• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.635-644
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• 1994

A mathematical model was developed to predict the concentrations of various nutrients in supernatants during aerobic digestion which is suitable to be employed in small wastewater treatment plants with such advantages as low capital cost and stable process. Significant reactions were determined with observing the behavior of nitrgen and phosphorus, and the model equations were built up in the form of simultaneous differential equations considering Mass Balance. Laboratory batch experiments were carried out at $20^{\circ}C$ and pH $7.5{\pm}0.5$ on the aerobic digestion of waste activated sludge at different solid levels. Nonlinear regression analysis was performed to estimate various reaction rate constants. The developed model can predict the behavior of Biomass N, dissolved organic N, $NH_4{^-}$-N, $NO_x{^-}$-N, and Biomass P, dissolved organic P, $PO_4{^-}$-P in aerobic digestion process. In this study, the results of simulation showed that dissolved nutrients had more effects on supernatants than nutrients in biomass, and phosphorus was more effective on supernatants than nitrogen.

• Journal of Energy Engineering
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• v.26 no.2
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• pp.64-72
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• 2017

The performance analysis of the 70 W class LED lighting system suitable for the Middle East environment was performed using the lumped parameter model. The LED light is composed of a heating substrate, a heat pipe, and a heat sink. We divided the LED lights into four objects and applied energy equilibrium to each of them to establish four lumped nonlinear differential equations. The solution of the simultaneous equations was obtained by the Runge-Kutta method. Convective heat transfer coefficients of the lumped model were obtained by multidimensional CFD analysis. As a result of comparison with experiment, it was found that the heating substrate had an error of $1.5^{\circ}C$ and the upper heat sink had an error of $1.8^{\circ}C$ and the relative error was about 0.6 %. Using this model, temperature distribution analysis was performed for normal operating conditions with an ambient temperature of $55^{\circ}C$, with sunlight only, with abnormal operating conditions with sunlight, and without an upper heat sink.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.55-64
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• 2003

Desiccation of a soil is basically the removal of water by evaporation, which is controlled by evaporativity and evaporability. Surface evaporation improves the trafficability which is essential for the access of construction equipment in the area reclaimed with soft clay. The existing traditional methods for evaluating evaporation can not account for the deformation of reclaimed soft soils during evaporation. Therefore, a theoretical model for predicting the rate of evaporation from the surface of a deformable material is proposed. The model is based on a system of equations for coupled heat and mass transfer in unsaturated soils. The modified pressure plate extractor test and glass desiccator test were carried out to obtain the soil-water characteristic curve for a deformable soil. The column drying test was conducted to investigate one dimensional water flow, heat flow and evaporation in the surface. A finite difference program was developed to solve the coupled nonlinear partial differential equations, which permit the study of water, vapor and heat flows in the deformable soil. Comparison between measured and simulated values shows a reasonably good matching between the two.

• Membrane Journal
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• v.16 no.3
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• pp.204-212
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• 2006

A numerical analysis was carried out for separation of carbon dioxide from carbon dioxide/nitrogen gas mixture by a polyethersulfone hollow fiber membrane which has shown a good stability against plasticization by carbon dioxide and an excellent separation efficiency fur carbon dioxide from its gas mixture. A computer program for carbon dioxide separation was developed using the Compaq Visual Fortran 6.6 software. Governing module equations were thought to be an initial-value problem and the nonlinear ordinary differential equations were simultaneously solved using the Runge-Kutta-Verner fifth-order method. From results of numerical analysis, the carbon dioxide partial pressure of the feed stream, the pressure ratio of the feed side to the permeate side and the feed gas residence time at the inside of a membrane were found to be very important factors to affect the permeation characteristics of carbon dioxide.

• Geomechanics and Engineering
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• v.8 no.4
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• pp.559-594
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• 2015

A nonlinear creep function incorporated into the elastic visco-plastic model may describe the long-term soil deformation more accurately. However, by applying the conventional procedure, there are challenges to determine the model parameters due to limitation of suitable data points. This paper presents a numerical solution to obtain several parameters simultaneously for a nonlinear elastic visco-plastic (EVP) model using the available consolidation data. The finite difference scheme using the Crank-Nicolson procedure is applied to solve a set of coupled partial differential equations of the time dependent strain and pore water pressure dissipation. The model parameters are determined by applying the algorithm of trust-region reflective optimisation in conjunction with the finite difference solution. The proposed method utilises all available consolidation data during dissipation of the excess pore water pressure to determine the required model parameters. Moreover, the reference time in the elastic visco-plastic model can readily be adopted as a unit of time; denoting creep is included in the numerical predictions explicitly from the very first time steps. In this paper, the settlement predictions of thick soft clay layers are presented and discussed to evaluate and compare the accuracy and reliability of the proposed method against the graphical procedure to obtain the model parameters. In addition, comparison of the available experimental results to the numerical predictions confirms the accuracy of the numerical procedure.

