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2022

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Articles 1441 - 1470 of 1657

Full-Text Articles in Mechanical Engineering

Nebraska Summary: 1241 John Deere 6r 250 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Summary: 1241 John Deere 6r 250 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Tractor Summary: 1238 John Deere 6r 195 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Tractor Summary: 1238 John Deere 6r 195 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Summary: 1237 John Deere 6r 175 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Summary: 1237 John Deere 6r 175 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Tractor Summary: 1236 John Deere 6r 165 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Tractor Summary: 1236 John Deere 6r 165 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Summary : 1235 John Deere 6r 155 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Summary : 1235 John Deere 6r 155 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Summary: 1233 John Deere 6r 140 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Summary: 1233 John Deere 6r 140 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Tractor Summary: 1232 John Deere 6r 130 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Tractor Summary: 1232 John Deere 6r 130 Diesel Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Nebraska Tractor Summary: 1230 John Deere 6r 110 Infinitely Variable Transmission, Nebraska Tractor Test Lab Jan 2022

Nebraska Tractor Summary: 1230 John Deere 6r 110 Infinitely Variable Transmission, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Microscale Transverse Compression Modeling: A Comparative Study Of The Analytical Mac/Gmc Methods To Experimental Results, Emily Zeitunian Jan 2022

Microscale Transverse Compression Modeling: A Comparative Study Of The Analytical Mac/Gmc Methods To Experimental Results, Emily Zeitunian

Dissertations, Master's Theses and Master's Reports

Composite materials require a multi-scale approach to fully understand its behavior. At the micro level, material behavior analysis is conducted most often using numerical or analytical approaches. These models, however, require validation from experimental data to ensure material predictions are accurate. This study compares a semi-analytical micromechanical analysis tool, MAC/GMC, to experimental results of in-situ microscale transverse compression testing conducted at AFRL facilities. Effective properties, stress-strain curves, stress and strain fields, and damage predictions are compared with experimental outputs. Both generalized method of cells (GMC) and high-fidelity generalized method of cells (HFGMC) theories implemented within MAC/GMC show results that agree …


Nebraska Summary 1242s: Fendt 514 Vario Gen3 Diesel, Nebraska Tractor Test Lab Jan 2022

Nebraska Summary 1242s: Fendt 514 Vario Gen3 Diesel, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …


Evaluating Mixed Reality Training For Calibrating Operators’ Mental Models Of Advanced Driver Assistance Systems, Ganesh Pai Mangalore Jan 2022

Evaluating Mixed Reality Training For Calibrating Operators’ Mental Models Of Advanced Driver Assistance Systems, Ganesh Pai Mangalore

Link Foundation Modeling, Simulation and Training Fellowship Reports

Advanced Driver Assistance Systems (ADAS) offer safety benefits by handling active driving tasks. However, due to limited operational design domain, these systems may require driver intervention, making drivers’ mental models about system limitations and capabilities an important factor when operating them. Literature suggests most drivers are uninformed or unaware of their systems (McDonald et al, 2018), lacking complete or accurate mental models. Mental models (MM) are described as reflections of operators’ knowledge of system’s purpose and various functioning states (Seppelt & Victor, 2020). Incomplete MM of systems’ limitations may also adversely affect drivers’ hazard avoidance behavior.


Satellite Drag Coefficient Modeling For Thermosphere Science And Mission Operations, Piyush M. Mehta, Smriti N. Paul, Nicholas H. Crisp, Philip L. Sheridan, Christian Siemes, Günther March, Sean Bruinsma Jan 2022

Satellite Drag Coefficient Modeling For Thermosphere Science And Mission Operations, Piyush M. Mehta, Smriti N. Paul, Nicholas H. Crisp, Philip L. Sheridan, Christian Siemes, Günther March, Sean Bruinsma

