Search results for: shallow water equations

Authors: Rajendra Kumar Isaac, Monisha Isaac

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India, having a vast cultivable area and regional climatic variability, encounters water Resource Management Problems at various levels. The agricultural production of India needs to be increased to meet out projected population growth. Sustainable water resource is the only option to ensure food security, especially in northern Indian states, where the ground and surface water resources are fast depleting. Various tools and technologies available for management of scarce water resources have been discussed. It was concluded that multiple use of water, adopting latest water management options, identification of climate adoptable cropping and farming systems, can enhance water productivity and would encounter the fast growing water management and water shortage problems in Indian agriculture.

Keywords: water resource management, sustainable, water management technologies, water productivity, agriculture

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Ashim Sattar, Ajanta Goswami, Anil V. Kulkarni

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Glacial lake outburst floods (GLOF) highly contributes to mountain hazards in the Himalaya. Over the past decade, high altitude lakes in the Himalaya has been showing notable growth in their size and number. The key reason is rapid retreat of its glacier front. Hydrodynamic modeling GLOF using shallow water equations (SWE) would result in understanding its impact in the downstream region. The present study incorporates remote sensing based ice thickness modeling to determine the future extent of the Dhauliganga Lake to map the over deepening extent around the highest lake in the Dhauliganga basin. The maximum future volume of the lake calculated using area-volume scaling is used to model a GLOF event. The GLOF hydrograph is routed along the channel using one dimensional and two dimensional model to understand the flood wave propagation till it reaches the 1st hydropower station located 72 km downstream of the lake. The present extent of the lake calculated using SENTINEL 2 images is 0.13 km². The maximum future extent of the lake, mapped by investigating the glacier bed has a calculated scaled volume of 3.48 x 106 m³. The GLOF modeling releasing the future volume of the lake resulted in a breach hydrograph with a peak flood of 4995 m³/s at just downstream of the lake. Hydraulic routing

Keywords: GLOF, glacial lake outburst floods, mountain hazard, Central Himalaya, future projection

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Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: Hassan Jebreen

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These models of a conservative pollutant in groundwater do not include representation of processes in soils and in the unsaturated zone, or biogeochemical processes in groundwater, These demonstration models can be used as the basis for more detailed simulations of the impacts of pollution sources at a local scale, but such studies should address processes related to specific pollutant species, and should consider local hydrogeology in more detail, particularly in relation to possible impacts on shallow systems which are likely to respond more quickly to changes in pollutant inputs. The results have demonstrated the interaction between groundwater flow fields and pollution sources in abstraction areas, and help to emphasise that wadi development is one of the key elements of water resources planning. The quality of groundwater in the Hebron area indicates a gradual increase in chloride and nitrate with time. Since the aquifers in Hebron districts are highly vulnerable due to their karstic nature, continued disposal of untreated domestic and industrial wastewater into the wadi will lead to unacceptably poor water quality in drinking water, which may ultimately require expensive treatment if significant health problems are to be avoided. Improvements are required in wastewater treatment at the municipal and domestic levels, the latter requiring increased public awareness of the issues, as well as improved understanding of the hydrogeological behaviour of the aquifers.

Keywords: groundwater, models, pollutants, wadis, hebron

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Authors: Rohit Tripathi, Sumit Tiwari, G. N. Tiwari

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In present study, an approach is adopted where photovoltaic thermal flat plate collector is integrated with compound parabolic concentrator. Analytical expression of temperature dependent electrical efficiency of N number of partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) water collector connected in series has been derived with the help of basic thermal energy balance equations. Analysis has been carried for winter weather condition at Delhi location, India. Energy and exergy performance of N - partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) Water collector system has been compared for two cases: (i) 25% area of water collector covered by PV module, (ii) 75% area of water collector covered by PV module. It is observed that case (i) has been best suited for thermal performance and case (ii) for electrical energy as well as overall exergy.

Keywords: compound parabolic concentrator, energy, photovoltaic thermal, temperature dependent electrical efficiency

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Authors: Pius Babuna

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Sustainable water use is important for the existence of the human race. Water resources carrying capacity (WRCC) measures the sustainability of water use; however, the calculation and optimization of WRCC remain challenging. This study used a mathematical model (the Logistics Growth of Water Resources -LGWR) and a linear objective function to model water sustainability. We tested the validity of the models using data from Ghana. Total freshwater resources, water withdrawal, and population data were used in MATLAB. The results show that the WRCC remains sustainable until the year 2132 ±18, when half of the total annual water resources will be used. The optimized water treatment cost suggests that Ghana currently wastes GHȼ 1115.782± 50 cedis (~$182.21± 50) per water treatment plant per month or ~ 0.67 million gallons of water in an avoidable loss. Adopting an optimized water treatment scheme and a watershed management approach will help sustain the WRCC.

