Mathematics

Editorial

Jump to: Research

3 pages, 172 KiB

Open AccessEditorial

Preface to the Special Issue on “Computational Mechanics in Engineering Mathematics”

by Michael R. Booty

Mathematics 2023, 11(3), 781; https://doi.org/10.3390/math11030781 - 03 Feb 2023

Viewed by 869

Abstract

Increases in computational resources and the constant development of numerical methods have greatly expanded the range and complexity of systems that can be simulated numerically [...] Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

Research

Jump to: Editorial

20 pages, 1028 KiB

Open AccessArticle

Dynamics of Eyring–Powell Nanofluids When Bioconvection and Lorentz Forces Are Significant: The Case of a Slender Elastic Sheet of Variable Thickness with Porous Medium

by Abdul Manan, Saif Ur Rehman, Nageen Fatima, Muhammad Imran, Bagh Ali, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(17), 3039; https://doi.org/10.3390/math10173039 - 23 Aug 2022

Cited by 11 | Viewed by 1206

Abstract

We examine thermal management in the heat exchange of compact density nanoentities in crude base liquids. It demands the study of the heat and flow problem with non-uniform physical properties. This study was conceived to analyze magnetohydrodynamic Eyring–Powell nanofluid transformations due to slender [...] Read more.

We examine thermal management in the heat exchange of compact density nanoentities in crude base liquids. It demands the study of the heat and flow problem with non-uniform physical properties. This study was conceived to analyze magnetohydrodynamic Eyring–Powell nanofluid transformations due to slender sheets with varying thicknesses. Temperature-dependent thermal conductivity and viscosity prevail. Bioconvection due to motivated and dynamic microorganisms for Eyring–Powell fluid flow is a novel aspect herein. The governing PDEs are transmuted into a nonlinear differential structure of coupled ODEs using a series of viable similarity transformations. An efficient code for the Runge–Kutta method is developed in MATLAB script to attain numeric solutions. These findings are also compared to previous research to ensure that current findings are accurate. Computational activities were carried out with a variation in pertinent parameters to perceive physical insights on the quantities of interest. Representative outcomes for velocity, temperature, nanoparticles concentration, and bioconvection distributions as well as the local thermal transport for different inputs of parameters are portrayed in both graphical and tabular forms. The results show that the fluid’s velocity increases with mixed convection parameters due to growing buoyancy effects and the fluid’s temperature also increased with higher Brownian motion

N b

and thermophoretic

N t

. The numerical findings might be used to create efficient heat exchangers for increasingly challenging thermo-technical activities in manufacturing, construction, and transportation. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

13 pages, 1889 KiB

Open AccessArticle

Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives

by Jesús Amo-Navarro, Ricardo Vinuesa, J. Alberto Conejero and Sergio Hoyas

Mathematics 2021, 9(19), 2508; https://doi.org/10.3390/math9192508 - 07 Oct 2021

Cited by 2 | Viewed by 2217

Abstract

In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier–Stokes equations to the vorticity–velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An [...] Read more.

In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier–Stokes equations to the vorticity–velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

18 pages, 10878 KiB

Open AccessArticle

Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model

by Mikel Brun, Fernando Cortés and María Jesús Elejabarrieta

Mathematics 2021, 9(15), 1731; https://doi.org/10.3390/math9151731 - 22 Jul 2021

Cited by 2 | Viewed by 1513

Abstract

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different [...] Read more.

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

22 pages, 2637 KiB

Open AccessArticle

Theoretical Efficiency Study of Output Lubricant Flow Rate Regulating Principle on the Example of a Two-Row Aerostatic Journal Bearing with Longitudinal Microgrooves and a System of External Combined Throttling

by Vladimir Kodnyanko, Stanislav Shatokhin, Andrey Kurzakov, Yuri Pikalov, Lilia Strok, Iakov Pikalov, Olga Grigorieva and Maxim Brungardt

Mathematics 2021, 9(14), 1698; https://doi.org/10.3390/math9141698 - 19 Jul 2021

Cited by 4 | Viewed by 1549

Abstract

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance [...] Read more.

