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Femtosecond Laser Shock Peening And The Dynamics Of Femtosecond Laser-Induced Shock Waves, Yuxin Li Dec 2023

Femtosecond Laser Shock Peening And The Dynamics Of Femtosecond Laser-Induced Shock Waves, Yuxin Li

All Dissertations

Laser shock peening (LSP) is an important material surface strengthening technique that uses laserinduced shock waves to cause severe plastic deformation near material surfaces. It can significantly improve material properties like hardness, strength, fatigue life, and corrosion resistance and is widely used in industrial sectors such as automotive, aerospace, nuclear, and medical areas. The conventional nanosecond laser shock peening (ns-LSP) has demonstrated effectiveness but faces challenges such as complex setup, low throughput, high energy consumption, and inflexibility for complex geometries. Femtosecond laser shock peening (fs-LSP) offers a promising alternative to overcome these issues, thanks to its ultra-high laser intensity and …


Impacts Of Connected And Automated Vehicles On Energy And Traffic Flow: Optimal Control Design And Verification Through Field Testing, Tyler Ard Dec 2023

Impacts Of Connected And Automated Vehicles On Energy And Traffic Flow: Optimal Control Design And Verification Through Field Testing, Tyler Ard

All Dissertations

This dissertation assesses eco-driving effectiveness in several key traffic scenarios that include passenger vehicle transportation in highway driving and urban driving that also includes interactions with traffic signals, as well as heavy-duty line-haul truck transportation in highway driving with significant road grade. These studies are accomplished through both traffic microsimulation that propagates individual vehicle interactions to synthesize large-scale traffic patterns that emerge from the eco-driving strategies, and through experimentation in which real prototyped connected and automated vehicles (CAVs) are utilized to directly measure energy benefits from the designed eco-driving control strategies. In particular, vehicle-in-the-loop is leveraged for the CAVs driven …


Deep Reinforcement Learning For The Design Of Structural Topologies, Nathan Brown Dec 2023

Deep Reinforcement Learning For The Design Of Structural Topologies, Nathan Brown

All Dissertations

Advances in machine learning algorithms and increased computational efficiencies have given engineers new capabilities and tools for engineering design. The presented work investigates using deep reinforcement learning (DRL), a subset of deep machine learning that teaches an agent to complete a task through accumulating experiences in an interactive environment, to design 2D structural topologies. Three unique structural topology design problems are investigated to validate DRL as a practical design automation tool to produce high-performing designs in structural topology domains.

The first design problem attempts to find a gradient-free alternative to solving the compliance minimization topology optimization problem. In the proposed …


Process-Structure-Property Relationships Of Nanofibers For Biomedical Applications, Dipasree Bhowmick Dec 2023

Process-Structure-Property Relationships Of Nanofibers For Biomedical Applications, Dipasree Bhowmick

Theses and Dissertations

This thesis explores the fabrication, characterization, and applications of nanofiber membranes utilizing Forcespinning® technology. Two distinct nanofiber systems were developed and evaluated, one focusing on pH-responsive Eudragit-baicalin loaded nanofibrous membranes for wound healing and the second one on thermo-responsive nanofiber-hydrogel (PNIPAAm) systems for biosensing applications, specifically dopamine detection. In the first project, nanofiber membranes loaded with Eudragit and baicalin demonstrated superior antibacterial properties against both gram-negative (E. coli) and gram-positive (B. meg) bacteria. Additionally, these membranes exhibited antioxidant properties and enhanced cell proliferation of 3TT cells, making them promising candidates for wound healing dressings. In the second project, a …


Husker Motorsports Active Drag Reduction System, Creighton Hughes, Evan Killian, Micah Busboom, Aj Johnson, Jude Steffen Dec 2023

Husker Motorsports Active Drag Reduction System, Creighton Hughes, Evan Killian, Micah Busboom, Aj Johnson, Jude Steffen

Honors Program: Senior Projects (Public)

Formula SAE is a multifaceted competition that involves student teams designing and competing with an open-wheel style race car. There are 5 different dynamic events included in the competition. Each event requires a unique aerodynamic setup to have the best performance possible. This design project focuses on a drag reduction system (DRS) that will improve aerodynamic performance, resulting in faster lap times and increased competitiveness. Key features include a direct electronic actuation mechanism that will allow the rear wing to be adjusted during a race. The benefits of the DRS system, include increased speed, improved handling, and greater fuel efficiency …