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Satellite drag modeling remains the largest source of uncertainty affecting space operations in low Earth orbit. The uncertainty stems from inaccurate models for mass density and drag coefficient. Drag coefficient modeling also impacts scientific knowledge on the physics and dynamics of the upper atmosphere through the estimation of high-fidelity mass density from measurements of acceleration on-board satellites. Efforts over the last decade have pushed drag coefficient modeling in the right direction, however, have resulted in multiple methods and tools. We provide a comprehensive review of the drag coefficient modeling methods and tools. Current scale differences between thermospheric data sets mostly …


Effects Of Wheel Rotation On Long-Period Wake Dynamics Of The Drivaer Fastback Model, Matthew Aultman, Rodrigo Auza-Gutierrez, Kevin Disotell, Lian Duan Jan 2022

Effects Of Wheel Rotation On Long-Period Wake Dynamics Of The Drivaer Fastback Model, Matthew Aultman, Rodrigo Auza-Gutierrez, Kevin Disotell, Lian Duan

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Lattice Boltzmann method (LBM) simulations were performed to capture the long-period dynamics within the wake of a realistic DrivAer fastback model with stationary and rotating wheels. The simulations showed that the wake developed as a low-pressure torus regardless of whether the wheels were rotating. This torus shrank in size on the base in the case of rotating wheels, leading to a reduction in the low-pressure footprint on the base, and consequently a 7% decrease in the total vehicle drag in comparison to the stationary wheels case. Furthermore, the lateral vortex shedding experienced a long-period switching associated with the bi-stability in …


Feature Learning For Optimal Control With B-Spline Representations, Vinay Kenny, Sixiong You, Chaoying Pei, Ran Dai Jan 2022

Feature Learning For Optimal Control With B-Spline Representations, Vinay Kenny, Sixiong You, Chaoying Pei, Ran Dai

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The paper develops a feature learning-based method to solve optimal control problems using B-splines to approximate the optimal solutions. The feature learning-based optimal control method can quickly generate near-optimal trajectories for general optimal control problems subject to system dynamics and constraints. The steps in the proposed method are as follows: Firstly, by representing the state and control variables with B-spline functions, the optimal control problem is converted into an approximate nonlinear programming (NLP) problem, where parameters of the B-splines are identified as features of the optimal solution. Secondly, for a specific problem with designated inputs, a dataset of the optimal …


Juggling A Devil-Stick: Hybrid Orbit Stabilization Using The Impulse Controlled Poincaré Map, Nilay Kant, Ranjan Mukherjee Jan 2022

Juggling A Devil-Stick: Hybrid Orbit Stabilization Using The Impulse Controlled Poincaré Map, Nilay Kant, Ranjan Mukherjee

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The control design for juggling a devil-stick between two symmetric configurations is proposed. Impulsive forces are applied to the devil-stick at the two configurations; and impulse of the force and its point of application are modeled as the control inputs. The dynamics of the devil-stick is described by a single return Poincaré map, and it is shown that the control objective of juggling can be achieved by stabilizing a hybrid orbit. The impulse controlled Poincaré map (ICPM) approach, recently proposed for stabilization of continuous-time orbits of underactuated systems, is extended to achieve asymptotic stabilization of the hybrid orbit. The applicability …


Assembly Of Alumina Particles In Aqueous Suspensions Induced By High‐Frequency Ac Electric Field, James E. John, Shizhi Qian, Dipankar Ghosh Jan 2022

Assembly Of Alumina Particles In Aqueous Suspensions Induced By High‐Frequency Ac Electric Field, James E. John, Shizhi Qian, Dipankar Ghosh

Mechanical & Aerospace Engineering Faculty Publications

The role of high-frequency alternating current (AC) electric field in the assembly of alumina particles in aqueous media was investigated. Field–particle interactions were in situ investigated for coarse and fine powder particles in very dilute suspensions. For both coarse and fine particles, AC field-induced assembly led to the formation of chains of particles within a minute, which were aligned in the field direction. However, a much finer network of particle chains evolved in fine particle suspensions. Threshold field strength for chain formation was also lower for fine particles (28 V/mm) than for coarse particles (50 V/mm), suggesting stronger interactions for …