Keywords: water resources carrying capacity, smart water management, optimization, sustainable water use, water withdrawal

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Chenhong Peng

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Beijing, the capital city of China, is running out of water. The water resource per capita in Beijing is only 106 cubic meter, accounts for 5% of the country’s average level and less than 2% of the world average level. The tension between water supply and demand is extremely serious. For one hand, the surface and ground water have been over-exploited during the last decades; for the other hand, water demand keep increasing as the result of population and economic growth. There is a massive gap between water supply and demand. This paper will focus on addressing the water shortage in Beijing city by increasing water use efficiency in domestic sector. First, we will emphasize on the changing structure of water supply and demand in Beijing under the economic development and restructure during the last decade. Second, by analyzing the water use efficiency in agriculture, industry and domestic sectors in Beijing, we identify that the key determinant for addressing the water crisis is to increase the water use efficiency in domestic sector. Third, this article will explore the two primary causes for the water use inefficiency in Beijing: The ineffective water pricing policy and the poor water education and communication policy. Finally, policy recommendation will offered to improve the water use efficiency in domestic sector by making and implementing an effective water pricing policy and people-engaged water education and communication policy.

Keywords: Beijing, water use efficiency, domestic sector, water pricing policy, water education policy

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Jun Ming Moey, Zhiyaun Chen, David Nicholson

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Bad actors are often hard to detect in data that imprints their behaviour patterns because they are comparatively rare events embedded in non-bad actor data. An unsupervised machine learning framework is applied here to detect bad actors in financial crime datasets that record millions of transactions undertaken by hundreds of actors (<0.01% bad). Specifically, the framework combines ‘shallow’ (PCA, Isolation Forest) and ‘deep’ (Autoencoder) methods to detect outlier patterns. Detection performance analysis for both the individual methods and their combination is reported.

Keywords: detection, machine learning, deep learning, unsupervised, outlier analysis, data science, fraud, financial crime

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Authors: Miled Amel, Ben Maad Hatem, Askri Faouzi, Ben Nasrallah Sassi

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Metal hydride water pumping system uses hydrogen as working fluid to pump water for low head and high discharge. The principal operation of this pump is based on the desorption of hydrogen at high pressure and its absorption at low pressure by a metal hydride. This work is devoted to study a concept of the dynamic behavior of a metal hydride pump using unsteady model and LaNi5 as hydriding alloy. This study shows that with MHP, it is possible to pump 340l/kg-cycle of water in 15 000s using 1 Kg of LaNi5 at a desorption temperature of 360 K, a pumping head equal to 5 m and a desorption gear ratio equal to 33. This study reveals also that the error given by the steady model, using LaNi5 is about 2%.A dimensional mathematical model and the governing equations of the pump were presented to predict the coupled heat and mass transfer within the MHP. Then, a numerical simulation is carried out to present the time evolution of the specific water discharge and to test the effect of different parameters (desorption temperature, absorption temperature, desorption gear ratio) on the performance of the water pumping system (specific water discharge, pumping efficiency and pumping time). In addition, a comparison between results obtained with steady and unsteady model is performed with different hydride mass. Finally, a geometric configuration of the reactor is simulated to optimize the pumping time.

Keywords: dynamic behavior, LaNi5, performance of water pumping system, unsteady model

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Nader Parsazadeh

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The variety of bed sediment load relationships, insufficient information and data, and the influence of river conditions make the selection of an optimum relationship for a given river extremely difficult. Hence, in order to select the best formulae, the bed load equations should be evaluated. The affecting factors need to be scrutinized, and equations should be verified. Also, re-evaluation may be needed. In this research, sediment bed load of Dez Dam at Tal-e Zang Station has been studied. After reviewing the available references, the most common formulae were selected that included Meir-Peter and Muller, using MS Excel to compute and evaluate data. Then, 52 series of already measured data at the station were re-measured, and the sediment bed load was determined. 1. The calculated bed load obtained by different equations showed a great difference with that of measured data. 2. r difference ratio from 0.5 to 2.00 was 0% for all equations except for Nilsson and Shields equations while it was 61.5 and 59.6% for Nilsson and Shields equations, respectively. 3. By reviewing results and discarding probably erroneous measured data measurements (by human or machine), one may use Nilsson Equation due to its r value higher than 1 as an effective equation for estimating bed load at Tal-e Zang Station in order to predict activities that depend upon bed sediment load estimate to be determined. Also, since only few studies have been conducted so far, these results may be of assistance to the operators and consulting companies.