Quantifying The Effect Of Stable Stratification On Low-Reynolds Number Flow Past A Horizontal Cylinder, Holland Kartchner Dec 2023

Quantifying The Effect Of Stable Stratification On Low-Reynolds Number Flow Past A Horizontal Cylinder, Holland Kartchner

All Graduate Theses and Dissertations, Fall 2023 to Present

In this research, we study the behavior of flow around a cylinder in the presence of stable stratification, which refers to variations in density throughout the fluid. This phenomenon is observed in natural and industrial settings. We use computer simulations to analyze how stratification affects the flow patterns created by the cylinder. Specifically, we investigate situations where the stratification is perpendicular to the flow direction, and the wake exhibits two-dimensional characteristics. We use spectral-element method based computational fluids dynamics to simulate the phenomena. During the simulations, we vary two important parameters: the Densimetric Froude Number (Fr) and the …


An Apparatus To Quantify Lengthwise Flexural Rigidity Profiles Of Endovascular Devices, Charles B. Suskin Dec 2023

An Apparatus To Quantify Lengthwise Flexural Rigidity Profiles Of Endovascular Devices, Charles B. Suskin

McKelvey School of Engineering Graduate Student Theses & Dissertations

Endovascular procedures require access to distal anatomical sites through the vasculature using catheters and guidewires. Quantitative frameworks for device behavior during procedures hold the potential to drive device design through greater understanding of the mechanical behavior of endovascular devices, and offer the potential to personalize care based on a patient's particular vascular anatomy. However, data that would facilitate this technology are lacking, partly due to undisclosed material properties from manufacturers and partly due to the intricate variations along the length of each device due to material changes and the intersections between them. We developed a three-point bend test methodology on …


Affordances Of Mobile Technology To Facilitate Learning In Undergraduate Thermal-Fluid Sciences, Maeve Raphael Bakic Dec 2023

Affordances Of Mobile Technology To Facilitate Learning In Undergraduate Thermal-Fluid Sciences, Maeve Raphael Bakic

Boise State University Theses and Dissertations

In recent years, the pandemic has affected learning at all levels, in particular higher education, where higher levels of independence and self-motivation are required during distance learning. In engineering in particular, distance learning adds another degree of difficulty to an already complex field. Comprehension in engineering requires the repeated use of diagrams, high-level charts, and practice problems. Mobile devices, combined with a technology-enhanced curriculum, provide an excellent platform for learning in engineering as it allows for clear illustration and the transfer of complex ideas at any time and place. In alignment with the social-constructivist framework, these facets of mobile technology …


Effects Of The Build Orientation And Support Patterns On The Geometric Accuracy In Printing Parts With Overhang Structure: An Experimental Study, Bala Murali Krishna Mohan Dec 2023

Effects Of The Build Orientation And Support Patterns On The Geometric Accuracy In Printing Parts With Overhang Structure: An Experimental Study, Bala Murali Krishna Mohan

Theses and Dissertations

Additive manufacturing is becoming increasingly popular in industries such as manufacturing due to its ability to use raw materials more efficiently and require less machining than traditional methods(Calignano et al., 2017). However, constructing overhanging structures in additive manufacturing can be challenging, potentially affecting the overall geometric quality of the printed components. The objective of this study was to identify the most effective printing orientation for overhanging designs in Fused Deposition Modeling (FDM) using two different support structures. To achieve this, the researchers used a laser scanner to collect point cloud data and conducted a comparative study to determine the …


Examining The Efficacy Of Using Irt As An Nde Method For Cfrp And Ztcfrp Composites, William Wyatt Taylor Dec 2023

Examining The Efficacy Of Using Irt As An Nde Method For Cfrp And Ztcfrp Composites, William Wyatt Taylor

Graduate Theses and Dissertations (2019 - present)

A film adhesive is commonly used to form the bond-line between composite parts. The bond-line's quality and performance can be affected by defects such as voids, impurities, and agglomerations. Identifying these defects is possible with non-destructive evaluation testing (NDE). In this thesis, the joule-heating effect (JH) through carbon nanofiber (CNF) and carbon nanotube (CNT) modified film adhesive bonded to control carbon fiber reinforced polymer (CCFRP) was used along with infrared thermography testing (IRT) for bond-line defect inspection as a preliminary study. Due to the difference in the electrical conductivity between the modified epoxy and the defect, JH can cause a …