Can We Make Our Robot Play Soccer? Influence Of Collaborating With Preservice Teachers And Fifth Graders On Undergraduate Engineering Students' Learning During A Robotic Design Process (Work In Progress), Krishnanand Kaipa, Jennifer Kidd, Julia Noginova, Francisco Cima, Stacie Ringleb, Orlando Ayala, Pilar Pazos, Kristie Gutierrez, Min Jung Lee Jan 2022

Can We Make Our Robot Play Soccer? Influence Of Collaborating With Preservice Teachers And Fifth Graders On Undergraduate Engineering Students' Learning During A Robotic Design Process (Work In Progress), Krishnanand Kaipa, Jennifer Kidd, Julia Noginova, Francisco Cima, Stacie Ringleb, Orlando Ayala, Pilar Pazos, Kristie Gutierrez, Min Jung Lee

Mechanical & Aerospace Engineering Faculty Publications

This work-in-progress paper describes engineering students’ experiences in an NSF-funded project that partnered undergraduate engineering students with pre-service teachers to plan and deliver robotics lessons to fifth graders at a local school. This project aims to address an apparent gap between what is taught in academia and industry’s expectations of engineers to integrate perspectives from outside their field to solve modern societal problems requiring a multidisciplinary approach. Working in small teams over Zoom, participating engineering, education, and fifth grade students designed, built, and coded bio-inspired COVID companion robots. The goal for the engineering students was to build new interprofessional skills, …


Investigating Ground Interactions Of A Rotocraft Landing Vehicle On Titan, Adam Rozman Jan 2022

Investigating Ground Interactions Of A Rotocraft Landing Vehicle On Titan, Adam Rozman

Honors Undergraduate Theses

The exploration of celestial bodies has recently advanced from rovers to rotorcraft. This includes the recent flights of Mars Ingenuity and the upcoming Dragonfly mission to explore the terrain of Saturn’s moon Titan as part of NASA’s New Frontiers Program. Flight-based landers can travel quickly to sites kilometers apart and land in complex terrain. Although cruise conditions for these rotorcrafts are well understood, studies are necessary to understand take-off and landing. In ground effect conditions, a rotor wake impinges and reflects off the ground, creating changes in aerodynamics such as increased lift. Additionally, operating over loose surfaces, the rotors can …


Autoignition Delay Time Measurements And Chemical Kinetic Modeling Of Hydrogen/Ammonia/Natural Gas Mixtures, Jessica Baker Jan 2022

Autoignition Delay Time Measurements And Chemical Kinetic Modeling Of Hydrogen/Ammonia/Natural Gas Mixtures, Jessica Baker

Electronic Theses and Dissertations, 2020-2023

In recent years, hydrogen-carrying compounds have accrued interest as an alternative to traditional fossil fuels due to their function as zero-emission fuels. As such, there is interest in investigating hydrogen-carrying compounds to improve understanding of the fuels' characteristics for use in high pressure systems. In the current study, the oxidation of ammonia/natural gas/hydrogen mixtures was carried out to study CO formation profiles as well as the ignition delay times behind reflected shock waves in order to refine chemical kinetic models. Experiments were carried out in the University of Central Florida's shock tube facility by utilizing chemiluminescence to obtain OH* emission …


Prediction And Validation Of Residual Stresses In Additively Manufactured Metal Parts, Jose Mayi Rivas Jan 2022

Prediction And Validation Of Residual Stresses In Additively Manufactured Metal Parts, Jose Mayi Rivas

Electronic Theses and Dissertations, 2020-2023

Selective Laser Melted (SLM) Additively Manufactured (AM) metal parts are of special interest to many industries because their designs can be made arbitrarily complex while still maintaining bulk type mechanical properties. However, the large thermal gradients inherent to the SLM process generate residual stresses (RS) and distortions that are detrimental to the fit, functionality and integrity of parts. Predicting the state of stresses in as-built 3D printed parts is a difficult problem that currently has only been approached with the use of transient thermomechanical Finite Element Models (FEMs). The nonlinearities associated with AM processes are difficult to capture in these …


