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Articles 631 - 660 of 4190
Full-Text Articles in Engineering
Model And Experimental Validation Of A Controllable Membrane-Type Humidifier For Fuel Cell Applications, Denise A. Mckay, Anna G. Stefanopoulou, Jeffrey Cook
Model And Experimental Validation Of A Controllable Membrane-Type Humidifier For Fuel Cell Applications, Denise A. Mckay, Anna G. Stefanopoulou, Jeffrey Cook
Engineering: Faculty Publications
For temperature and humidity control of fuel cell reactants, a gas humidification apparatus was designed and constructed. We then developed a low-order, control-oriented model of the humidification system thermal dynamics based on first principles. A simple and reproducible methodology is then employed for parameterizing the humidification system model using experimental data. Finally, the system model is experimentally validated under a wide range of operating conditions. It is shown that a physics based estimation of the air-vapor mixture relative humidity leaving the humidifier system (supplied to the fuel cell) is possible using temperature and pressure measurements. This estimation eliminates the need …
Modeling And Validation Of Fuel Cell Water Dynamics Using Neutron Imaging, Jason B. Siegel, Denise A. Mckay, Anna G. Stefanopoulou
Modeling And Validation Of Fuel Cell Water Dynamics Using Neutron Imaging, Jason B. Siegel, Denise A. Mckay, Anna G. Stefanopoulou
Engineering: Faculty Publications
Using neutron imaging, the mass of liquid water within the gas diffusion layer and flow channels of an operating polymer electrolyte membrane fuel cell (PEMFC) is measured under a range of operating conditions. Between anode purge events, it is demonstrated that liquid water accumulates and is periodically removed from the anode gas channels; this event is well correlated with the dynamic cell voltage response. The estimation of flooding and cell performance is achieved by a spatially distributed (through-membrane plane), temporally-resolved, and two-phase (liquid and vapor) water model. Neutron imaging techniques have never before been applied to characterize flooding with a …
High Temperature Heat Exchanger Annual Report, Anthony Hechanova
High Temperature Heat Exchanger Annual Report, Anthony Hechanova
Publications (NSTD)
Objectives
• Identify candidate materials for heat exchanger components.
• Test candidate materials for heat exchanger components.
• Design critical components in the interface between the reactor and hydrogen production plant and within the sulfur iodine thermochemical process.
• Fabricate prototypical components.
• Test prototypical components.
Hand-Held Flyback Driven Coaxial Dielectric Barrier Discharge: Development And Characterization, Victor J. Law, Vladimir Milosavljevic, Neil O’Connor, James F. Lalor, Steven Daniels
Hand-Held Flyback Driven Coaxial Dielectric Barrier Discharge: Development And Characterization, Victor J. Law, Vladimir Milosavljevic, Neil O’Connor, James F. Lalor, Steven Daniels
Articles
The development of a handheld single and triple chamber atmospheric pressure coaxial dielectric barrier discharge driven by Flyback circuitry for helium and argon discharges is described. The Flyback uses external metal-oxide-semiconductor field-effect transistor power switching technology and the transformer operates in the continuous current mode to convert a continuous dc power of 10–33 W to generate a 1.2–1.6 kV 3.5 μs pulse. An argon discharge breakdown voltage of ∼768 V is measured. With a 50 kHz, pulse repetition rate and an argon flow rate of 0.5–10 argon slm (slm denotes standard liters per minute), the electrical power density deposited in …
Link Foundation Fellowship Report, Elisabeth A. Gilmore
Link Foundation Fellowship Report, Elisabeth A. Gilmore
Link Foundation Energy Fellowship Reports
Peak hour electricity demand is associated with wholesale electricity prices that are sometimes more than 10 times higher than in off-peak periods. During these high-demand periods congested transmission lines and insufficient generation capacity can lead to brownouts and blackouts. This problem can be especially acute in urban centers. One way to alleviate this problem is to build new peaking plants. We investigated the costs and benefits, including expenditures and adverse health effects, of using existing backup generators and battery based electrical storage facilities to meet peak load demands rather than investing in a new power plant. Using small-scale generation located …
Sequestration And Ultrasound-Induced Release Of Doxorubicin From Stabilized Pluronic P105 Micelles, John D. Pruitt, William G. Pitt
Sequestration And Ultrasound-Induced Release Of Doxorubicin From Stabilized Pluronic P105 Micelles, John D. Pruitt, William G. Pitt
Faculty Publications
Controlled drug delivery from micelles requires that the micelles remain stable when diluted below their critical micelle concentration, such as upon injection into blood. A cross-linked, interpenetrating network of N,N-diethylacrylamide (NNDEA) was polymerized in the core of Pluronic P105 micelles to stabilize temporarily the micelles at concentrations below the critical micellar concentration of free P105. The stabilized Pluronic micelles (called Plurogels) were able to sequester the drug doxorubicin (Dox) and protect HL-60 cells from the drug at concentrations where non-stabilized Pluronic provided no protection. The protection lasted ~ 12 hr, which is similar to the half-life of the particles. Application …
Surface Magnetoelectric Effect In Ferromagnetic Metal Films, Chun-Gang Duan, Julian P. Velev, Renat F. Sabirianov, Ziqiang Zhu, Junhao Chu, Sitaram Jaswal, Evgeny Y. Tsymbal
Surface Magnetoelectric Effect In Ferromagnetic Metal Films, Chun-Gang Duan, Julian P. Velev, Renat F. Sabirianov, Ziqiang Zhu, Junhao Chu, Sitaram Jaswal, Evgeny Y. Tsymbal
Nebraska Center for Materials and Nanoscience: Faculty Publications
A surface magnetoelectric effect is revealed by density-functional calculations that are applied to ferromagnetic Fe(001), Ni(001), and Co(0001) films in the presence of an external electric field. The effect originates from spin-dependent screening of the electric field which leads to notable changes in the surface magnetization and the surface magnetocrystalline anisotropy. These results are of considerable interest in the area of electrically controlled magnetism and magnetoelectric phenomena.
A Parallel Spectral Element Method For Dynamic Three-Dimensional Nonlinear Elasticity Problems, S. Dong, Z. Yosibash
A Parallel Spectral Element Method For Dynamic Three-Dimensional Nonlinear Elasticity Problems, S. Dong, Z. Yosibash
PRISM: NNSA Center for Prediction of Reliability, Integrity and Survivability of Microsystems
We present a high-order method employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics, for solving dynamic three-dimensional geometrically nonlinear elasticity problems. We demonstrate that the method has an exponential convergence rate spatially and a second-order accuracy temporally for the four classes of problems of linear/geometrically nonlinear elastostatics/elastodynamics. The method is parallelized through domain decomposition and message passing interface (MPI), and is scaled to over 2000 processors with high parallel performance.
Effect Of Nitrification On Lead Corrosion In Chloraminated Distribution Systems, Michael Shade
Effect Of Nitrification On Lead Corrosion In Chloraminated Distribution Systems, Michael Shade
All Theses
Water treatment facilities have been shifting from using chlorination to chloramination as a primary disinfectant since 2004, when the EPA enacted the Disinfectants/Disinfection By-Products (D/DBP) Rule mandating the decrease of DBPs. After the switch to chloramination, an unexpected lead concentration increase was detected in the Washington, D. C., and Greenville, NC water systems. These increases may be associated with the switch from chlorination to chloramination. Decomposition of chloramines results in higher ammonia loading to drinking water distribution systems, which may increase nitrification. Nitrifying bacteria may facilitate lead corrosion via two mechanisms: use of nitrite or nitrate as an alternative electron …
Fatigue Testing Of Three Peristernal Median Sternotomy Closure Techniques, Cameron Wangsgard, David J. Cohen, Lanny V. Griffin
Fatigue Testing Of Three Peristernal Median Sternotomy Closure Techniques, Cameron Wangsgard, David J. Cohen, Lanny V. Griffin
Biomedical Engineering
Failure of a sternotomy closure because of closure system fatigue is a complication that may result in dehiscence and put the individual at risk for serious complications. The purpose of this study was to assess the fatigue performance of three peristernal median sternotomy closure techniques (figure-of-eight stainless-steel wires, figure-of-eight stainless-steel cables, or Pectofix Dynamic Sternal Fixation [DSF] stainless-steel plates) in order to quantify the potential risk of fatigue failure of these devices when subject to cyclic loads in physiologically relevant loading directions.