• Journal of Navigation and Port Research
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• v.40 no.6
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• pp.361-368
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• 2016

A ship's rolling motion can make crew and passengers sick and/or apply forces to the structure that cause damage.. Therefore bilge keels are equipped in most ships for anti-rolling. In special cases, anti-rolling tanks (ARTs), fin stabilizers, or gyroscopes can be installed. However, ARTs require a large area to install, and fin stabilizers and gyroscopes are costly to install and expensive to operate. This paper suggests a Anti-rolling pendulum (ARP) to reduce roll motion. ARPs acts like ARTs. However, the ARP has a circular shaped guidance arc instead of the string or wire of a simple pendulum. The device suggested has about 1/ 8 the weight and 1/ 6 the volume of a ART and is more effective. This study derives the nonlinear and linear differential equations of system motion.

• 한국신재생에너지학회:학술대회논문집
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• 2009.06a
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• pp.373-373
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• 2009

Relative humidity, membrane conductivity and water activity are critical parameters of polymer electrolyte membrane fuel cells (PEMFC) for high performance and reliability. These parameters are closely related with temperature. Moreover, the ideal values of these parameters are not always identical along the channels. Therefore, the cooling channel design and its operating condition should be well optimized along the all location of the channels. In the present study, we have performed a numerical investigation on the effects of cooling channels on performance of a PEMFC. Three-dimensional Navier-Stokes equations are solved with the energy equation including heat generated by the electrochemical reactions in the fuel cell. The present numerical model includes the gas diffusion layers (GDL) and serpentine channels for both anode and cathode gas flows, as well as cooling channels. To accurately predict the water transport across the membrane, the distribution of water content in the membrane is calculated by solving a nonlinear differential equation with a nonlinear coefficient, i.e., the water diffusivity which is a function of water content as well as temperature. Main emphasis is placed on the heat transfer between the solid bipolar plate and coolant flow. The present results show that local current density is affected by cooling channels due to the change of the oxygen concentration and the membrane conductivity as well as the water content. It is also found that the relative humidity is influenced by the generated water and the gas temperature and thus it affects the distribution of fuel concentration and the conductivity of the membrane, ultimately fuel cell performance. Unit-cell experiments are also carried out to validate the numerical models. The performance curves between the models and experiments show reasonable results.

• Steel and Composite Structures
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• v.26 no.6
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• pp.673-691
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• 2018

The main goal of this research is to examine the in-plane and out-of-plane forced vibration of a curved nanocomposite microbeam. The in-plane and out-of-plane displacements of the structure are considered based on the first order shear deformation theory (FSDT). The curved microbeam is reinforced by functionally graded carbon nanotubes (FG-CNTs) and thus the extended rule of mixture is employed to estimate the effective material properties of the structure. Also, the small scale effect is captured using the strain gradient theory. The structure is rested on a nonlinear orthotropic viscoelastic foundation and is subjected to concentrated transverse harmonic external force, thermal and magnetic loads. The derivation of the governing equations is performed using energy method and Hamilton's principle. Differential quadrature (DQ) method along with integral quadrature (IQ) and Newmark methods are employed to solve the problem. The effect of various parameters such as volume fraction and distribution type of CNTs, boundary conditions, elastic foundation, temperature changes, material length scale parameters, magnetic field, central angle and width to thickness ratio are studied on the frequency and force responses of the structure. The results indicate that the highest frequency and lowest vibration amplitude belongs to FGX distribution type while the inverse condition is observed for FGO distribution type. In addition, the hardening-type response of the structure with FGX distribution type is more intense with respect to the other distribution types.

• Korean Chemical Engineering Research
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• v.49 no.5
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• pp.560-564
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• 2011

The objective of this study is to propose a mathematical model for a pervaporation process for concentrating hydrogen peroxide. The process was developed by NASA, which consists of a shell and membrane tubes, where a liquid hydrogen peroxide solution flows in the shell, and a sweep gas flows in the tubes countercurrent to each other. The liquid retentate is concentrated as more water molecules permeate and evaporate through the membrane than hydrogen peroxide. For this process, a mathematical model has been developed in the form of a system of nonlinear partial differential algebraic equations based on a sorption-diffusion mechanism for permeation, an Arrhenius relationship for the temperature dependency of the permeate flux, and mass and momentum balances for the liquid concentrations and flows in the membrane module. The dynamic behavior of the concentration of hydrogen peroxide in the retentate side has been simulated by solving a simplified version of the proposed model, and the result is compared with the experimental data reported in the NASA patent.

• Journal of Microbiology and Biotechnology
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• v.17 no.1
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• pp.146-153
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• 2007

A mathematical competition model between normal flora and an invading pathogen was devised to allow analysis of bacterial infections in a host. The normal flora includes the various microorganisms that live on or within the host and act as a primary human immune system. Despite the important role of the normal flora, no mathematical study has been undertaken on models of the interaction between it and invading pathogens against a background of antibiotic treatment. To quantify key elements of bacterial behavior in a host, pairs of nonlinear differential equations were used to describe three categories of human health conditions, namely, healthy, latent infection, and active infection. In addition, a cutoff value was proposed to represent the minimum population level required for survival. The recovery of normal flora after antibiotic treatment was also included in the simulation because of its relation to human health recovery. The significance of each simulation parameter for the bacterial growth model was investigated. The devised simulation showed that bacterial proliferation rate, carrying capacity, initial population levels, and competition intensity have a significant effect on bacterial behavior. Consequently, a model was established to describe competition between normal flora and an infiltrating pathogen. Unlike other population models, the recovery process described by the devised model can describe the human health recovery mechanism.