Generative Adversarial Networks For Extrapolation Of Corrosion In Automobile Images, Andre Von Zuben Jan 2022

Generative Adversarial Networks For Extrapolation Of Corrosion In Automobile Images, Andre Von Zuben

Electronic Theses and Dissertations, 2020-2023

Deep learning has shown success in several applications involving pattern recognition, expert systems, and scientific discovery. However, existing methods struggle with industrial applications, which are often challenged by non-ideal datasets. In many cases, the datasets are small, poorly labeled, noisy, or have unbalanced class distribution or any combination of such problems. In this Master's research, we propose a generative adversarial network (GAN) strategy that is able to circumvent limitations imposed by tiny datasets. As a case study, we use the extrapolation of corrosion in automobiles and feed our deep learning framework with only a few dozen images instead of the …


Simulation Of A Comprehensive Heat Recovery Steam Generator, Jose Chalarca Castro Jan 2022

Simulation Of A Comprehensive Heat Recovery Steam Generator, Jose Chalarca Castro

Electronic Theses and Dissertations, 2020-2023

With the increasing prevalence of renewables, it is important to optimize combined cycle power plants during transient conditions to better compliment the variable generation of renewable energy generators. There is a demand for dynamic heat recovery steam generators (HRSG) models that may enable improved control designs. Sufficiently accurate real-time simulations of HRSGs may serve as soft sensors and state estimators during transient conditions. Furthermore, real-time simulations of HRSGs can be used for operator training which does not incur the inherit risk of using plant hardware. The focus of this research is on the development towards an integrated dynamic closed loop …


The Fluid Dynamics Of A Spanwise-Morphing Wing: An Experimental And Analytical Study, Kamlesh Joshi Jan 2022

The Fluid Dynamics Of A Spanwise-Morphing Wing: An Experimental And Analytical Study, Kamlesh Joshi

Electronic Theses and Dissertations, 2020-2023

The unsteady forces and fluid flow structure of a morphing wing are investigated for low Reynolds number (Re) flows, i.e., Re < 20,000. The morphing wing is designed to change shape in the spanwise direction in a controlled manner using internal actuation. The two types of wing morphing are studied in this work, i.e., spanwise bending and spanwise twisting. The wing morphing is named based on the overall shape of the wing after it is dynamically morphed.


Empirical Comparison Of Machine Learning Methods For Wind Power Predictions, Sidny M. Stewart Jan 2022

Empirical Comparison Of Machine Learning Methods For Wind Power Predictions, Sidny M. Stewart

EWU Masters Thesis Collection

No abstract provided.


Laptop Recycling Case Study: Estimating The Contained Value And Value Recovery Process Feasibility Of End-Of-Life Consumer Electronics, Zebulon Hart Jan 2022

Laptop Recycling Case Study: Estimating The Contained Value And Value Recovery Process Feasibility Of End-Of-Life Consumer Electronics, Zebulon Hart

Theses and Dissertations--Mining Engineering

Work has been done to establish, through the development and use of novel assay techniques and analysis metrics, the contained value of a sampling of laptop computers (as an analog for myriad e-waste sources). This work has conceptualized e-waste as an alternative to geologic-origin complex metallic ores and has likewise evaluated the feasibility of value recovery from e-waste sources in a similar manner to an ore. The application of conventional and novel mineral separation techniques to e-waste recycling processes has been evaluated and positive results are demonstrated. Further, this work has demonstrated the ability to identify the presence of base …


Modeling Human Control Behavior In Command-Following Tasks, Sajad Koushkbaghi Jan 2022

