Symmetry

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28 pages, 20882 KiB

Open AccessArticle

Iterative Solutions for the Nonlinear Heat Transfer Equation of a Convective-Radiative Annular Fin with Power Law Temperature-Dependent Thermal Properties

by R. S. Varun Kumar, Ioannis E. Sarris, G. Sowmya and Amal Abdulrahman

Symmetry 2023, 15(6), 1204; https://doi.org/10.3390/sym15061204 - 4 Jun 2023

Cited by 15 | Viewed by 1670

Abstract

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized in the present investigation. The nonlinear variation of thermal conductivity and heat transfer coefficient governed by the power law is considered. The analytical approximation for the non-dimensional [...] Read more.

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized in the present investigation. The nonlinear variation of thermal conductivity and heat transfer coefficient governed by the power law is considered. The analytical approximation for the non-dimensional temperature profile is obtained using the differential transform method (DTM)-Pade approximant. The nondimensionalization of the governing energy equation using dimensionless terms yields a nonlinear ordinary differential equation (ODE) with corresponding boundary conditions. The resulting ODE is analytically solved with the assistance of the DTM-Pade approximant procedure. Furthermore, the impact of thermal parameters on the temperature field and thermal stress is elaborated with graphs. The important results of the report divulge that temperature distribution greatly enhances with an augmentation of the heat generation parameter, but it gradually reduces with an increment in the magnitude of the thermogeometric and radiative-conductive parameter. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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20 pages, 788 KiB

Open AccessArticle

The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces

by Uma Bharti, Pramod Kumar Vaishnav, Shao-Wen Yao and Hijaz Ahmad

Symmetry 2023, 15(2), 491; https://doi.org/10.3390/sym15020491 - 13 Feb 2023

Viewed by 1697

Abstract

The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we [...] Read more.

The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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14 pages, 4318 KiB

Open AccessArticle

An Update on the Momentum 360 Method of Vehicle Impact Reconstruction through 3D Modeling and Computer Simulation

by Stanimir Karapetkov and Lubomir Dimitrov

Symmetry 2022, 14(12), 2628; https://doi.org/10.3390/sym14122628 - 12 Dec 2022

Cited by 4 | Viewed by 1819

Abstract

Although vehicles as a whole are symmetric, car crashes rarely follow the symmetric line (crashes are axisymmetric). In this paper, we examine car crashes by an updated Momentum 360 method, and car symmetry helps us easily find out what happens within the accident. [...] Read more.

Although vehicles as a whole are symmetric, car crashes rarely follow the symmetric line (crashes are axisymmetric). In this paper, we examine car crashes by an updated Momentum 360 method, and car symmetry helps us easily find out what happens within the accident. We propose an improvement of the Momentum 360 method by taking into account the frictional forces between the wheels and the road surface during the time of impact. According to the momentum change theorem for the duration of the impact for each car and the kinetic moment change theorem for the relative motion of the given vehicle around its center of mass, the impact problem is introduced and solved. The solution considers the impulses of the principal vectors of the wheel friction forces, the gravity force, and the aerodynamic force for each car at the time of impact, as well as the principal moments of the friction forces between the tires and the road surface as a function of time. A mechano-mathematical multi-mass 3D model and a computer simulation of the movement (“Expertcar” software) are used to study the movement of each vehicle after the impact. Through successive approximations, the velocity vectors of the mass centers of the vehicle immediately before the impact are determined, and the location of the impact is identified. The presented decision model significantly improves the accuracy of road accident investigations. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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18 pages, 4184 KiB

Open AccessArticle

MHD and Thermal Slip Effects on Viscous Fluid over Symmetrically Vertical Heated Plate in Porous Medium: Keller Box Analysis

by Zia Ullah, Muhammad Bilal, Ioannis E. Sarris and Abid Hussanan

Symmetry 2022, 14(11), 2421; https://doi.org/10.3390/sym14112421 - 15 Nov 2022

Cited by 14 | Viewed by 1872

Abstract

The heat transfer characteristics along the non-magnetized shapes have been performed in various previous studies numerically. Due to excessive heating, these mechanisms are less interesting in engineering and industrial processes. In the current analysis, the surface is magnetized, and the fluid is electrically [...] Read more.

