Mathematics

Research

21 pages, 24718 KiB

Open AccessArticle

A Closed-Form Parametrization and an Alternative Computational Algorithm for Approximating Slices of Minkowski Sums of Ellipsoids in

R^{3}

by Amirreza Fahim Golestaneh

Mathematics 2023, 11(1), 137; https://doi.org/10.3390/math11010137 - 27 Dec 2022

Viewed by 1874

Abstract

The current work aims to develop an approximation of the slice of a Minkowski sum of finite number of ellipsoids, sliced up by an arbitrarily oriented plane in Euclidean space

R^{3}

that, to the best of the author’s knowledge, has not been [...] Read more.

The current work aims to develop an approximation of the slice of a Minkowski sum of finite number of ellipsoids, sliced up by an arbitrarily oriented plane in Euclidean space

R^{3}

that, to the best of the author’s knowledge, has not been addressed yet. This approximation of the actual slice is in a closed form of an explicit parametric equation in the case that the slice is not passing through the zones of the Minkowski surface with high curvatures, namely the “corners”. An alternative computational algorithm is introduced for the cases that the plane slices the corners, in which a family of ellipsoidal inner and outer bounds of the Minkowski sum is used to construct a “narrow strip” for the actual slice of Minkowski sum. This strip can narrow persistently for a few more number of constructing bounds to precisely coincide on the actual slice of Minkowski sum. This algorithm is also applicable to the cases with high aspect ratio of ellipsoids. In line with the main goal, some ellipsoidal inner and outer bounds and approximations are discussed, including the so-called “Kurzhanski’s” bounds, which can be used to formulate the approximation of the slice of Minkowski sum. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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29 pages, 2597 KiB

Open AccessArticle

Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation

by Fatima Zohra Zaoui, Djamel Ouinas, Belkacem Achour, Mabrouk Touahmia, Mustapha Boukendakdji, Enamur R. Latifee, Ahmed A. Alawi Al-Naghi and Jaime Aurelio Viña Olay

Mathematics 2022, 10(24), 4764; https://doi.org/10.3390/math10244764 - 15 Dec 2022

Cited by 6 | Viewed by 2410

Abstract

This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined [...] Read more.

This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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15 pages, 3796 KiB

Open AccessArticle

Numerical Investigation of Heat Transfer Enhancement in a Microchannel with Conical-Shaped Reentrant Cavity

by Syarif Syahrul Syazwan Muzhaimey, Nik Nazri Nik Ghazali, Mohd Zamri Zainon, Irfan Anjum Badruddin, Mohamed Hussien, Sarfaraz Kamangar and N. Ameer Ahammad

Mathematics 2022, 10(22), 4330; https://doi.org/10.3390/math10224330 - 18 Nov 2022

Cited by 3 | Viewed by 1900

Abstract

The current study is focused on improving the thermal performance of the microchannel heat sink (MCHS) using the passive reentrant cavity approach. The MCHS physical model’s single channel was used in a three-dimensional numerical simulation. The basic geometrical layout of the MCHS’s computational [...] Read more.

The current study is focused on improving the thermal performance of the microchannel heat sink (MCHS) using the passive reentrant cavity approach. The MCHS physical model’s single channel was used in a three-dimensional numerical simulation. The basic geometrical layout of the MCHS’s computational domain was drawn from previously published research and verified using numerical and analytical correlations that were already in existence. The innovative conical-shaped microchannel heat sink’s (CMCHS) properties for heat transmission and fluid flow were examined numerically under steady-state conditions with laminar flow and a constant heat flux. At various flow velocities and configurations, the impacts of the geometrical parameters on pressure drops and heat transfer were examined. The outcome demonstrates a tremendously positive thermal performance with a significantly greater pressure drop than the traditional straight channel. In the microchannels with the conical-shaped reentrant cavities and minimal pressure loss, convection heat transfer is significantly improved. The findings of the present investigation demonstrate that the conical-shaped MCHS is practical and has a good chance of being used in real-world settings. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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24 pages, 5897 KiB

Open AccessArticle

Non-Linear Dynamic Movements of CNT/Graphene/Aluminum Oxide and Copper/Silver/Cobalt Ferrite Solid Particles in a Magnetized and Suction-Based Internally Heated Surface: Sensitivity and Response Surface Optimization

by C. S. K. Raju, M. Dinesh Kumar, N. Ameer Ahammad, Ahmed A. El-Deeb, Barakah Almarri and Nehad Ali Shah

Mathematics 2022, 10(21), 4066; https://doi.org/10.3390/math10214066 - 1 Nov 2022

Cited by 12 | Viewed by 1866

Abstract

Hybrid nanofluids combine two or more nano properties with a base fluid such as water ethylene. Usually, this helps enhance the heat transfer rate; in this article, using new similarity transformations created by Lie group analysis, the governing nonlinear partial differential equations are [...] Read more.

