems under a Magnetic Field
by Walid Aich, Fatih Selimefendigil, Badreddine Ayadi, Lotfi Ben Said, Badr M. Alshammari, Lioua Kolsi, Sid Ali Betrouni and Hatem Gasmi
Mathematics 2022, 10(15), 2578; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152578 - 25 Jul 2022
Cited by 2 | Viewed by 1037
Abstract
A novel porous object for the control of the convective heat transfer of confined slot nanojet impingement is offered under magnetic field effects, while optimization-assisted computational fluid dynamics is used to find the best working conditions to achieve the best performance of the [...] Read more.
A novel porous object for the control of the convective heat transfer of confined slot nanojet impingement is offered under magnetic field effects, while optimization-assisted computational fluid dynamics is used to find the best working conditions to achieve the best performance of the system. The flow, thermal patterns, and heat transfer characteristics were influenced by the variation in rotational Reynolds number (Rew), Hartmann number (Ha), permeability of the porous object (Da) and its location (Mx). There was a 14.5% difference in the average Nusselt number (Nu) at the highest Rew when motionless object configuration at Ha = 5 was compared, while it was less than 2% at Ha = 25. At Rew = −600, the average Nu variation was 22% when cases with the lowest and highest magnetic field strength were compared. The porous object provides an excellent tool for convective heat transfer control, while the best performance was achieved by using optimization-assisted computational fluid dynamics. The optimal sets of (Rew, Da, Mx, AR) for porous object were (−315.97, 0.0188, −1.456, 0.235), (−181.167, 0.0167, −1.441, 0.2), and (−483.13, 0.0210, −0.348, 0.2) at Ha = 5, 10, and 25, respectively. At the optimal operating point, the local Nu enhancements were 19.46%, 44.86%, and −0.54% at Ha = 5, 10, and 15, respectively, when the no-object case was compared, while the average values were 7.87%, 8.09% and 5.04%. Full article
(This article belongs to the Special Issue Numerical Methods for Problems Arising in Mechanics)
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21 pages, 2206 KiB  
Article
Forced Convection of Non-Newtonian Nanofluid Flow over a Backward Facing Step with Simultaneous Effects of Using Double Rotating Cylinders and Inclined Magnetic Field
by Lioua Kolsi, Fatih Selimefendigil, Lotfi Ben Said, Abdelhakim Mesloub and Faisal Alresheedi
Mathematics 2021, 9(23), 3002; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233002 - 23 Nov 2021
Cited by 8 | Viewed by 1526
Abstract
The forced convection of non-Newtonian nanofluid for a backward-facing flow system was analyzed under the combined use of magnetic field and double rotating cylinders by using finite element method. The power law nanofluid type was used with different solid volume fractions of alumina [...] Read more.
The forced convection of non-Newtonian nanofluid for a backward-facing flow system was analyzed under the combined use of magnetic field and double rotating cylinders by using finite element method. The power law nanofluid type was used with different solid volume fractions of alumina at 20 nm in diameter. The effects of the Re number (100≤Re≤300), rotational Re number (−2500≤Rew≤3000), Ha number (0≤Ha≤50), and magnetic field inclination (0≤γ≤90) on the convective heat transfer and flow features were numerically assessed. The non-Newtonian fluid power law index was taken between 0.8 and 1.2 while particle volume fractions up to 4% were considered. The presence of the rotating double cylinders made the flow field complicated where multiple recirculation regions were established near the step region. The impacts of the first (closer to the step) and second cylinders on the heat transfer behavior were different depending upon the direction of rotation. As the first cylinder rotated in the clockwise direction, the enhancement in the average heat transfer of 20% was achieved while it deteriorated by approximately 2% for counter-clockwise directional rotation. However, for the second cylinder, both the rotational direction resulted in heat transfer augmentation while the amounts were 14% and 18% at the highest speeds. Large vortices on the upper and lower channel walls behind the step were suppressed with magnetic field effects. The average Nu number generally increased with the higher strengths of the magnetic field and inclination. Up to 30% increment with strength was obtained while this amount was 44% with vertical orientation. Significant impacts of power law fluid index on the local and average Nu number were seen for an index of n = 1.2 as compared to the fluid with n = 0.8 and n = 1 while an average Nu number of 2.75 times was obtained for the flow system for fluid with n = 1.2 as compared to case for fluid with the n value of 0.8. Further improvements in the local and average heat transfer were achieved with using nanoparticles while at the highest particle amount, the enhancements of the average Nu number were 34%, 36% and 36.6% for the fluid with n values of 0.8, 1 and 1.2, respectively. Full article
(This article belongs to the Special Issue Numerical Methods for Problems Arising in Mechanics)
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14 pages, 2920 KiB  
Article
Multiple Slip Impact on the Darcy–Forchheimer Hybrid Nano Fluid Flow Due to Quadratic Convection Past an Inclined Plane
by Fouad Othman Mallawi and Malik Zaka Ullah
Mathematics 2021, 9(22), 2934; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222934 - 18 Nov 2021
Cited by 3 | Viewed by 1285
Abstract
Nowadays, the problem of solar thermal absorption plays a vital role in energy storage in power plants, but within this phenomenon solar systems have a big challenge in storing and regulating energies at extreme temperatures. The solar energy absorber based on hybrid nanofluids [...] Read more.
Nowadays, the problem of solar thermal absorption plays a vital role in energy storage in power plants, but within this phenomenon solar systems have a big challenge in storing and regulating energies at extreme temperatures. The solar energy absorber based on hybrid nanofluids tends to store thermal energy, and the hybrid nanofluids involve the stable scattering of different nano dimension particles in the conventional solvent at a suitable proportion to gain the desired thermophysical constraints. The authors focus on the behavior of the inclined plate absorber panel as the basic solution of water is replaced by a hybrid nanofluid, including Cu (Copper) and Al2O3 (Aluminum Oxide), and water is utilized as a base surfactant in the current investigation. The inclined panel is integrated into a porous surface with the presence of solar radiations, Joule heating, and heat absorption. The fundamental equations of the flow and energy model are addressed with the similarity transformations. The homotopy analysis method (HAM) via Mathematica software is used to explore the solution to this problem. Furthermore, the important physical characteristics of the rate of heat transfer, omission and absorption of solar radiation, and its impact on the solar plant are observed. Full article
(This article belongs to the Special Issue Numerical Methods for Problems Arising in Mechanics)
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