Keywords: bed load, empirical relation ship, sediment, Tale Zang Station

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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Authors: Davood Yazdani Cherati, Ali Pak, Mehrdad Jafarzadeh

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This research contains the formulation of a two-dimensional analytical solution to transient heat, and moisture flow in a semi-infinite unsaturated soil environment under the influence of daily temperature changes. For this purpose, coupled energy conservation and mass fluid continuity equations governing hydrothermal behavior of unsaturated soil media are presented in terms of temperature and volumetric moisture content. In consideration of the soil environment as an infinite half-space and by linearization of the governing equations, Laplace–Fourier transformation is conducted to convert differential equations with partial derivatives (PDEs) to ordinary differential equations (ODEs). The obtained ODEs are solved, and the inverse transformations are calculated to determine the solution to the system of equations. Results indicate that heat variation induces moisture transport in both horizontal and vertical directions.

Keywords: analytical solution, heat conduction, hydrothermal analysis, laplace–fourier transformation, two-dimensional

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Authors: Tarek S. Duzan, Abdulaziz F. Ettir

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Wave velocities, Core and Log petrophysical data were collected from recently drilled four new wells scattered through-out the Dahra/Jofra (PL-5) Reservoir. The collected data were analyzed for the relationships of Wave Velocities with rock property such as Porosity, permeability and Bulk Density. Lots of Literature review reveals a number of differing results and conclusions regarding wave velocities (Compressional Waves (Vp) and Shear Waves (Vs)) versus rock petrophysical property relationships, especially in carbonate reservoirs. In this paper, we focused on the relationships between wave velocities (Vp , Vs) and the ratio Vp/Vs with rock properties for shallow marine libyan carbonate reservoir (Real Case). Upon data analysis, a relationship between petrophysical properties and wave velocities (Vp, Vs) and the ratio Vp/Vs has been found. Porosity and bulk density properties have shown exponential relationship with wave velocities, while permeability has shown a power relationship in the interested zone. It is also clear that wave velocities (Vp , Vs) seems to be a good indicator for the lithology change with true vertical depth. Therefore, it is highly recommended to use the output relationships to predict porosity, bulk density and permeability of the similar reservoir type utilizing the most recent seismic data.

Keywords: conventional core analysis (porosity, permeability bulk density) data, VS wave and P-wave velocities, shallow carbonate reservoir in D/J field

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Xiao-Dong Wang, Wei-Mon Yan

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The flow field design in the bipolar plates affects the performance of the proton exchange membrane (PEM) fuel cell. This work adopted a combined optimization procedure, including a simplified conjugate-gradient method and a completely three-dimensional, two-phase, non-isothermal fuel cell model, to look for optimal flow field design for a single serpentine fuel cell of size 9×9 mm with five channels. For the direct solution, the two-fluid method was adopted to incorporate the heat effects using energy equations for entire cells. The model assumes that the system is steady; the inlet reactants are ideal gases; the flow is laminar; and the porous layers such as the diffusion layer, catalyst layer and PEM are isotropic. The model includes continuity, momentum and species equations for gaseous species, liquid water transport equations in the channels, gas diffusion layers, and catalyst layers, water transport equation in the membrane, electron and proton transport equations. The Bulter-Volumer equation was used to describe electrochemical reactions in the catalyst layers. The cell output power density Pcell is maximized subjected to an optimal set of channel heights, H1-H5, and channel widths, W2-W5. The basic case with all channel heights and widths set at 1 mm yields a Pcell=7260 Wm-2. The optimal design displays a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5, producing a Pcell=8894 Wm-2, about 22.5% increment. The reduced channel heights of channels 2-4 significantly increase the sub-rib convection and widths for effectively removing liquid water and oxygen transport in gas diffusion layer. The final diverging channel minimizes the leakage of fuel to outlet via sub-rib convection from channel 4 to channel 5. Near-optimal design without huge loss in cell performance but is easily manufactured is tested. The use of a straight, final channel of 0.1 mm height has led to 7.37% power loss, while the design with all channel widths to be 1 mm with optimal channel heights obtained above yields only 1.68% loss of current density. The presence of a final, diverging channel has greater impact on cell performance than the fine adjustment of channel width at the simulation conditions set herein studied.

Keywords: optimization, flow field design, simplified conjugate-gradient method, serpentine flow field, sub-rib convection

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Authors: Aybike Ayfer Karadağ

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Today, the amount of water available is decreasing day by day due to global warming, environmental problems and population increase. To protect water resources, it is necessary to take a lot of measures from the global scale to the local scale. Some of these measures are related to spatial planning studies. In this study, the impact of water process analysis was assessed in the development of spatial planning for water conservation. The study was conducted in the Kovada sub-watershed (Isparta, Turkey). By means of water process analysis, the way to reach underground water of surface water in the study area is mapped. In this context, plant cover, soil and rock permeability were evaluated holistically with geographic information systems technologies. Then, on the map, water permeability is classified and this is spatially expressed. The findings show that the permeability of the water is different in the study case. As a result, the water permeability map needs to be included in the planning for water conservation planning.