Hybrid nanofluids combine two or more nano properties with a base fluid such as water ethylene. Usually, this helps enhance the heat transfer rate; in this article, using new similarity transformations created by Lie group analysis, the governing nonlinear partial differential equations are transformed into a system of connected nonlinear ordinary differential equations. The resulting design is numerically solved using a BVP4C solver with the shooting method (MATLAB). The magneto hydrodynamic flow of an incompressible fluid and the rate of heat and mass transfer were investigated for two cases, with various nanoparticle shapes including cylindrical, spherical, and platelet. Case 1 was CNT (1%), graphene (1%), and aluminum oxide (1%), and Case 2 was copper (1%), silver (1%), and cobalt ferrite (1%). When the Hartmann number rises, velocity and temperature exhibit inverse behavior: the velocity profile increases, and the temperature profile decreases. When the suction rises, the velocity and temperature profiles both increase. Optimization techniques were used from response surface methodology (RSM) to set factorial variables so that the response met the desired maximum or minimum value. Factorial methods like ANOVA were used to model the response, but they were expanded to simulate the effects in terms of extrapolation. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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24 pages, 4847 KiB

Open AccessArticle

Analysis of a Transversely Isotropic Annular Circular Cylinder Immersed in a Magnetic Field Using the Moore–Gibson–Thompson Thermoelastic Model and Generalized Ohm’s Law

by Osama Moaaz, Ahmed E. Abouelregal and Fahad Alsharari

Mathematics 2022, 10(20), 3816; https://doi.org/10.3390/math10203816 - 16 Oct 2022

Cited by 3 | Viewed by 1855

Abstract

The main objective of this work is to study the homogeneous thermoelastic interactions in an isotropic hollow thin cylinder immersed in an electric–magnetic field using the linear Moore–Gibson–Thompson theory of thermoelasticity, taking into account the generalized Ohm’s law. The MGT system of thermoelastic [...] Read more.

The main objective of this work is to study the homogeneous thermoelastic interactions in an isotropic hollow thin cylinder immersed in an electric–magnetic field using the linear Moore–Gibson–Thompson theory of thermoelasticity, taking into account the generalized Ohm’s law. The MGT system of thermoelastic equations for the new model is created by incorporating a relaxation period in the Green–Naghdi type III framework. In addition, the Maxwell equations that investigate the effect of the electromagnetic field are presented. While the outer surface of the hollow cylinder is thermally insulated and free of traction, the interior surface is both free of traction and subject to thermal shock. To convert the problem to the space domain only, the Laplace transform methodology is used to solve the governing equations generated in the transformed domain. The theoretical results are computed dynamically and are graphically displayed for a transversely isotropic material using the Honig and Hirdes approach. A comparison of findings based on different (classical and generalized) thermoelastic theories is provided, followed by a discussion on the impact of the applied electromagnetic field. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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22 pages, 10148 KiB

Open AccessArticle

Irreversibility Analysis in the Ethylene Glycol Based Hybrid Nanofluid Flow amongst Expanding/Contracting Walls When Quadratic Thermal Radiation and Arrhenius Activation Energy Are Significant

by Bommana Lavanya, Jorige Girish Kumar, Macherla Jayachandra Babu, Chakravarthula Sivakrishnam Raju, Nehad Ali Shah and Prem Junsawang

Mathematics 2022, 10(16), 2984; https://doi.org/10.3390/math10162984 - 18 Aug 2022

Cited by 8 | Viewed by 1720

Abstract

In this new era of the fluid field, researchers are interested in hybrid nanofluids because of their thermal properties and potential, which are better than those of nanofluids when it comes to increasing the rate at which heat is transferred. Compared to the [...] Read more.

In this new era of the fluid field, researchers are interested in hybrid nanofluids because of their thermal properties and potential, which are better than those of nanofluids when it comes to increasing the rate at which heat is transferred. Compared to the dynamics of radiative Ethylene Glycol-Zinc Oxide (nanofluid) and Ethylene Glycol-Zinc Oxide-Titanium Dioxide (hybrid nanofluid) flows between two permeable expanding/contracting walls, nothing is known in terms of Lorentz force, heat source, and the activation energy. The thermo-physical characteristics of Ethylene Glycol, Zinc Oxide nanoparticles, and Titanium Dioxide nanoparticles are used in this study to derive the governing equations for the transport of both dynamics. Governing equations are converted as a set of nonlinear ordinary differential equations (with the aid of suitable similarity mutations), and then the MATLAB bvp4c solver is used to solve the equations. This study’s significant findings are that rise in the reaction rate constant increases mass transfer rate, whereas an increase in the activation energy parameter decreases it. The mass transfer rate decreases at a rate of 0.04669 (in the case of hybrid nanofluid) and 0.04721 (in the case of nanofluid) when activation energy (

E

) takes input in the range

0 \leq E \leq 5

. It has been noticed that the velocity profiles are greater when the walls are expanding as opposed to when they are contracting. It is detected that the heat transfer rate reduces as the heat source parameter increases. The heat transfer rate drops at a rate of 0.9734 (in the case of hybrid Nanofluid) and 0.97925 (in the case of nanofluid) when the heat source parameter (

Q

) takes input in the range

0 \leq Q \leq 0.3

. In addition, it has been observed that the entropy generation increases as the Brinkmann number rises. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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14 pages, 1156 KiB

Open AccessArticle

The Casson Dusty Nanofluid: Significance of Darcy–Forchheimer Law, Magnetic Field, and Non-Fourier Heat Flux Model Subject to Stretch Surface

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

Mathematics 2022, 10(16), 2877; https://doi.org/10.3390/math10162877 - 11 Aug 2022

Cited by 57 | Viewed by 2316

Abstract

This work aims to offer a mathematical model for two-phase flow that investigates the interaction of Casson nanofluid and dust particles across a stretching surface. MHD Darcy–Forchheimer porous medium and Fourier’s law through Cattaneo–Christove thermal flux are also considered. The governing equations for [...] Read more.