Effects Of Environmental Factors On Construction Of Soil-Cement Pavement Layers, John E. Michener
Effects Of Environmental Factors On Construction Of Soil-Cement Pavement Layers, John E. Michener
Theses and Dissertations
The specific objectives of this research were to quantify the effects of certain environmental factors on the relative strength loss of soil-cement subjected to compaction delay and to develop a numerical tool that can be easily used by engineers and contractors for determining a maximum compaction delay time for a given project. These objectives were addressed through extensive laboratory work and statistical analyses. The laboratory work involved testing an aggregate base material and a subgrade soil, each treated with two levels of cement. Environmental factors included in the experimentation were wind speed, temperature, and relative humidity, and three levels of …
Mechanistic Investigation Of Ash Deposition In Pulverized-Coal And Biomass Combustion, Shrinivas Sadashiv Lokare
Mechanistic Investigation Of Ash Deposition In Pulverized-Coal And Biomass Combustion, Shrinivas Sadashiv Lokare
Theses and Dissertations
This investigation details the effects of fuel constituents on ash deposition through systematic experimental and theoretical analyses of fundamental particle experiments and a suite of fuels with widely varying inorganic contents and compositions. The experiments were carried out in the Multifuel Flow Reactor (MFR) at Brigham Young University. Fuels included several biomass fuels (straw, sawdust and mixtures of straw-sawdust with other additives such as Al(OH)3, CaCO3, etc.) and four commercially-used coals (Illinois#6, Powder River Basin – Caballo and Cordero, Blind Canyon, and Lignite – Beulah Zap). The data from the series of experiments quantitatively illustrate the effects of fuel properties, …
Ceas E-News 09.23.2008, College Of Engineering And Applied Sciences
Ceas E-News 09.23.2008, College Of Engineering And Applied Sciences
College of Engineering and Applied Sciences News
Summer Institute offers computer interfacing experience
Lester Larsen: Progress Of Tractor Test Work 1946 -1956, Tractor Museum
Lester Larsen: Progress Of Tractor Test Work 1946 -1956, Tractor Museum
Individuals Associated with the Nebraska Tractor Test
When Lester F. Larsen was hired as Engineer in Charge of the Nebraska Tractor Test, the laboratory had been inactive since 1941 due to World War II. Much of the test equipment was out of order and in need of repair. He kept a journal called the Progress of Tractor Test Work. This journal of day to day activities extended from 1946 through 1956.
Real Time Signal Reconstruction From Spikes On A Digital Signal Processor, John G. Harris, Jie Xu, Manu Rastogi, Alexander Singh-Alvarado, Vaibhav Garg, José C. Principe, Kalyana Vuppamandla
Real Time Signal Reconstruction From Spikes On A Digital Signal Processor, John G. Harris, Jie Xu, Manu Rastogi, Alexander Singh-Alvarado, Vaibhav Garg, José C. Principe, Kalyana Vuppamandla
Electrical and Computer Engineering Faculty Research & Creative Works
There has been significant interest in encoding information into asynchronous timing events or spikes using models of biological neurons. It has been shown that these neurons can act as lossless encoders and software algorithms can reconstruct the encoded information. We present here, a real time implementation of a reconstruction algorithm on a TI TMS320C6713 DSK board. This implementation reconstructs the signal from a spike train which was encoded by a fabricated neuron chip. A signal to error ratio of 32 dB with an average firing rate of 8 KHz is obtained. We discuss the practical implementation, challenges and possible future …
Modeling Multilayer Power Distribution Network By Systematically Incorporating Via And Cavity Models, Yaojiang Zhang, Francesco De Paulis, Jun Fan
Modeling Multilayer Power Distribution Network By Systematically Incorporating Via And Cavity Models, Yaojiang Zhang, Francesco De Paulis, Jun Fan
Electrical and Computer Engineering Faculty Research & Creative Works
A closed-form expression for via barrel-plate capacitances is derived. This results in a more accurate equivalent circuit model for decoupling capacitors including both parasitic inductances and via capacitances. Multilayer power distribution network (PDN) is then analyzed by incorporating the circuit models of both vias and parallel plane pair. Circuit simulator is used to evaluate the coupling properties among various locations in the multilayer PDN structures.
The Time Derivative Neuron, Jie Xu, John G. Harris
The Time Derivative Neuron, Jie Xu, John G. Harris
Electrical and Computer Engineering Faculty Research & Creative Works
We have developed the time derivative neuron to reduce the bandwidth needed to encode continuous-time input signals using spiking neuron models. Unlike conventional spiking neuron models, the time derivative neuron generates more spikes in regions of high change and is essentially invariant to DC shifts of the input. We describe the model and develop an efficient reconstruction algorithm to demonstrate its reconstruction accuracy and transmission bandwidth. The idea has both digital and analog hardware realizations and we show a SPICE transistor-level simulation of an efficient analog CMOS implementation. ©2008 IEEE.
Pulse-Based Signal Compression For Implanted Neural Recording Systems, John G. Harris, José C. Principe, Justin C. Sanchez, Du Chen, Christy She
Pulse-Based Signal Compression For Implanted Neural Recording Systems, John G. Harris, José C. Principe, Justin C. Sanchez, Du Chen, Christy She
Electrical and Computer Engineering Faculty Research & Creative Works
Today's implanted neural systems are bound by tight constraints on power and communication bandwidth. Most conventional ADC-based approaches fall into two categories. Either they transmit all of the information at the Nyquist rate but are ultimately limited to only a handful of channels due to communication bandwidth constraints. Or they perform spike detection on the front-end which allows a scale up to 100 or more channels but prevents the use of spike sorting on the backend. Spike sorting is an important step that provides a labeling to multiple neurons on each channel and further improves the accuracy of spike detection. …
Description Of Versatile Optical Polarimetric Scatterometer That Measures All 16 Elements Of The Mueller Matrix For Reflection And Transmission: Application To Measurements Of Scatter Cross Sections, Ellipsometric Parameters, Optical Activity, And The Complex Chiral Parameters, Ezekiel Bahar, Robert D. Kubik
Description Of Versatile Optical Polarimetric Scatterometer That Measures All 16 Elements Of The Mueller Matrix For Reflection And Transmission: Application To Measurements Of Scatter Cross Sections, Ellipsometric Parameters, Optical Activity, And The Complex Chiral Parameters, Ezekiel Bahar, Robert D. Kubik
Department of Electrical and Computer Engineering: Faculty Publications
A detailed description of an optical polarimetric scatterometer, its capabilities, and special application are presented. This instrument measures the 44 Mueller matrix elements as well as bidirectional reflective distribution functions scatter cross sectionsfor light that is scattered from a target. Incident polarized light at wavelengths =0.6328 and =1.06 m can be directed toward the target in an arbitrary direction. The receiver can be located anywhere in the solid angle 4. Backscatter measurements, most commonly used in remote sensing, can also be obtained. The scatterometer has been used to validate different analytical/numerical solutions to a broad class of electromagnetic scattering problems, …
The Interactive Research Guide: Will Function Bring Users Content? A Project Model Illustrated By A Proposed Paper-Writing Guide, Barry J. Bailey
The Interactive Research Guide: Will Function Bring Users Content? A Project Model Illustrated By A Proposed Paper-Writing Guide, Barry J. Bailey
Library Papers and Presentations
After reviewing the history of subject guides and their movement into an electronic format, their is an opportunity to change the format of information providing. Whereas a user goes to guides for lists of content, perhaps a user can go to guides to execute a function. By walking through the creation of a paper-writing guide, this idea of a functioning guide is illustrated.