Additive Manufacturing Of Composites For Sensing And Harsh Environments Application, Md Sahid Hassan Dec 2023

Additive Manufacturing Of Composites For Sensing And Harsh Environments Application, Md Sahid Hassan

Open Access Theses & Dissertations

Composite materials are made by combining two or more materials, such as fibers and resins to create a material system that has improved mechanical and physical properties compared to its individual components. The use of 3D printing technology in composite manufacturing allows for the creation of complex and custom shapes with precise control over the placement of the materials. This makes it possible to create composite parts with enhanced performance characteristics and reduced weight. The work presented in this dissertation lies in the design and development of highly flexible impact propagation sensor through material extrusion 3D printing technique. By using …


An Optimization Procedure To Design Nozzle Contours For Hypersonic Wind Tunnels, Omar Antonio Dominguez Dec 2023

An Optimization Procedure To Design Nozzle Contours For Hypersonic Wind Tunnels, Omar Antonio Dominguez

Open Access Theses & Dissertations

Supersonic wind tunnels allow scientists and researchers to evaluate and analyze the behaviors of objects under real-life conditions when subjected to supersonic speeds. One of the main complexities when building a wind tunnel is the design of the convergent-divergent nozzle that is used to produce high-speed and high-quality flows. To achieve supersonic speeds, this nozzle adopts a specialized approach that incorporates the complexities of flow compressibility. The compressible effect is accurately evaluated using isentropic relations, allowing for precise determination of stagnation pressure and temperature, and static pressure and temperature relevant to the desired Mach number. Isentropic equations used to define …


Cfrp Delamination Density Propagation Analysis By Magnetostriction Theory, Brandon Eugene Williams Dec 2023

Cfrp Delamination Density Propagation Analysis By Magnetostriction Theory, Brandon Eugene Williams

All Dissertations

While Carbon Fiber Reinforced Polymers (CFRPs) have exceptional mechanical properties concerning their overall weight, their failure profile in demanding high-stress environments raises reliability concerns in structural applications. Two crucial limiting factors in CFRP reliability are low-strain material degradation and low fracture toughness. Due to CFRP’s low strain degradation characteristics, a wide variety of interlaminar damage can be sustained without any appreciable change to the physical structure itself. This damage suffered by the energy transfer from high- stress levels appears in the form of microporosity, crazes, microcracks, and delamination in the matrix material before any severe laminate damage is observed. This …


Improving Hexapod Platform Pose Accuracy - A Photogrammetry-Based Approach, Sourabh Karmakar Dec 2023

Improving Hexapod Platform Pose Accuracy - A Photogrammetry-Based Approach, Sourabh Karmakar

All Dissertations

The aim of this research is to make a newly constructed Stewart-Gough Platform-based test frame Tiger 66.1 operational by developing control software and estimating the error in its pose accuracy. The accuracy of the platform is affected by one source or multiple sources. The typical error sources are kinematic and structural, some of them originate from manufacturing imperfections, assembly deviations, elastic deformations, thermal deformations, and joint clearances which change the expected kinematic behavior of the manipulator. Also, some non-mechanical errors like transmission error, sensor accuracy, algorithm error, and truncation error in calculation contribute significantly in some cases. Using pose deviations …


Damage Detection With An Integrated Smart Composite Using A Magnetostriction-Based Nondestructive Evaluation Method: Integrating Machine Learning For Prediction, Christopher Nelon Dec 2023

Damage Detection With An Integrated Smart Composite Using A Magnetostriction-Based Nondestructive Evaluation Method: Integrating Machine Learning For Prediction, Christopher Nelon

All Dissertations

The development of composite materials for structural components necessitates methods for evaluating and characterizing their damage states after encountering loading conditions. Laminates fabricated from carbon fiber reinforced polymers (CFRPs) are lightweight alternatives to metallic plates; thus, their usage has increased in performance industries such as aerospace and automotive. Additive manufacturing (AM) has experienced a similar growth as composite material inclusion because of its advantages over traditional manufacturing methods. Fabrication with composite laminates and additive manufacturing, specifically fused filament fabrication (fused deposition modeling), requires material to be placed layer-by-layer. If adjacent plies/layers lose adhesion during fabrication or operational usage, the strength …