Keywords: water, conservation, spatial planning, water process analysis

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Olumuyiwa Olusola Falowo

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One of the objectives of the Millennium Development Goals is to have sustainable access to safe drinking water and basic sanitation. In line with this objective, an assessment of groundwater quality was carried out in Odigbo Local Government Area of Ondo State in November – February, 2019 to assess the drinking, domestic and irrigation uses of the water. Samples from 30 randomly selected ground water sources; 16 shallow wells and 14 from boreholes and analyzed using American Public Health Association method for the examination of water and wastewater. Water quality index calculation, and diagrams such as Piper diagram, Gibbs diagram and Wilcox diagram have been used to assess the groundwater in conjunction with irrigation indices such as % sodium, sodium absorption ratio, permeability index, magnesium ratio, Kelly ratio, and electrical conductivity. In addition statistical Principal component analysis were used to determine the homogeneity and source(s) influencing the chemistry of the groundwater. The results show that all the parameters are within the permissible limit of World Health Organization. The physico-chemical analysis of groundwater samples indicates that the dominant major cations are in decreasing order of Na+, Ca2+, Mg2+, K+ and the dominant anions are HCO-3, Cl-, SO-24, NO-3. The values of water quality index varies suggest a Good water (WQI of 50-75) accounts for 70% of the study area. The dominant groundwater facies revealed in this study are the non-carbonate alkali (primary salinity) exceeds 50% (zone 7); and transition zone with no one cation-anion pair exceeds 50% (zone 9), while evaporation; rock–water interaction, and precipitation; and silicate weathering process are the dominant processes in the hydrogeochemical evolution of the groundwater. The study indicates that waters were found within the permissible limits of irrigation indices adopted, and plot on excellent category on Wilcox plot. In conclusion, the water in the study area are good/suitable for drinking, domestic and irrigation purposes with low equivalent salinity concentrate and moderate electrical conductivity.

Keywords: equivalent salinity concentration, groundwater quality, hydrochemical facies, principal component analysis, water-rock interaction

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Authors: A. Elsariti, T. Evans

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The propagation mechanisms in the trabecular bone are poorly understood and have been the subject of extended debate; also, steel wool has been evaluated as a potential bone mimic, Its advantages are ready availability, low cost and a wide range of sizes. In this study, both distilled and tap water were used to estimate the ultrasonic attenuation in coarse steel wool. It is clear from the results that the attenuation of coarse steel wool increased as the distance between the transducers decreased, and it is higher in tap water than distilled water. At 9cm distance between the transducers the attenuation was approximately 0.97 and 4.7 dB in distilled and tap water respectively. While it is 6.97 and 12.2 dB in distilled and tap water respectively at distance 4cm. This change in the attenuation between both distilled and tap water is probably due to gas bubbles in the tap water.

Keywords: bone mimic, porosity, tap water, distilled water, ultrasonic attenuation

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Authors: K. Jagannath, Akhilesh Kotian, S. S. Sharma, Achutha Kini U., P. R. Prabhu

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Boiling process is characterized by the rapid formation of vapour bubbles at the solid–liquid interface (nucleate boiling) with pre-existing vapour or gas pockets. Computational fluid dynamics (CFD) is an important tool to study bubble dynamics. In the present study, CFD simulation has been carried out to determine the bubble detachment diameter and its terminal velocity. Volume of fluid method is used to model the bubble and the surrounding by solving single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. In the simulation, bubble is generated by allowing water-vapour to enter a cylinder filled with liquid water through an inlet at the bottom. After the bubble is fully formed, the bubble detaches from the surface and rises up during which the bubble accelerates due to the net balance between buoyancy force and viscous drag. Finally when these forces exactly balance each other, it attains a constant terminal velocity. The bubble detachment diameter and the terminal velocity of the bubble are captured by the monitor function provided in FLUENT. The detachment diameter and the terminal velocity obtained is compared with the established results based on the shape of the bubble. A good agreement is obtained between the results obtained from simulation and the equations in comparison with the established results.

Keywords: bubble growth, computational fluid dynamics, detachment diameter, terminal velocity

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Authors: H. Bayat, M. Majidi, M. Bolhasani, A. Karbalaie Alilou, A. Mirabdolah Lavasani

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Unsteady flow and heat transfer from a circular cylinder in cross-flow is studied numerically. The governing equations are solved by using finite volume method. Reynolds number varies in range of 50 to 200, in this range flow is considered to be laminar and unsteady. Al2O3 nanoparticle with volume fraction in range of 5% to 20% is added to pure water. Effects of adding nanoparticle to pure water on lift and drag coefficient and Nusselt number is presented. Addition of Al2O3 has inconsiderable effect on the value of drags and lift coefficient. However, it has significant effect on heat transfer; results show that heat transfer of Al2O3 nanofluid is about 9% to 36% higher than pure water.

Keywords: nanofluid, heat transfer, unsteady flow, forced convection, cross-flow

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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