Ceas E-News 09.16.2008, College Of Engineering And Applied Sciences
Ceas E-News 09.16.2008, College Of Engineering And Applied Sciences
College of Engineering and Applied Sciences News
"Aspire to a Career" connects job-seekers to more than 80 employeers
Novel Variable Step Size Nlms Algorithms For Echo Cancellation, Mohammad Asif Iqbal, Steven L. Grant
Novel Variable Step Size Nlms Algorithms For Echo Cancellation, Mohammad Asif Iqbal, Steven L. Grant
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper we present two new variable step size (VSS) methods for adaptive filters. These vs.S methods are so effective; they eliminate the need for a separate double-talk detection algorithm in echo cancellation applications. the key feature of both approaches is the introduction of a new near-end signal energy estimator (NE-SEE) that provides accurate and computationally efficient estimates even during double-talk and echo path change events. the first vs.S algorithm applies the NESEE to the recently proposed Nonparametric vs.S NLMS (NPVSS-NLMS) algorithm. the resulting algorithm has excellent convergence characteristics with an intrinsic immunity to double-talk. the second approach is …
Metabolic Engineering Of A Thermophilic Bacterium To Produce Ethanol At High Yield, A. Joe Shaw, Kara K. Podkaminer, Sunil G. Desai, John S. Bardsley, Stephen R. Rogers, Philip G. Thorne, David A. Hogsett, Lee R. Lynd
Metabolic Engineering Of A Thermophilic Bacterium To Produce Ethanol At High Yield, A. Joe Shaw, Kara K. Podkaminer, Sunil G. Desai, John S. Bardsley, Stephen R. Rogers, Philip G. Thorne, David A. Hogsett, Lee R. Lynd
Dartmouth Scholarship
We report engineering Thermoanaerobacterium saccharolyticum, a thermophilic anaerobic bacterium that ferments xylan and biomass-derived sugars, to produce ethanol at high yield. Knockout of genes involved in organic acid formation (acetate kinase, phosphate acetyltransferase, and L-lactate dehydrogenase) resulted in a strain able to produce ethanol as the only detectable organic product and substantial changes in electron flow relative to the wild type. Ethanol formation in the engineered strain (ALK2) utilizes pyruvate:ferredoxin oxidoreductase with electrons transferred from ferredoxin to NAD(P), a pathway different from that in previously described microbes with a homoethanol fermentation. The homoethanologenic phenotype was stable for >150 generations …
A-Priori Analysis Of Conditional Moment Closure Modeling Of A Temporal Ethylene Jet Flame With Soot Formation Using Direct Numerical Simulation, David O. Lignell, John C. Hewson, Jacqueline H. Chen
A-Priori Analysis Of Conditional Moment Closure Modeling Of A Temporal Ethylene Jet Flame With Soot Formation Using Direct Numerical Simulation, David O. Lignell, John C. Hewson, Jacqueline H. Chen
Faculty Publications
Modeling soot formation in turbulent nonpremixed combustion is a difficult problem. Unlike most gaseous combustion species, soot lacks a strong state relationship with the mixture fraction due to unsteady formation rates which overlap transport timescales, and strong differential diffusion between gaseous species and soot. The conditional moment closure model (CMC) has recently been applied to the problem of turbulent soot formation. A challenge in CMC modeling is the treatment of differential diffusion. Three-dimensional direct numerical simulation (DNS) of a nonpremixed ethylene jet flame with soot formation has been performed using a 19 species reduced ethylene mechanism and a four-step, three-moment, …
Verification Of Asphalt Concrete Performance Prediction Using Level 2 And Level 3 Inputs Of Mechanistic-Empirical Pavement Design Guide For Flexible Pavements Of The State Of New Jersey, Nusrat Siraj
Theses and Dissertations
The purpose of this thesis is to present the results of the verification study of the Mechanistic-Empirical Pavement Design Guide (M-EPDG) using level 2 and level 3 inputs. In addition, the challenges of verification of the predicted performance with the help of field-measured data of existing flexible pavements are also presented. In this study, twenty-five sections were analyzed covering a broad range of soil, environmental conditions, traffic volumes and pavement structures observed in the state of New Jersey. Predicted performance of various distresses, such as rutting, alligator cracking, longitudinal cracking, thermal cracking and International Roughness Index (IRI) were verified for …
Massively Parallel Full-Wave Modeling Of Advanced Packaging Structures On Bluegene Supercomputer, J. D. Morsey, Lijun Jiang, B. J. Rubin, A. Deutsch, C. W. Surovic, D. Becker, A. Haridass
Massively Parallel Full-Wave Modeling Of Advanced Packaging Structures On Bluegene Supercomputer, J. D. Morsey, Lijun Jiang, B. J. Rubin, A. Deutsch, C. W. Surovic, D. Becker, A. Haridass
Electrical and Computer Engineering Faculty Research & Creative Works
A parallel, distributed memory version of a full wave Method of Moments (MoM) solution combined with the Reduced Coupling approximation technique is presented on the largest parallel-server. Modeling results for product-level simulation of a single-chip module are correlated with time-domain measurements for validation of the technique. Scaling for this and other representative examples are shown for up to 16,384 compute nodes on IBM's BlueGene supercomputer, the largest parallel-platform ever reported for MoM based solutions. © 2008 IEEE.