This work aims to offer a mathematical model for two-phase flow that investigates the interaction of Casson nanofluid and dust particles across a stretching surface. MHD Darcy–Forchheimer porous medium and Fourier’s law through Cattaneo–Christove thermal flux are also considered. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. The Runge–Kutta method with the shooting tool is utilized numerically to solve the boundary layer equations computed in MATLAB to obtain numerical results for various pertinent parameters. The numerical outcomes of momentum, temperature, and concentration distribution are visible for both phases. The results of the skin friction, heat transfer coefficients, and the Sherwood number are also visible in the graphs. Furthermore, by comparing the current findings to the existing literature, the validity of the results is confirmed and found to be in good agreement. The fluid velocity is reduced against increasing strength of Casson fluid parameter, enhanced the fluid phase and dust phase fluid temperature. The temperature declines against the growing values of the relaxation time parameter in both phases. Dusty fluids are used in various engineering and manufacturing sectors, including petroleum transportation, car smoke emissions, power plant pipes, and caustic granules in mining. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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13 pages, 510 KiB

Open AccessArticle

Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed

by I-Chi Chan

Mathematics 2022, 10(16), 2838; https://doi.org/10.3390/math10162838 - 9 Aug 2022

Viewed by 1586

Abstract

We present an analytical solution for the scattering of linear progressive waves by a surface rectangular obstacle above a muddy seabed. The bottom cohesive mud is assumed to act as a Newtonian fluid, and the thickness of the mud layer is considered to [...] Read more.

We present an analytical solution for the scattering of linear progressive waves by a surface rectangular obstacle above a muddy seabed. The bottom cohesive mud is assumed to act as a Newtonian fluid, and the thickness of the mud layer is considered to be comparable to the Stokes boundary layer thickness. Our analytical results based on the matched eigenfunction expansions incorporate the combined effects of obstacles and a fluid mud bottom. By reducing the mud layer thickness or the dimensions of the obstacle to zero, the present study recovers the classical solution for wave scattering by a surface obstacle above a solid bed or wave propagation over a layer of fluid mud. Our analytical predictions of wave amplitudes and wave forces acting on the bottom of the obstacle agree satisfactorily with the available numerical results. The most prominent effect of a muddy seabed is a strong damping of wave amplitude. Parameter study reveals that the obstacle submerged depth, mud layer thickness, and wave frequency can have significant impacts on the attenuation of wave amplitude due to the presence of a muddy seabed. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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22 pages, 6045 KiB

Open AccessArticle

FEM-Based Simulative Study for Multi-Response Optimization of Powder Bed Fusion Process

by Anoop Kumar Sood, Azhar Equbal, Zahid A. Khan, Irfan Anjum Badruddin and Mohamed Hussien

Mathematics 2022, 10(14), 2505; https://doi.org/10.3390/math10142505 - 19 Jul 2022

Viewed by 1658

Abstract

Laser powder bed fusion (LPBF) is an additive manufacturing technology which uses a heat source (laser) to sinter or fuse atomized powder particles together. A new layer of powder is spread over the previous layer using a roller, and then the laser power [...] Read more.

Laser powder bed fusion (LPBF) is an additive manufacturing technology which uses a heat source (laser) to sinter or fuse atomized powder particles together. A new layer of powder is spread over the previous layer using a roller, and then the laser power fuses them. This mechanism is repeated until the part model is completed. To reduce the time, effort, and cost, the present study incorporated the design of an experimental approach conjoined with finite element analysis (FEA) to simulate the LPBF process. A three-dimensional (3D) bi-material model was subjected to FEA with variations in temporal and spatial material characteristics. A Gaussian moving heat source model for the multi-scanning of a single layer was developed to understand the effect of process parameters, namely laser power, scan speed, and scan pattern on melt pool dimensions. Although, similar simulation models have been reported in the literature, the majority of these did not consider parametric variations. A few studies adopted multiple parameters which varied simultaneously, but the major limitation of these studies was that most of them did not consider multiple characteristics under a constrained environment. In the present research, the multi-parameter multi-level simulation study was performed to understand the process mechanism with fewer simulations. Results showed that the studied dimensions were sensitive to parameter setting, and that temperature variation within the melt pool was dependant on the material phase in the vicinity of the melt pool. This research proposed that melt pool dimensions must be accurately controlled for optimum process performance to achieve proper overlap between the adjacent scan lines and sufficient depth to complete bonding with the bottom layer. Since the involved criteria were of a conflicting nature, the problem of determining a single factor setting to obtain the desired results was solved using grey relational analysis (GRA). It was found that, among all the considered process parameters, scan velocity was the most significant one. This research recommended a maximum scan velocity i.e., v = 1.5 m/s, with a minimum laser power i.e., P = 80 W. In addition, it was also suggested that low energy density be used to melt the powder layer properly. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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31 pages, 16369 KiB

Open AccessArticle

Dynamics of Triple Diffusive Free Convective MHD Fluid Flow: Lie Group Transformation

by Vellaboyina Nagendramma, Putta Durgaprasad, Narsu Sivakumar, Battina Madhusudhana Rao, Chakravarthula Siva Krishnam Raju, Nehad Ali Shah and Se-Jin Yook

Mathematics 2022, 10(14), 2456; https://doi.org/10.3390/math10142456 - 14 Jul 2022

Cited by 16 | Viewed by 2162

Abstract

This analysis is interested in the dynamic flow of incompressible triple diffusive fluid flowing through a linear stretched surface. The current study simulates when Boussinesq approximation and MHD are significant. As for originality, a comparative study of all the results for opposing and [...] Read more.

This analysis is interested in the dynamic flow of incompressible triple diffusive fluid flowing through a linear stretched surface. The current study simulates when Boussinesq approximation and MHD are significant. As for originality, a comparative study of all the results for opposing and assisting flow cases is provided. Lie-group transformation is utilized to determine symmetry depletions of partial differential equations. The transformed system of ordinary differential equations is solved using the Runge-Kutta shooting technique. The impacts of magnetic parameter, buoyancy ratio parameter of temperature and concentration, and Lewis number on velocity, temperature, and concentration are depicted through graphs. We observed that the magnetic field parameter decelerates in velocity distribution for both fluid flow cases. Additionally, the same phenomenon was noticed with the buoyancy ratio parameters on both salt concentration distributions. Finally, the influence of heat and mass transfer rates decreases for both fluid flow cases with an increase in Lewis number. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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17 pages, 4633 KiB

Open AccessArticle

A General Design Method of Cam Profile Based on Cubic Splines and Dynamic Model: Case Study of a Gravity-Driven Tricycle

by Zhihao Jiang, Tao Zhu, Zhongxiang Chen, Ruilin Fan, Yi Gao, Hanlu Zhang and Lingming Wang

Mathematics 2022, 10(12), 1979; https://doi.org/10.3390/math10121979 - 8 Jun 2022

Cited by 1 | Viewed by 2592

Abstract

This paper proposes a general design method for cams based on the kinematics and dynamics of a mechanical system. According to the actuator’s trajectory, the cam profile is generated in reverse based on the kinematic model of the system. Firstly, the cam design’s [...] Read more.

This paper proposes a general design method for cams based on the kinematics and dynamics of a mechanical system. According to the actuator’s trajectory, the cam profile is generated in reverse based on the kinematic model of the system. Firstly, the cam design’s optimising problem is converted into the execution trajectory’s optimisation to obtain the optimum operation trajectory according to the actuator’s requirements. Secondly, the relationship between the cam profile and the actuation trajectory is modelled based on the kinematics and dynamics of the mechanical system. Then, applying the cubic spline interpolation method, the cam profile is generated, and the error compensation methods are illustrated through numerical analysis. Finally, the validity of the presented design method is verified through experiments, which demonstrate the reliability of this method. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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18 pages, 4548 KiB

Open AccessArticle

Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO₂ + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction

by Gopinath Veeram, Pasam Poojitha, Harika Katta, Sanakkayala Hemalatha, Macherla Jayachandra Babu, Chakravarthula S. K. Raju, Nehad Ali Shah and Se-Jin Yook

Mathematics 2022, 10(10), 1706; https://doi.org/10.3390/math10101706 - 16 May 2022

Cited by 10 | Viewed by 2063

Abstract

The heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose [...] Read more.

The heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose of this study was to evaluate the significance of the higher order chemical reaction parameter on the radiative flow of hybrid nanofluid (polyethylene glycol (PEG)–water combination: base fluid and zirconium dioxide, magnesium oxide: nanoparticles) via a curved shrinking sheet with viscous dissipation. Flow-driven equations were transformed into nonlinear ODEs using appropriate similarity transmutations, and then solved using the bvp4c solver (MATLAB built-in function). The results of two scenarios,

P E G - W a t e r + Z r O_{2} + M g O

(hybrid nanofluid) and

P E G - W a t e r + Z r O_{2}

, (nanofluid) are reported. In order to draw important inferences about physical features, such as heat transfer rate, a correlation coefficient was used. The main findings of this study were that curvature parameter lowers fluid velocity, and Eckert number increases the temperature of fluid. It was observed that the volume fraction of nanoparticles enhances the skin friction coefficient and curvature parameter lessens the same. It was noticed that when curvature parameter (K) takes input in the range

0.5 \leq K \leq 2.5

, the skin friction coefficient decreases at a rate of 1.46633 (i.e., 146.633%) (in the case of hybrid nanofluid) and 1.11236 (i.e., 111.236%) (in the case of nanofluid) per unit value of curvature parameter. Increasing rates in the skin friction parameter were 3.481179 (i.e., 348.1179%) (in the case of hybrid nanofluid) and 2.745679 (in the case of nanofluid) when the volume fraction of nanoparticle (

ϕ_{1}

) takes input in the range

0 \leq ϕ_{1} \leq 0.2

. It was detected that, when Eckert number

(E_{c k})

increases, Nusselt number decreases. The decrement rates were observed as 1.41148 (i.e., 141.148%) (in the case of hybrid nanofluid) and 1.15337 (i.e., 153.337%) (in the case of nanofluid) when Eckert number takes input in the range

0 \leq E_{c k} \leq 0.2

. In case of hybrid nanofluid, it was discovered that the mass transfer rate increases at a rate of 1.497214 (i.e., 149.7214%) when chemical reaction

(K r)

takes input in the range

0 \leq K r \leq 0.2

. In addition, we checked our findings against those of other researchers and discovered a respectable degree of agreement. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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17 pages, 4871 KiB

Open AccessArticle

Effect of Thermal Radiation and Double-Diffusion Convective Peristaltic Flow of a Magneto-Jeffrey Nanofluid through a Flexible Channel

by Asha S. Kotnurkar, Joonabi Beleri, Irfan Anjum Badruddin, Khaleed H.M.T., Sarfaraz Kamangar and Nandalur Ameer Ahammad

Mathematics 2022, 10(10), 1701; https://doi.org/10.3390/math10101701 - 16 May 2022

Cited by 6 | Viewed by 1879

Abstract

The noteworthiness of double-diffusive convection with magneto-Jeffrey nanofluid on a peristaltic motion under the effect of MHD and porous medium through a flexible channel with the permeable wall has been theoretically examined. A non-linearized Rosseland approximation is utilized to show the thermal radiation [...] Read more.

The noteworthiness of double-diffusive convection with magneto-Jeffrey nanofluid on a peristaltic motion under the effect of MHD and porous medium through a flexible channel with the permeable wall has been theoretically examined. A non-linearized Rosseland approximation is utilized to show the thermal radiation effect. The governing equations are converted to standard non-linear partial differential equations by using suitable non-dimensional parameters. Solutions of emerging equations are obtained by using the multi-step differential transformation method (Ms-DTM). The differential transformation method (DTM) can be applied directly to nonlinear differential equations without requiring linearization and discretization; therefore, it is not affected by errors associated with discretization. The role of influential factors on concentration, temperature, volume fraction, and velocity are determined using graphs. A significant outcome of the present article is that the presence of double-diffusive convection can change the nature of convection in the system. The present results have a wide biological applicability, including for biomicrofluidic devices that regulate the fluid flow through a flexible endoscope and other medical pumping systems. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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18 pages, 5127 KiB

Open AccessArticle

3D Flow of Hybrid Nanomaterial through a Circular Cylinder: Saddle and Nodal Point Aspects

by Javali K. Madhukesh, Gosikere K. Ramesh, Govinakovi S. Roopa, Ballajja C. Prasannakumara, Nehad Ali Shah and Se-Jin Yook

Mathematics 2022, 10(7), 1185; https://doi.org/10.3390/math10071185 - 5 Apr 2022

Cited by 19 | Viewed by 2110

Abstract

This mathematical model explains the behavior of sinusoidal radius activity in stagnation point three-dimensional flow of hybrid nanoparticles through a circular cylinder. The energy equation of heat source/sink effect and the mass equation of Arrhenius energy of activation and chemical reaction effects are [...] Read more.

This mathematical model explains the behavior of sinusoidal radius activity in stagnation point three-dimensional flow of hybrid nanoparticles through a circular cylinder. The energy equation of heat source/sink effect and the mass equation of Arrhenius energy of activation and chemical reaction effects are incorporated. Self-relation transformations are adopted to reduce the PDEs to ODEs, then the RKF-45 method is solved with shooting proficiency. The nodal and saddle point action is studied in pertinent parameters for thermal, mass, and velocity curves. Further statistical values of skin friction, Nusselt number, and Sherwood number of both nodal and saddle points are portrayed in tables format. It is ascertained that higher values of activation energy and reaction rate enhance the concentration curve. In addition, the nodal point curves are always less than saddle point curves. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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17 pages, 3710 KiB

Open AccessArticle

Peristaltic Transport of Carreau Nanofluid in Presence of Triple Diffusion in an Asymmetric Channel by Multi-Step Differential Transformation Method

by Asha S. Kotnurkar, Joonabi Beleri, Irfan Anjum Badruddin, Sarfaraz Kamangar and Nandalur Ameer Ahammad

Mathematics 2022, 10(5), 807; https://doi.org/10.3390/math10050807 - 3 Mar 2022

Cited by 5 | Viewed by 2113

Abstract

The present work investigates the influence of triple diffusion on Carreau nanoliquid in peristaltic flow through an asymmetric channel. By using appropriate non-dimensional parameters, governing equations are transformed to conventional non-linear partial differential equations. The Ms-DTM is used to find solutions to developing [...] Read more.

The present work investigates the influence of triple diffusion on Carreau nanoliquid in peristaltic flow through an asymmetric channel. By using appropriate non-dimensional parameters, governing equations are transformed to conventional non-linear partial differential equations. The Ms-DTM is used to find solutions to developing equations. Because of the buoyancy force that prevails inside the boundary layer, velocity is impacted by the buoyancy ratio. The current investigation found that as the varied values of the modified Dufour parameter were increased, the temperature profile increased. The thermal conductivity increases as thermal diffusivity increases. It has also been discovered that the existence of triple-diffusing components with low diffusivity might alter the type of convection in the system. Graphs depict the influence of several parameters on velocity, salt1 and salt2 concentrations, solute concentration, and temperature. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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19 pages, 2943 KiB

Open AccessArticle

Theoretical Disquisition on the Static and Dynamic Characteristics of an Adaptive Stepped Hydrostatic Thrust Bearing with a Displacement Compensator

by Vladimir Kodnyanko, Andrey Kurzakov, Olga Grigorieva, Maxim Brungardt, Svetlana Belyakova, Ludmila Gogol, Alexey Surovtsev and Lilia Strok

Mathematics 2021, 9(22), 2949; https://doi.org/10.3390/math9222949 - 18 Nov 2021

Cited by 4 | Viewed by 1681

Abstract

Stepped hydrostatic thrust bearings used in metal-cutting machines are characterized by high load capacity and damping, which ensure the stable operation of structures. However, in comparison with throttle thrust bearings, they have a high compliance. It is preferable that, in addition to the [...] Read more.

Stepped hydrostatic thrust bearings used in metal-cutting machines are characterized by high load capacity and damping, which ensure the stable operation of structures. However, in comparison with throttle thrust bearings, they have a high compliance. It is preferable that, in addition to the main bearing function, a modern hydrostatic bearing has the ability to provide low (including negative) compliance for the implementation of an adaptive function in order to actively compensate for the deformation of the machine resilient system, thereby increasing the accuracy of metalworking. This paper considers the design of a stepped hydrostatic thrust bearing, which, in order to reduce the compliance to negative values, features a technical improvement consisting of the use of an active displacement compensator on an elastic suspension. In this paper, the results of mathematical modeling and theoretical research of stationary and non-stationary modes of operation of the adaptive thrust bearing are presented. The possibility of a significant reduction in the static compliance of the structure, including the negative compliance values, is shown. It was found that negative compliance is provided in a wide range of loads, which can be up to 80% of the range of permissible bearing loads. The study of the dynamic characteristics showed that with a targeted selection of parameters that ensure optimal performance, the adaptive thrust bearing is able to operate stably in the entire range of permissible loads. It has been established that an adaptive stepped hydrostatic thrust bearing with a displacement compensator has a high stability margin, sufficient to ensure its operability when implementing the adaptive function. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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14 pages, 3161 KiB

Open AccessArticle

Automatically Tightening Tiny Screw Using Two Images and Positioning Control

by Shou-Yu Chen, Jeng-Rong Ho, Pi-Cheng Tung and Chih-Kuang Lin

Mathematics 2021, 9(19), 2521; https://doi.org/10.3390/math9192521 - 7 Oct 2021

Viewed by 2300

Abstract

This paper describes how to tighten M1.4 screws by controlling a manipulator. The whole process is based on a human–machine interface designed using Visual Studio C++ to run image processing algorithms and control the position of a manipulator. Two charge-coupled device cameras are [...] Read more.

This paper describes how to tighten M1.4 screws by controlling a manipulator. The whole process is based on a human–machine interface designed using Visual Studio C++ to run image processing algorithms and control the position of a manipulator. Two charge-coupled device cameras are used. One is fixed on the stationary frame above screw holes and used to take pictures of the holes. The positions of the holes are determined using image processing algorithms and then transformed into the coordinate system of the manipulator by using coordinate transformation. The other camera, installed on the end effect of the manipulator, photographs the screw hole to fine-tune the position of the manipulator, improving positioning control. The image processing methods including grayscale, Gaussian filter, bilateral filter, binarization, edge detection, center of gravity, and minimum circumcircle are used to find the center coordinates of the target holes. Experimental study shows that M1.4 screws can be tightened into the target holes with the manipulator. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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16 pages, 2469 KiB

Open AccessArticle

Analysis of the Use of a Wind Turbine as an Energy Recovery Device in Transport Systems

by Francisco Rubio and Carlos Llopis-Albert

Mathematics 2021, 9(18), 2265; https://doi.org/10.3390/math9182265 - 15 Sep 2021

Cited by 8 | Viewed by 3715

Abstract

A wind turbine can act as an energy recovery device (ERS) in a comparable way to brakes (regenerative braking). When the velocity of a vehicle changes, the amount of energy related to it also changes. When its velocity decreases, the energy tends to [...] Read more.

A wind turbine can act as an energy recovery device (ERS) in a comparable way to brakes (regenerative braking). When the velocity of a vehicle changes, the amount of energy related to it also changes. When its velocity decreases, the energy tends to dissipate. Over time, this dissipated energy has been ignored. For example, during the braking process, the kinetic energy of the vehicle was converted into heat. In recent years, society’s greater awareness of climate change, pollution, and environmental issues has led to a great deal of interest in developing energy recovery systems. It allows the recovery of kinetic energy from braking (KERS), resulting in consumption reductions (efficiency gains) of up to 45%. The usefulness of installing a wind turbine as an energy recovery device is analysed, evaluating the savings that can be achieved with its two possible working modes: as an energy recovery device and as a system for utilizing aerodynamic force. The wind turbine has a horizontal axis and a diameter of 50 cm and is installed on the front of a vehicle. This vehicle will undergo three particular driving schemes, which will operate under different experimental conditions and operational parameters characterized by speeds, accelerations, stops, and driving time. The results clearly show the advantages of using the proposed technology. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

19 pages, 6145 KiB

Open AccessArticle

Optimization of Microjet Location Using Surrogate Model Coupled with Particle Swarm Optimization Algorithm

by Mohammad Owais Qidwai, Irfan Anjum Badruddin, Noor Zaman Khan, Mohammad Anas Khan and Saad Alshahrani

Mathematics 2021, 9(17), 2167; https://doi.org/10.3390/math9172167 - 5 Sep 2021

Cited by 8 | Viewed by 2851

Abstract

This study aimed to present the design methodology of microjet heat sinks with unequal jet spacing, using a machine learning technique which alleviates hot spots in heat sinks with non-uniform heat flux conditions. Latin hypercube sampling was used to obtain 30 design sample [...] Read more.

This study aimed to present the design methodology of microjet heat sinks with unequal jet spacing, using a machine learning technique which alleviates hot spots in heat sinks with non-uniform heat flux conditions. Latin hypercube sampling was used to obtain 30 design sample points on which three-dimensional Computational Fluid Dynamics (CFD) solutions were calculated, which were used to train the machine learning model. Radial Basis Neural Network (RBNN) was used as a surrogate model coupled with Particle Swarm Optimization (PSO) to obtain the optimized location of jets. The RBNN provides continuous space for searching the optimum values. At the predicted optimum values from the coupled model, the CFD solution was calculated for comparison. The percentage error for the target function was 0.56%, whereas for the accompanied function it was 1.3%. The coupled algorithm has variable inputs at user discretion, including gaussian spread, number of search particles, and number of iterations. The sensitivity of each variable was obtained. Analysis of Variance (ANOVA) was performed to investigate the effect of the input variable on thermal resistance. ANOVA results revealed that gaussian spread is the dominant variable affecting the thermal resistance. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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22 pages, 4371 KiB

Open AccessArticle

Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach

by Lidia M. Belmonte, Eva Segura, Antonio Fernández-Caballero, José A. Somolinos and Rafael Morales

Mathematics 2021, 9(12), 1424; https://doi.org/10.3390/math9121424 - 19 Jun 2021

Cited by 6 | Viewed by 2630

Abstract

This paper applies a robust generalised proportional integral (GPI) controller to address the problems of stabilisation and position tracking in voltage-controlled magnetic levitation systems, with consideration of the system’s physical parameters, non-linearities and exogenous disturbance signals. The controller has been developed using as [...] Read more.

This paper applies a robust generalised proportional integral (GPI) controller to address the problems of stabilisation and position tracking in voltage-controlled magnetic levitation systems, with consideration of the system’s physical parameters, non-linearities and exogenous disturbance signals. The controller has been developed using as a basis a model of the tangent linearised system around an arbitrary unstable equilibrium point. Since the approximate linearised system is differentially flat, it is therefore controllable. This flatness gives the resulting linearised system a relevant cascade characteristic, thus allowing simplification of the control scheme design. The performance of the proposed GPI controller has been analysed by means of numerical simulations and compared with two controllers: (i) a standard proportional integral derivative (PID) control, and (ii) a previously designed exact feedforward-GPI controller. Simulation results show that the proposed GPI control has a better dynamic response than the other two controllers, along with a better performance in terms of the integral squared tracking error (ISE), the integral absolute tracking error (IAE), and the integral time absolute tracking error (ITAE). Finally, experimental results have been included to illustrate the effectiveness of the proposed controller in terms of position stabilisation and tracking performance when appreciable non-linearities and uncertainties exist in the underlying system. Comparative graphs and metrics have shown a superior performance of the proposed GPI scheme to control the magnetic levitation platform. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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19 pages, 4902 KiB

Open AccessArticle

Design Optimization of 3-DOF Redundant Planar Parallel Kinematic Mechanism Based Finishing Cut Stage for Improving Surface Roughness of FDM 3D Printed Sculptures

by Minbok Lee, Hyungjin Jeong and Donghun Lee

Mathematics 2021, 9(9), 961; https://doi.org/10.3390/math9090961 - 25 Apr 2021

Cited by 4 | Viewed by 2206

Abstract

This paper describes the optimal design of a 3-DOF redundant planar parallel kinematic mechanism (PKM) based finishing cut stage to improve the surface roughness of FDM 3D printed sculptures. First, to obtain task-optimized and singularity minimum workspace of the redundant PKM, a weighted [...] Read more.

This paper describes the optimal design of a 3-DOF redundant planar parallel kinematic mechanism (PKM) based finishing cut stage to improve the surface roughness of FDM 3D printed sculptures. First, to obtain task-optimized and singularity minimum workspace of the redundant PKM, a weighted grid map based design optimization was applied for a task-optimized workspace without considering the redundancy. For the singularity minimum workspace, the isotropy and manipulability of the end effector of the PKM were carefully modeled under the previously obtained redundancy for optimality. It was confirmed that the workspace size increased by 81.4%, and the internal singularity significantly decreased. To estimate the maximum rated torque and torsional stiffness of all active joints and prevent an undesired end effector displacement of more than 200 μ

μ m

, a kinematic stiffness model composed of active and passive kinematic stiffness was derived from the virtual work theorem, and the displacement characteristic at the end effector was examined by applying the reaction force for the PLA surface finishing as an external force acting at the end effector. It was confirmed that the displacement of the end effector of a 1-DOF redundant PKM was not only less than 200 μ

μ m

but also decreased from 40.9% to 67.4% compared to a nonredundant actuation. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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20 pages, 4666 KiB

Open AccessArticle

Multidisciplinary Lightweight Optimization for Front Impact Structure of Body Frame Based on Active and Passive Safety

by Tingting Wang, Mengjian Wang, Xia Li and Dongchen Qin

Mathematics 2021, 9(8), 907; https://doi.org/10.3390/math9080907 - 19 Apr 2021

Cited by 3 | Viewed by 2539

Abstract

The Analytic Target Cascading (ATC) is an effective method for solving hierarchical Multidisciplinary Design Optimization (MDO) problems. At the same time, this method suffers from poor convergence and low accuracy, which is caused by the inconsistency of system constraints. In this paper, a [...] Read more.

The Analytic Target Cascading (ATC) is an effective method for solving hierarchical Multidisciplinary Design Optimization (MDO) problems. At the same time, this method suffers from poor convergence and low accuracy, which is caused by the inconsistency of system constraints. In this paper, a novel ATC method based on dynamic relaxation factor is proposed. The dynamic relaxation factor of consistency constraint is added in the system level and is adjusted by the deviation of the linking variables between the levels to ensure the feasible region of the design space. The effectiveness and accuracy of this method are verified by a mathematical example. This method is used to solve the lightweight problem of the trussed front part of the vehicle body frame based on active and passive safety to achieve the collaborative optimization of lightweight trussed frame, crash safety, and aerodynamic characteristics. The important value of the novel ATC method based on dynamic relaxation factor in engineering applications is proven. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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16 pages, 3727 KiB

Open AccessArticle

Identification of Inertial Parameters for Position and Force Control of Surgical Assistance Robots

by Pau Zamora-Ortiz, Javier Carral-Alvaro, Ángel Valera, José L. Pulloquinga, Rafael J. Escarabajal and Vicente Mata

Mathematics 2021, 9(7), 773; https://doi.org/10.3390/math9070773 - 2 Apr 2021

Cited by 3 | Viewed by 2648

Abstract

Surgeries or rehabilitation exercises are hazardous tasks for a mechanical system, as the device has to interact with parts of the human body without the hands-on experience that the surgeon or physiotherapist acquires over time. For various gynecological laparoscopic surgeries, such as laparoscopic [...] Read more.

Surgeries or rehabilitation exercises are hazardous tasks for a mechanical system, as the device has to interact with parts of the human body without the hands-on experience that the surgeon or physiotherapist acquires over time. For various gynecological laparoscopic surgeries, such as laparoscopic hysterectomy or laparoscopic pelvic endometriosis, Uterine Manipulators are used. These medical devices allow the uterus to be suitably mobilized. A gap needs to be filled in terms of the precise handling of this type of devices. In this sense, this manuscript first describes the mathematical procedure to identify the inertial parameters of uterine manipulators. These parameters are needed to establish an accurate position and force control for an electromechanical system to assist surgical operations. The method for identifying the mass and the center of mass of the manipulator is based on the solution of the equations for the static equilibrium of rigid solids. Based on the manipulator inertial parameter estimation, the paper shows how the force exerted by the manipulator can be obtained. For this purpose, it solves a matrix system composed of the torques and forces of the manipulator. Different manipulators have been used, and it has been verified that the mathematical procedures proposed in this work allow us to calculate in an accurate and efficient way the force exerted by these manipulators. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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13 pages, 536 KiB

Open AccessArticle

Modelling an Industrial Robot and Its Impact on Productivity

by Carlos Llopis-Albert, Francisco Rubio and Francisco Valero

Mathematics 2021, 9(7), 769; https://doi.org/10.3390/math9070769 - 1 Apr 2021

Cited by 8 | Viewed by 3068

Abstract

This research aims to design an efficient algorithm leading to an improvement of productivity by posing a multi-objective optimization, in which both the time consumed to carry out scheduled tasks and the associated costs of the autonomous industrial system are minimized. The algorithm [...] Read more.

This research aims to design an efficient algorithm leading to an improvement of productivity by posing a multi-objective optimization, in which both the time consumed to carry out scheduled tasks and the associated costs of the autonomous industrial system are minimized. The algorithm proposed models the kinematics and dynamics of the industrial robot, provides collision-free trajectories, allows to constrain the energy consumed and meets the physical characteristics of the robot (i.e., restriction on torque, jerks and power in all driving motors). Additionally, the trajectory tracking accuracy is improved using an adaptive fuzzy sliding mode control (AFSMC), which allows compensating for parametric uncertainties, bounded external disturbances and constraint uncertainties. Therefore, the system stability and robustness are enhanced; thus, overcoming some of the limitations of the traditional proportional-integral-derivative (PID) controllers. The trade-offs among the economic issues related to the assembly line and the optimal time trajectory of the desired motion are analyzed using Pareto fronts. The technique is tested in different examples for a six-degrees-of-freedom (DOF) robot system. Results have proved how the use of this methodology enhances the performance and reliability of assembly lines. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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26 pages, 501 KiB

Open AccessArticle

A 2D Membrane MEMS Device Model with Fringing Field: Curvature-Dependent Electrostatic Field and Optimal Control

by Paolo Di Barba, Luisa Fattorusso and Mario Versaci

Mathematics 2021, 9(5), 465; https://doi.org/10.3390/math9050465 - 25 Feb 2021

Cited by 4 | Viewed by 2055

Abstract

An important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field

E

near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is [...] Read more.

An important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field

E

near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is applied. In the framework of a 2D circular membrane MEMS, representing the fringing-field effect depending on

{| \nabla u |}^{2}

with the u profile of the membrane, and since strong

E

produces strong deformation of the membrane, we consider

| E |

proportional to the mean curvature of the membrane, obtaining a new nonlinear second-order differential model without explicit singularities. In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter

δ

that weighs the terms

{| \nabla u |}^{2}

. However, even if the the study of the model did not ensure the uniqueness of the solution, it made it possible to achieve the goal of finding a stable equilibrium position. Moreover, a range of admissible values of V were obtained in order, on the one hand, to win the mechanical inertia of the membrane and, on the other hand, to ensure that the membrane did not touch the upper disk of the device. Lastly, some optimal control conditions based on the variation of potential energy are presented and discussed. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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