Restricted Nonlinear Scales Of Turbulent Secondary Flows Over Spanwise Heterogeneous Roughness, Benjamin A. Minnick, Xiaowei Zhu, Dennice F. Gayme Dec 2023

Restricted Nonlinear Scales Of Turbulent Secondary Flows Over Spanwise Heterogeneous Roughness, Benjamin A. Minnick, Xiaowei Zhu, Dennice F. Gayme

Mechanical and Materials Engineering Faculty Publications and Presentations

Recent studies, e.g., Wangsawijaya et al. (2020) have revealed the prevalence of streak meandering in turbulent flow over spanwise heterogeneous roughness. Here we exploit the scale decomposition inherent in the Restricted Nonlinear (RNL) modeling approach to further investigate this behavior. The RNL decomposition comprises a large-scale streamwise averaged mean with small-scale fluctuations about that mean defined through a dynamical restriction that leads to computational tractability. The simplified setting facilitates the study of secondary flow interacting with the large-scale streak via one-way coupling, thus enabling additional insight into relevant interaction mechanisms. In agreement with the experimental work, our results indicate that …


A Dynamic Scoring Methodology For Morphing Airfoil Designs With Application To A Stalling Scenario, Stone Wachs Dec 2023

A Dynamic Scoring Methodology For Morphing Airfoil Designs With Application To A Stalling Scenario, Stone Wachs

UNLV Theses, Dissertations, Professional Papers, and Capstones

Shape Changing Airfoils (SCAs) are a developing technology with potential aircraft applications. Leading aerospace corporations are actively researching SCA capabilities. The necessity for this technology stems from the requirement of control surfaces for safe aircraft control. However, the process of testing and determining optimal SCA designs can be costly and time-consuming. While methodologies exist, they often require specific scenario examples and lack a standard approach. To address this issue, a standardized methodology is needed that can be applied to various applications and scenarios. This methodology consists of computational/experimentally produced data for airfoils, a subjective and strategic scoring equation, an algorithmic …


Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre Dec 2023

Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Mechanical metamaterials built up of compliant units can support the propagation of linear and nonlinear waves. A popular architecture consists of a one-dimensional chain of bistable elements connected by linear springs. This type of chain can support nonlinear transition waves that switch each element from one stable state to the other as they propagate along the chain. One way to manipulate the propagation of such waves is via introduction of a local inhomogeneity, i.e., a defect in the otherwise periodic chain. Recent analytical and numerical work has shown that based on its initial velocity, a transition wave may be reflected, …


Design Space Visualization And Exploration For Many Goal Problems Under Uncertainity, Niharika Balaji Dec 2023

Design Space Visualization And Exploration For Many Goal Problems Under Uncertainity, Niharika Balaji

Theses and Dissertations

ABSTRACT

Designing a complex engineered system is challenging due to many conflicting goals, uncertainties, and multiple interactions. Traditional optimization approaches often yield single-point solutions, which may not be suitable for early design stages due to their susceptibility to changes in conditions and uncertainties. To address this challenge, a satisficing approach is employed. This approach enables designers to effectively navigate the design space and identify satisficing solutions that balance conflicting goals in the face of uncertainties and changes in conditions. From a systems design perspective, we view design as an iterative process that involves making informed decisions based on available information …


Underwater Image Enhancement: A Pipeline For Underwater Computer Visions, Humberto Lebron Rivera Dec 2023

Underwater Image Enhancement: A Pipeline For Underwater Computer Visions, Humberto Lebron Rivera

Theses and Dissertations

Ocean exploration has surged in popularity and significance in recent years, including diverse areas like maritime archeology, underwater resources, and submerged structure inspection. The activities mentioned above heavily depend on vision and imagery, a challenge in the unpredictable marine world. This thesis presents a conditional generative adversarial network model for image-to-image translation problems. We designed and trained the model with the end goal of enhancing underwater images. Five metrics were employed for validation to quantify our model’s resulting enhanced images. By doing so, we aim to establish a pipeline that can leverage aerial computer vision algorithms for marine applications.