Determining The Repair Ranking Of Existing Rc Bridges Using Multi-Pole Fuzzy Pattern Recognition Evaluation Method, Ming-Te Liang, Ting- Bang Chu, Wen-Hu Tsao, Chi-Jang Yeh
Determining The Repair Ranking Of Existing Rc Bridges Using Multi-Pole Fuzzy Pattern Recognition Evaluation Method, Ming-Te Liang, Ting- Bang Chu, Wen-Hu Tsao, Chi-Jang Yeh
Journal of Marine Science and Technology–Taiwan
This paper proposes a technique for determining the repair ranking of existing reinforced concrete (RC) bridges using the multi-pole fuzzy pattern recognition evaluation method. The differences between bridges and grades are expressed by weighted generalized weight distance. To find the optimal relative membership degree of an evaluated bridge attributed to any grade, the operative principle is that the sum of the square of weighted generalized weight distance is minimum. Based on this principle, the problem of extreme value is established by the objective function in connection with constraint condition. Using the Lagrangean method, the multi-pole fuzzy pattern recognition evaluation method …
Treatability Of U.S. Environmental Protection Agency Contaminant Candidate List Viruses: Removal Of Coxsackievirus And Echovirus Using Enhanced Coagulation, Brooke K. Mayer, Hodon Ryu, Morteza Abbaszadegan
Treatability Of U.S. Environmental Protection Agency Contaminant Candidate List Viruses: Removal Of Coxsackievirus And Echovirus Using Enhanced Coagulation, Brooke K. Mayer, Hodon Ryu, Morteza Abbaszadegan
Civil and Environmental Engineering Faculty Research and Publications
Enhanced coagulation was evaluated for removal efficacy of coxsackievirus and echovirus (Contaminant Candidate List [CCL] enteroviruses), poliovirus, four potential surrogate bacteriophages, and dissolved organic carbon (DOC). Viruses and DOC were effectively removed using enhanced coagulation, with removals generally improving as dose increased and pH decreased. Optimal enhanced coagulation conditions of 40 mg/L FeCl3 and pH between 5 and 6.5 resulted in a maximum removal of 3.0 logs of coxsackievirus B6, 1.75 logs of echovirus 12, 2.5 logs of poliovirus 1, 1.8 logs of fr, 1.3 logs of phi-X174, 0.36 logs of MS2, 0.29 logs of PRD1, and 41% DOC. …
Web-Based Information Management System For The Long Term Ecological Research Program In Kenting, Taiwan, Yang-Chi Chang, Meng-Tsung Lee, Kun-Chi Lai
Web-Based Information Management System For The Long Term Ecological Research Program In Kenting, Taiwan, Yang-Chi Chang, Meng-Tsung Lee, Kun-Chi Lai
Journal of Marine Science and Technology–Taiwan
This paper introduces a web-based information management system which has been set up as a collaborative facility to allow key environmental and ecological information access for the Long Term Ecological Research (LTER) in Kenting, Taiwan. The coral reef ecosystem degradation in Kenting has concerned both public and private sectors, for which a LTER team was formed to investigate the problem. A multi-functional web-based system integrates diverse data collections and analyses efforts of team members during the project span. It also provides authorities with effective information and knowledge for sustainable coral reef management. Three information technologies, web Database Management System (DBMS), …
Dynamic Reynolds Equation For Micropolar Fluid Lubrication Of Porous Slider Bearings, Neminath Bhujappa Naduvinamani, Gudadappagouda Basanagouda Marali
Dynamic Reynolds Equation For Micropolar Fluid Lubrication Of Porous Slider Bearings, Neminath Bhujappa Naduvinamani, Gudadappagouda Basanagouda Marali
Journal of Marine Science and Technology–Taiwan
In this paper an attempt has been made to study the rheological effects of micropolar fluid lubricants on the steady state and dynamic behavior of porous slider bearings by considering the squeezing action. The general modified Reynolds-type equation of porous sliding-squeezing surfaces with micropolar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined porous slider bearings by using perturbation method. Two Reynolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of …