Modeling Human Control Behavior In Command-Following Tasks, Sajad Koushkbaghi

Theses and Dissertations--Mechanical and Aerospace Engineering

Humans interact with a variety of complex dynamic systems on a daily basis. However, they are often the lesser understood component of human-in-the-loop (HITL) systems. In this dissertation, we present the results of two HITL experiments to investigate the control strategies that humans use when performing command-following tasks. The first experiment is designed to investigate the control strategies that humans use to interact with nonlinear dynamic systems. Two groups of human subjects interact with a dynamic system and perform a command-following task. One group interacts with a linear time-invariant (LTI) dynamic system and the other group interacts with a Wiener …


Energy And Economic Modeling Of Stillage Dewatering Processes In Kentucky Bourbon Distilleries, William Brennan Jan 2022

Energy And Economic Modeling Of Stillage Dewatering Processes In Kentucky Bourbon Distilleries, William Brennan

Theses and Dissertations--Mechanical and Aerospace Engineering

Stillage is a byproduct of alcohol distillation and must be managed in all distilleries to sustain operations. In the United States, fuel ethanol plants typically convert all stillage into Dried Distillers’ Grains with Solubles (DDGS). This process and its variations are well known. Typical stillage management approaches are not well known, however, for the Kentucky bourbon industry. A survey of stillage management approaches in operational bourbon distilleries was conducted. Process modeling was performed to evaluate the energy and economic considerations of the available stillage dewatering methods for a 7 Million Original Proof Gallon (MMOPG) distillery. Monte Carlo simulations were performed …


Quantitative Methods For Total Lifecycle Risk Likelihood And Impact Assessment In Sustainable Product Design Decision Making, Christian Enyoghasi Jan 2022

Quantitative Methods For Total Lifecycle Risk Likelihood And Impact Assessment In Sustainable Product Design Decision Making, Christian Enyoghasi

Theses and Dissertations--Mechanical and Aerospace Engineering

Sustainable products promise significant economic, environmental, and societal benefits. Numerous methods are available for use during the new product development process to identify alternate product designs that optimize sustainability performance. Once any such design is selected and the product is launched, many uncertainties are likely to affect its performance over the total lifecycle. Such uncertainties give rise to risks that can influence the overall product sustainability performance. However, comprehensive quantitative methods to evaluate the likelihood or the impact of different risks to enable sustainable product design decision making are lacking.

This research aims to address this gap by developing a …


In-Situ Characterization Of Surface Quality In Γ-Tial Aerospace Alloy Machining, David Adeniji Jan 2022

In-Situ Characterization Of Surface Quality In Γ-Tial Aerospace Alloy Machining, David Adeniji

Theses and Dissertations--Mechanical and Aerospace Engineering

The functional performance of critical aerospace components such as low-pressure turbine blades is highly dependent on both the material property and machining induced surface integrity. Many resources have been invested in developing novel metallic, ceramic, and composite materials, such as gamma-titanium aluminide (γ-TiAl), capable of improved product and process performance. However, while γ-TiAl is known for its excellent performance in high-temperature operating environments, it lacks the manufacturing science necessary to process them efficiently under manufacturing-specific thermomechanical regimes. Current finish machining efforts have resulted in poor surface integrity of the machined component with defects such as surface cracks, …


Radiative Conductivity Estimation Using Direct Approach For Fibrous Materials, Mohammad Khaleel Jan 2022

Radiative Conductivity Estimation Using Direct Approach For Fibrous Materials, Mohammad Khaleel

Theses and Dissertations--Mechanical and Aerospace Engineering

During planetary entry, space vehicles encounter high loads of thermal energy which requires a thermal protection system. Ablative thermal protection systems are usually made out of fibrous materials that exhibit internal radiation. In order to model the internal radiation response of a thermal protection system one should obtain proper radiative properties as well as thermal properties. The objective of this work is to provide a method that solves for the solid/gas thermal conductivity. Which can be used in coupled detailed radiative analysis.

Keywords: radiative conductivity, fibrous materials, radiative transfer, thermal protection system, P1 approximation, Finite Volume method.