Our …


Analyzing The Effects Of Ultrafast Laser Processing On Mechanical Properties Of 3d-Printed Pla Parts, Darshan Pramodbhai Yadav Dec 2023

Analyzing The Effects Of Ultrafast Laser Processing On Mechanical Properties Of 3d-Printed Pla Parts, Darshan Pramodbhai Yadav

Theses and Dissertations

Recent advances in additive manufacturing technologies have already led to wide-scale adoption of 3D-printed parts in various industries. The expansion in choice of materials that can be processed, particularly using Fused Deposition Modeling (FDM), and the steady advancements in dimensional accuracy control have extended the range of applications far beyond rapid prototyping. However, additive manufacturing still has considerable limitations compared to traditional and subtractive manufacturing processes. This work addresses limitations associated with the as-deposited surface roughness of 3D-printed parts. The effects of roughness-induced stress concentrations were studied on ultimate tensile strength and fatigue life. The samples were manufactured using a …


Path Planning Development Framework For Mobile Robots, Lauren-Ann Elizabeth Graham Dec 2023

Path Planning Development Framework For Mobile Robots, Lauren-Ann Elizabeth Graham

Theses and Dissertations

Planetary exploration relies on methods of path planning to achieve autonomous navigation in hazardous environments. Simulating harsh terrain, real-time varying physics, and robotics applications is vital for testing control algorithms here on Earth. Robotics Operating System (ROS) is a set of software libraries and tools that allow you to build and simulate robotic applications. Utilizing ROS, Gazebo, and Blender, a rough terrain simulation framework is created to explore and compare path planning algorithms using various desired robots and maps. ROS supports multiple path planning algorithms given its open-source abilities. This research focuses on path planning implementation of Proportional-Integral-Derivative (PID) control …


Deep Learning And Generative Ai Approaches For Automated Diagnosis And Personalized Treatment: Bridging Machine Learning, Medicine, And Biomechanics In Predicting Tissue Mechanics And Biomaterial Properties., Yasin Shokrollahi Dec 2023

Deep Learning And Generative Ai Approaches For Automated Diagnosis And Personalized Treatment: Bridging Machine Learning, Medicine, And Biomechanics In Predicting Tissue Mechanics And Biomaterial Properties., Yasin Shokrollahi

Theses and Dissertations

Machine learning, particularly deep neural networks, has demonstrated significant potential in predicting high-dimensional tasks across various domains. This work encompasses a detailed review of Generative AI in healthcare and three studies integrating machine learning with finite element analysis for predicting biomechanical behaviors and properties. Initially, we provide a comprehensive overview of Generative AI applications in healthcare, focusing on Transformers and Denoising Diffusion models and suggesting potential research avenues to address existing challenges.

Subsequently, we addressed soccer-related ocular injuries by combining finite element analysis and machine learning to predict retinal mechanics following a soccer ball hit rapidly. The prediction errors are …


Gpu Based Monte Carlo Estimation Of Eddy Current Losses In Electromagnetic Coil-Core System, Adwaith Ravichandran Dec 2023

Gpu Based Monte Carlo Estimation Of Eddy Current Losses In Electromagnetic Coil-Core System, Adwaith Ravichandran

Theses and Dissertations

A novel parallelizable probabilistic approach to model eddy currents in AC electromagnets is presented in this research. Consequently, power loss associated with the formation of these eddy currents is estimated and validated using experimental data. Furthermore, predicting the effect of ferromagnetic alternating field enhancement on power loss in the source excitation winding has been an active area of research. Unlike a stationary field, an alternating sinusoidal field diffuses partially into the ferromagnetic material leading to a predictably sub-optimal field enhancement. To model these physics, finite element techniques employ nonlinear iterative solvers which are time consuming. A novel method is developed …


Project Thetis: A Low-Cost, Low-Profile Inertial Data Logger, Braidan Duffy Dec 2023

Project Thetis: A Low-Cost, Low-Profile Inertial Data Logger, Braidan Duffy

Theses and Dissertations

This thesis details the design, testing, calibration, and verification of a nine degree of freedom inertial measurement data logger for use with floating bodies. The instrument was conceived to address limitations of equipment used in classes within the Ocean Engineering department at Florida Institute of Technology. By meeting with several stakeholders and end users, a series of stakeholder requirements, capabilities, and component-level requirements were de- veloped that informed the design constraints. There were several hardware iterations of the board, culminating in Revision F5 which was extensively tested and proven. The design was inspected after testing concluded to determine which capabilities …


Extremum Seeking Control Algorithms For Extremely High Frequency Antenna System Pointing, Scott Shore Dec 2023

Extremum Seeking Control Algorithms For Extremely High Frequency Antenna System Pointing, Scott Shore