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance and an increased tendency for instability. In radial bearings, it is possible to use longitudinal microgrooves, which practically exclude circumferential air leakage, and contributes to a significant increase in load-bearing capacity. To reduce compliance to zero and negative values, inlet diaphragm and elastic airflow regulators are used. Active flow compensation is inextricably linked to the problem of ensuring the stability of bearings due to the presence of relatively large volumes of gas in the regulator, which have a destabilizing effect. This problem was solved by using an external combined throttling system. Bearings with input flow regulators have a number of disadvantages-they are very energy-intensive and have an insufficiently stable load capacity. A more promising way to reduce compliance is the use of displacement compensators for the movable element. Such bearings also allow for a decrease in compliance to zero and negative values, which makes it possible to use them not only as supports, but also as active deformation compensators of the technological system of machine tools in order to reduce the time and increase the accuracy of metalworking. The new idea of using active flow compensators is to regulate the flow rate not at the inlet, but at the outlet of the air flow. This design has the energy efficiency that is inherent to a conventional bearing, but the regulation of the lubricant output flow allows the compliance to be reduced to zero and negative values. This article discusses the results of a theoretical study of the static and dynamic characteristics of a two-row radial aerostatic bearing with longitudinal microgrooves and an output flow regulator. Mathematical modeling and theoretical study of stationary modes have been carried out. Formulas for determining static compliance and load capacity are obtained. Iterative finite-difference methods for determining the dynamic characteristics of a structure are proposed. The calculation of dynamic quality criteria was carried out on the basis of the method of rational interpolation of the bearing transfer function, as a system with distributed parameters, developed by the authors. It was found that the volumes of the microgrooves do not have a noticeable effect on the bearing dynamics. It is shown that, in this design, the external combined throttling system is an effective means of maintaining stability and high dynamic quality of the design operating in the modes of low, zero and negative compliance. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

15 pages, 61065 KiB

Open AccessArticle

Numerical Modeling of Face Shield Protection against a Sneeze

by Ainara Ugarte-Anero, Unai Fernandez-Gamiz, Iñigo Aramendia, Ekaitz Zulueta and Jose Manuel Lopez-Guede

Mathematics 2021, 9(13), 1582; https://doi.org/10.3390/math9131582 - 05 Jul 2021

Cited by 9 | Viewed by 3174

Abstract

The protection provided by wearing masks has been a guideline worldwide to prevent the risk of COVID-19 infection. The current work presents an investigation that analyzes the effectiveness of face shields as personal protective equipment. To that end, a multiphase computational fluid dynamic [...] Read more.

The protection provided by wearing masks has been a guideline worldwide to prevent the risk of COVID-19 infection. The current work presents an investigation that analyzes the effectiveness of face shields as personal protective equipment. To that end, a multiphase computational fluid dynamic study based on Eulerian–Lagrangian techniques was defined to simulate the spread of the droplets produced by a sneeze. Different scenarios were evaluated where the relative humidity, ambient temperature, evaporation, mass transfer, break up, and turbulent dispersion were taken into account. The saliva that the human body generates was modeled as a saline solution of 8.8 g per 100 mL. In addition, the influence of the wind speed was studied with a soft breeze of 7 km/h and a moderate wind of 14 km/h. The results indicate that the face shield does not provide accurate protection, because only the person who is sneezed on is protected. Moreover, with a wind of 14 km/h, none of the droplets exhaled into the environment hit the face shield, instead, they were deposited onto the neck and face of the wearer. In the presence of an airflow, the droplets exhaled into the environment exceeded the safe distance marked by the WHO. Relative humidity and ambient temperature play an important role in the lifetime of the droplets. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

15 pages, 2702 KiB

Open AccessArticle

Dynamic Quality of an Aerostatic Thrust Bearing with a Microgroove and Support Center on Elastic Suspension

by Vladimir Kodnyanko, Stanislav Shatokhin, Andrey Kurzakov, Lilia Strok, Yuri Pikalov, Iakov Pikalov, Olga Grigorieva and Maxim Brungardt

Mathematics 2021, 9(13), 1492; https://doi.org/10.3390/math9131492 - 25 Jun 2021

Cited by 1 | Viewed by 1135

Abstract

The disadvantage of aerostatic bearings is their low dynamic quality. The negative impact on the dynamic characteristics of the bearing is exerted by the volume of air contained in the bearing gap, pockets, and microgrooves located at the outlet of the feeding diaphragms. [...] Read more.