The heat transfer characteristics along the non-magnetized shapes have been performed in various previous studies numerically. Due to excessive heating, these mechanisms are less interesting in engineering and industrial processes. In the current analysis, the surface is magnetized, and the fluid is electrically conducting, which is responsible for reducing excessive heating along the surface. The main objective of the present work is to analyze convective heat transfer analysis of viscous fluid flow with thermal slip and thermal radiation effects along the vertical symmetric heated plate immersed in a porous medium numerically. The results are deduced for viscous flow along a magnetized heated surface. The theoretical mechanism of heat and magnetic intensity along a vertical surface is investigated for numerical analysis. The nonlinear-coupled partial differential equations (PDEs) for the above viscous fluid flow mechanism with the symmetry of the conditions normal to the surface are transformed and then converted into non-similar formulations by applying appropriate and well-known similarity transformations for integration and solutions. The final non-similar equations are numerically integrated by employing the Keller box method. The discretized algebraic equations are plotted graphically and numerically on the MATLAB R2013a software package. The main finding of the current analysis is to compute physical quantities such as velocity graph, magnetic field graph, and temperature plot along with their slopes, that is, skin friction, magnetic intensity, and heat transfer for different parameters included in the flow model. First, the velocity graph, magnetic field graph, and temperature graph are obtained, and then their slopes are analyzed numerically along the vertical magnetic surface. It is noticed that fluid velocity is increased at lower magnetic force, but minimum velocity is noticed at maximum magnetic force. It is worth mentioning that with the increase in magnetic force, the magnetic energy increases, which extracts the kinetic energy of the fluid and causes the above-said behavior. Furthermore, the current issues have significant implications for the polymer industries, glass fiber production, petroleum production, fiber spinning, plastic film production, polymer sheet extraction, heat exchangers, catalytic reactors, and the production of electronic devices. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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18 pages, 2493 KiB

Open AccessArticle

Identification of Material Properties of Elastic Plate Using Guided Waves Based on the Matrix Pencil Method and Laser Doppler Vibrometry

by Mikhail V. Golub, Olga V. Doroshenko, Mikhail A. Arsenov, Ilya A. Bareiko and Artem A. Eremin

Symmetry 2022, 14(6), 1077; https://doi.org/10.3390/sym14061077 - 24 May 2022

Cited by 8 | Viewed by 1860

Abstract

Ultrasonic based inspection of thin-walled structures often requires prior knowledge of their mechanical properties. Their accurate estimation could be achieved in a non-destructive manner employing, e.g., elastic guided waves. Such procedures require efficient approaches for experimental data extraction and processing, which is still [...] Read more.

Ultrasonic based inspection of thin-walled structures often requires prior knowledge of their mechanical properties. Their accurate estimation could be achieved in a non-destructive manner employing, e.g., elastic guided waves. Such procedures require efficient approaches for experimental data extraction and processing, which is still a challenging task. An advanced automated technique for material properties identification of an elastic waveguide is proposed in this investigation. It relies on the information on dispersion characteristics of guided waves, which are extracted by applying the matrix pencil method to the measurements obtained via laser Doppler vibrometry. Two objective functions have been successfully tested, and the advantages of both approaches are discussed (accuracy vs. computational costs). The numerical analysis employing the synthetic data generated via the mathematical model as well as experimental data shows that both approaches are stable and accurate. The influence of the presence of various modes in the extracted data is investigated. One can conclude that the influence of the corruptions related to the extraction of dispersion curves is not critical if the majority of guided waves propagating in the considered frequency range are presented. Possible extensions of the proposed technique for damaged and multi-layered structures are also discussed. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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20 pages, 5749 KiB

Open AccessEditor’s ChoiceArticle

Exploration of Temperature Distribution through a Longitudinal Rectangular Fin with Linear and Exponential Temperature-Dependent Thermal Conductivity Using DTM-Pade Approximant

by Ravikumar Shashikala Varun Kumar, Rangaswamy Naveen Kumar, Ganeshappa Sowmya, Ballajja Chandrappa Prasannakumara and Ioannis E. Sarris

Symmetry 2022, 14(4), 690; https://doi.org/10.3390/sym14040690 - 26 Mar 2022

Cited by 27 | Viewed by 4125

Abstract

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying [...] Read more.

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying temperature-dependent thermal conductivity and linearly varying temperature-dependent thermal conductivity. Further, the thermal distribution of a longitudinal fin is examined by using ANSYS software with different fin materials. Many physical mechanisms can be explained by ordinary differential equations (ODEs) with symmetrical behavior, the significance of which varies based on the perspective. The governing equation of the considered problem is reduced to a non-linear ODE with the assistance of dimensionless terms. The resultant equation is solved analytically using the DTM-Pade approximant and is also solved numerically using Runge-Kutta Fehlberg’s fourth-fifth (RKF-45) order method. The features of dimensionless parameters influencing the fin efficiency and temperature profile are discussed through graphical representation for exponentially and linearly varying temperature-dependent thermal conductivity. This study ensures that the temperature field enhances for the higher magnitude of thermal conductivity parameter, whereas it diminishes for diverse values of the thermo-geometric parameter. Also, greater values of heat generation and heat transfer parameters enhance the temperature profile. Highlight: Thermal distribution through a rectangular profiled straight fin is examined. Linear and non-linear thermal properties are considered. The combined impact of conduction, convection, and internal heat generation is taken for modeling the energy equation of the fin. Thermal simulation is performed for Aluminum Alloy 6061 (AA 6061) and Cast Iron using ANSYS. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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14 pages, 1701 KiB

Open AccessArticle

Fault Diagnosis of Crack on Gearbox Using Vibration-Based Approaches

by Sufyan A. Mohammed, Nouby M. Ghazaly and Jamil Abdo

Symmetry 2022, 14(2), 417; https://doi.org/10.3390/sym14020417 - 19 Feb 2022

Cited by 17 | Viewed by 3663

Abstract

This study experimentally investigates vibration-based approaches for fault diagnosis of automotive gearboxes. The primary objective is to identify methods that can detect gear-tooth cracks, a common fault in gearboxes. Vibrational signals were supervised on a gearbox test rig under different operating conditions of [...] Read more.

This study experimentally investigates vibration-based approaches for fault diagnosis of automotive gearboxes. The primary objective is to identify methods that can detect gear-tooth cracks, a common fault in gearboxes. Vibrational signals were supervised on a gearbox test rig under different operating conditions of gears with three symmetrical crack depths (1, 2, and 3 mm). The severity of the gear-tooth cracks was predicted from the vibrational signal dataset using an artificial feedforward multilayer neural network with backpropagation (NNBP). The vibration amplitudes were the greatest when the crack size in the high-speed shaft was 3 mm, and the root mean square of its vibration speed was below 3.5 mm/s. The vibration amplitudes of the gearbox increased with increasing depth of the tooth cracks under different operating conditions. The NNBP predicted the states of gear-tooth cracks with an average recognition rate of 80.41% under different conditions. In some cases, the fault degree was difficult to estimate via time-domain analysis as the vibration level increases were small and not easily noticed. Results also showed that when using the same statistical features, the time-domain analysis can better detect crack degree compared to the neural network technique. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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23 pages, 3432 KiB

Open AccessArticle

Analysis of Transient Thermal Distribution in a Convective–Radiative Moving Rod Using Two-Dimensional Differential Transform Method with Multivariate Pade Approximant

by Ganeshappa Sowmya, Ioannis E. Sarris, Chandra Sen Vishalakshi, Ravikumar Shashikala Varun Kumar and Ballajja Chandrappa Prasannakumara

Symmetry 2021, 13(10), 1793; https://doi.org/10.3390/sym13101793 - 26 Sep 2021

Cited by 38 | Viewed by 3854

Abstract

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries are intrinsic and fundamental features of the differential equations of mathematical physics. The governing energy equation subjected [...] Read more.

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries are intrinsic and fundamental features of the differential equations of mathematical physics. The governing energy equation subjected to corresponding initial and boundary conditions is non-dimensionalized into a non-linear partial differential equation (PDE) with the assistance of relevant non-dimensional terms. Then the resultant non-dimensionalized PDE is solved analytically using the two-dimensional differential transform method (2D DTM) and multivariate Pade approximant. The consequential impact of non-dimensional parameters such as heat generation, radiative, temperature ratio, and conductive parameters on dimensionless transient temperature profiles has been scrutinized through graphical elucidation. Furthermore, these graphs indicate the deviations in transient thermal profile for both finite difference method (FDM) and 2D DTM-multivariate Pade approximant by considering the forced convective and nucleate boiling heat transfer mode. The results reveal that the transient temperature profile of the moving rod upsurges with the change in time, and it improves for heat generation parameter. It enriches for the rise in the magnitude of Peclet number but drops significantly for greater values of the convective-radiative and convective-conductive parameters. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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