Mechanical Engineering ETDs

The research examines the application of extremum seeking control (ESC) algorithms to ground station antenna pointing for extremely high frequency (EHF) communication systems. ESC algorithms search for local maxima or minima by locating where an objective function gradient goes to zero. With wireless communication expanding into higher frequencies, the ground station pointing requirement is increasing. ESC presents a method which utilizes available equipment and information to perform ground station pointing. Additionally, ESC algorithms do not rely on assumptions or approximations needed for other techniques. The dissertation demonstrates ESC algorithm feasibility for the ground station pointing problem, benchmarks the ESC algorithms …


Temperature Gradient Effect On Solid-Liqid Interface Properties Of Al-Cu Alloy: A Molecular Dynamics Study, Prashant Kumar Jha Dec 2023

Temperature Gradient Effect On Solid-Liqid Interface Properties Of Al-Cu Alloy: A Molecular Dynamics Study, Prashant Kumar Jha

All Theses

Aluminum-copper (Al-Cu) alloys are widely used in the aerospace industry due to their favorable strength-to-weight ratio, good fatigue resistance, and corrosion resistance. These properties make Al-Cu alloys an excellent choice for aircraft structural components that require high strength and low weight. Additive manufacturing (AM), also known as 3D printing, has emerged as a promising processing method for Al-Cu alloys in aerospace manufacturing. AM enables the production of lightweight optimized geometries difficult to manufacture through conventional subtractive methods. AM also reduces material waste by only depositing material where needed in the part geometry. The rapid solidification conditions in AM processes motivate …


Safe Navigation Of Quadruped Robots Using Density Functions, Andrew Zheng Dec 2023

Safe Navigation Of Quadruped Robots Using Density Functions, Andrew Zheng

All Theses

Safe navigation of mission-critical systems is of utmost importance in many modern autonomous applications. Over the past decades, the approach to the problem has consisted of using probabilistic methods, such as sample-based planners, to generate feasible, safe solutions to the navigation problem. However, these methods use iterative safety checks to guarantee the safety of the system, which can become quite complex. The navigation problem can also be solved in feedback form using potential field methods. Navigation function, a class of potential field methods, is an analytical control design to give almost everywhere convergence properties, but under certain topological constraints and …


Numerical Study On Resistance Of Stepped Planing Hull, Fajri Ashfi Rayhan, Andika Masrul, Arya Khairullah Akbar, Bima Anugerah Putra Nov 2023

Numerical Study On Resistance Of Stepped Planing Hull, Fajri Ashfi Rayhan, Andika Masrul, Arya Khairullah Akbar, Bima Anugerah Putra

Journal of Mechanical Engineering Science and Technology (JMEST)

A stepped planing hull, also known as a step hull, is a hull modification that reduces the wetted surface area. Although this type of hull has proven effective in several ships, it is still rarely used. The step hull possesses numerous advantages that make it ideal for activities involving small and fast boats. However, regrettably, its full potential remains untapped at present. The purpose of this study was to identify the effect of variations in the angle of the step hull on resistance or drag. The study utilized the CFD method, and three hull configuration models were used at each …


Heat Conduction In Cylindrical Coordinates With Time-Varying Conduction Coefficients: A Practical Engineering Approach, Lulut Alfaris, Ruben Cornelius Siagian, Aldi Cahya Muhammad, Ukta Indra Nyuswantoro, Budiman Nasution Nov 2023

Heat Conduction In Cylindrical Coordinates With Time-Varying Conduction Coefficients: A Practical Engineering Approach, Lulut Alfaris, Ruben Cornelius Siagian, Aldi Cahya Muhammad, Ukta Indra Nyuswantoro, Budiman Nasution

Journal of Mechanical Engineering Science and Technology (JMEST)

This research aims to develop a mathematical method for expressing the Laplace operator in cylindrical coordinates and applying it to solve heat conduction equations in various scenarios. The method commences by transforming Cartesian coordinates into cylindrical coordinates and identifying the necessary substitutions. The result is the expression of the Laplace operator in cylindrical coordinates, which is subsequently employed to address heat conduction equations within cylindrical coordinates. Various cases encompassing different initial and boundary conditions, as well as variations in the conduction coefficient over time, are meticulously considered. In each instance, precise mathematical solutions are determined and subjected to thorough analysis. …