The disadvantage of aerostatic bearings is their low dynamic quality. The negative impact on the dynamic characteristics of the bearing is exerted by the volume of air contained in the bearing gap, pockets, and microgrooves located at the outlet of the feeding diaphragms. Reducing the volume of air in the flow path is a resource for increasing the dynamic quality of the aerostatic bearing. This article presents an improved design of an axial aerostatic bearing with simple diaphragms, an annular microgroove, and an elastic suspension of the movable center of the supporting disk. A mathematical model is presented and a methodology for calculating the static characteristics of a bearing and dynamic quality indicators is described. The calculations were carried out using dimensionless quantities, which made it possible to reduce the number of variable parameters. A new method for solving linearized and Laplace-transformed boundary value problems for transformants of air pressure dynamic functions in the bearing layer was applied, which made it possible to obtain a numerical solution of problems sufficient for practice accuracy. The optimization of the criteria for the dynamic quality of the bearing was carried out. It is shown that the use of an elastic suspension of the support center improves its dynamic characteristics by reducing the volume of compressed air in the bearing layer and choosing the optimal volume of the microgroove. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

15 pages, 5520 KiB

Open AccessArticle

A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression

by Longgang Tian and Ziling Cheng

Mathematics 2021, 9(11), 1181; https://doi.org/10.3390/math9111181 - 24 May 2021

Cited by 4 | Viewed by 2744

Abstract

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular [...] Read more.

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

21 pages, 12043 KiB

Open AccessArticle

Effects of Damaged Rotor Blades on the Aerodynamic Behavior and Heat-Transfer Characteristics of High-Pressure Gas Turbines

by Thanh Dam Mai and Jaiyoung Ryu

Mathematics 2021, 9(6), 627; https://doi.org/10.3390/math9060627 - 16 Mar 2021

Cited by 7 | Viewed by 3029

Abstract

Gas turbines are critical components of combined-cycle power plants because they influence the power output and overall efficiency. However, gas-turbine blades are susceptible to damage when operated under high-pressure, high-temperature conditions. This reduces gas-turbine performance and increases the probability of power-plant failure. This [...] Read more.

Gas turbines are critical components of combined-cycle power plants because they influence the power output and overall efficiency. However, gas-turbine blades are susceptible to damage when operated under high-pressure, high-temperature conditions. This reduces gas-turbine performance and increases the probability of power-plant failure. This study compares the effects of rotor-blade damage at different locations on their aerodynamic behavior and heat-transfer properties. To this end, we considered five cases: a reference case involving a normal rotor blade and one case each of damage occurring on the pressure and suction sides of the blades’ near-tip and midspan sections. We used the Reynolds-averaged Navier-Stokes equation coupled with the k − ω SST γ turbulence model to solve the problem of high-speed, high-pressure compressible flow through the GE-E³ gas-turbine model. The results reveal that the rotor-blade damage increases the heat-transfer coefficients of the blade and vane surfaces by approximately 1% and 0.5%, respectively. This, in turn, increases their thermal stresses, especially near the rotor-blade tip and around damaged locations. The four damaged-blade cases reveal an increase in the aerodynamic force acting on the blade/vane surfaces. This increases the mechanical stress on and reduces the fatigue life of the blade/vane components. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

16 pages, 4750 KiB

Open AccessArticle

Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

by Syed M. Hussain, Rohit Sharma, Manas R. Mishra and Sattam S. Alrashidy

Mathematics 2020, 8(11), 1929; https://doi.org/10.3390/math8111929 - 02 Nov 2020

Cited by 33 | Viewed by 2335

Abstract

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations [...] Read more.

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

21 pages, 834 KiB

Open AccessArticle

Engineering Applications of Peristaltic Fluid Flow with Hall Current, Thermal Deposition and Convective Conditions

by Humaira Yasmin, Naveed Iqbal and Anum Tanveer

Mathematics 2020, 8(10), 1710; https://doi.org/10.3390/math8101710 - 04 Oct 2020

Cited by 26 | Viewed by 2111

Abstract

This article addresses the peristaltic flow in a compliant wall channel. Analysis has been carried out in the presence of a Hall current and chemical reaction. Convective conditions in terms of both heat and mass transfer are employed. Mathematical modeling is developed for [...] Read more.

This article addresses the peristaltic flow in a compliant wall channel. Analysis has been carried out in the presence of a Hall current and chemical reaction. Convective conditions in terms of both heat and mass transfer are employed. Mathematical modeling is developed for an incompressible Carreau fluid. Thermal deposition effect and convection at the channel walls are considered. Series solutions are obtained for small Weissenberg number

W e

. Solution expressions of velocity, temperature, concentration and stream function are obtained. These physical quantities are displayed and analyzed. Heat transfer coefficient and trapping are explored in detail. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Computational Mechanics in Engineering Mathematics

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (11 papers)

Editorial

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI