The existing **drawdown** solutions for radial **two**-**zone** con- fined **aquifers** of infinite extent under **constant**-flux **pumping** were all developed **in** Laplace domain except the one given by Yeh et al. (2003) which was a time domain **solution**. Yeh et al.’s (2003) **solution** is **in** terms of an improper integral integrating from zero to infinity and its integrand comprises a singularity at the origin. **In** addition, the integrand is an oscillatory function with many product terms of the Bessel functions of the first and second kinds of zero and first or- ders. The numerical calculation of their **solution** is therefore time-consuming and very difficult to achieve accurate results. The objective of this note is to develop an analytical so- lution from a mathematical model similar to that of Yeh et al. (2003), except that the aquifer is of horizontally **finite** ex- tent. The **solution** of the model is also obtained by applying the methods of Laplace transforms and Bromwich contour integral. The integration of the contour integral **in** Yeh et al. (2003) results **in** a single branch point with no singularity at zero of the complex variable. Thus, a branch cut along the negative real axis of the contour should be chosen and thus a closed contour is produced. Such a procedure finally results **in** a complicated **solution** presented **in** Yeh et al. (2003). On the other hand, the integration of the contour integral arisen from the Laplace domain **solution** **in** our model has a simple pole at the origin and **finite** number of poles at other loca- tions. The residue theorem is therefore adapted to obtain the time domain results for the skin **zone** and formation **zone**. These **two** results are **in** terms of a logarithmic function plus a summation term, rather than an integral, with Bessel func- tions of the first and second kinds of orders zero and first.

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our model has a simple pole at the origin and **finite** number of poles at other locations. The residue theorem is therefore adapted to obtain the time domain solutions for the skin **zone** or formation **zone**. These **two** solutions are **in** terms of a logarithmic function plus a summation term, rather than an integral, with the Bessel functions of the first and second kinds of orders zero and first. The solutions are much easier to calculate

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At the present, a time-domain analytical **solution** of **drawdown** for flow induced by the CFP at a **finite**-radius partially penetrating well **in** a **two**-**zone** **confined** aquifer has not been developed. The Laplace-domain result of the above-mentioned problem was presented by Chiu et al. (2007) with resort to a numerical inversion such as the Crump method. The application of their **solution** may therefore be inconvenient for those who

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Temperature decay **in** an aluminium plate is observed using Galerkin **finite** element method for 2D **transient** heat conduction equation. Taking ∆t of 0.001 hr , temperature variation is studied using unconditionally stable first order and second order accurate schemes - backward Euler and modified Crank- Nicholson respectively. A comparative study has been made taking different combinations of meshes and numerical schemes. Desired calculations are made taking into account the properties of aluminium plate.

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Abstract - **In** this Paper , a mathematical **solution** by using numerical technique to stochastic partial differential equation **in** reliability theory is being explained. This method is based upon **finite** difference methods to resolve and emerge the **transient** state of Markovian system **in** reliability theory .**In** reliability engineering the repair rates and failure rates are difficult to pursue on the basis of different parameters and demand **in** reliability theory .We use **finite** difference method for understand and get better valuation as per data prediction. The method Lagrange’s formula to interpolate the missing value of repair rates of the system which is required for analysis on the basis of different analytical techniques and computations. Results thus obtained are found to the efficient for studying the **transient** state behavior of the system.

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Computational procedure: The system of Equations (1)-(13) was solved for predicting temperature time variations during cooling of solids with pure convection heat transfer from the surface of the solids. The coordinate system for the fish package is shown **in** Fig. 3 and the mesh of time and space intervals during the **finite** difference solutions are **in** Fig. 4. **In** order to establish a **finite** difference scheme parameters which are accurate, reliable and efficient for heat transfer analyses during precooling of an infinite slab shaped body, a sample set of temperature- time data was chosen from the experimental work with relevant calculated thermo physical properties of Pangasius Sutchi fish as listed **in** Table 1. Calculations have been done for air-cooling with only heat transfer boundary condition.

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Abstract — The **Finite**-Difference Time-Domain (FDTD) method was applied **in** order to analyze the **transient** responses of geoelectrical soundings that use circular electric dipole (CED) as source over stratified formations. The model was developed **in** cylindrical coordinates and a perfectly matched layer (PML) was incorporated to the domain to absorb wave reflections at computational grid boundaries. Numeric results are validated with analytic solutions. Comparisons between the **transient** response of **two** different type of soundings are performed and results indicate that the **transient** response of soundings that excite purely TM mode are more sensitive to the variation of electrical characteristics of the medium.

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It is evident that the silicone oil based sample is the one with the best results, eliminating foam **in** less than 5 minutes even with three drops of FA. Although the impeccable results, this type of product is not food approved and therefore is not an option for the current consumer. Nevertheless, it is a very efficient antifoaming agent, and it can be used **in** other industries. Even though emulsion breaks after a few weeks, this problem can be solved by altering the formulation/its composition.

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IRF metrics and evaluation with PCA and cluster analysis indicate that there is a range of IRF characteristics describing different sites within a karst system. The IRF shape is a result of the aquifer’s pore geometry and connectivity, which is spatially heteroge- neous **in** karst **aquifers**, and thus similar site types do not necessarily display similar IRFs. Knowing which metrics correspond to the different principle components assists

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The confluence of boundary condition can cause singularities **in** the free surface displacement and velocities, as anticipated by the linear theory. These singularities appear to be avoided **in** the real fluid by the formation of jets which quickly break up into sprays under the action of surface tension. Therefore, for including nonlinearity effect **in** the water impact problem of a circular cylinder, a commercial VOF solver, i.e. FLOW-3D (FLOW-3D Manual, 2009), is employed. The FLOW-3D code applies the FVM (**finite** volume method) **in** combination with the volume of fluid **solution** for free surface flow. VOF is an excellent tool for the simulation of **two** phase flow which includes water and air **in** this study. **In** this numerical scheme, an additional transport equation is solved for the volume percentage of air **in** each cell. More details of FVM and VOF **solution** can be found **in** many reference books and articles (Versteeg and Malalasekera (1995), Jasak (1996), Kleefsman et al. (2005), Rhee et al. (2005), Sicilian (1990), Hirt (2004), and Barkhudarov (2004)).

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This paper makes use of the Galerkin FEM to solve the LWR model with **constant** speed. The road is divided into a number of road segments (elements) using the Galerkin FEM. Each element consists of **two** nodes. Each node has one degree of freedom (d.o.f.), namely the traffic density. The FEM provides a **solution** for the degrees of freedom, i.e. traffic densities of each node. The resulting simultaneous equations are solved at different time steps using the Euler backward time-integration algorithm.

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The model contains additional features compared with previous reported models, while retaining simplicity. The detailed consideration of an arc region coupled to the sur- rounding gas dynamics allows determining voltage drops and consequent delivered power with less assumptions than those **in** Refs.[2, 3], and at the same time reduces the set of parameters needed to determine the **solution**. Compa- red with the model **in** Ref.[4], it removes the conditions of isothermal evolution of the gas and of equal velocities of arc and gas flows, which are not well verified **in** the simulations **in** of Refs.[5, 6] as deduced from the temperature and Mach number profiles **in** the nozzle region. Moreover, Steenbeck’s principle is not required to determine the initial arc radius, as was done **in** Ref.[4].

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properties after specific treatment (e.g. toughening). Taking proper decision requires multifaceted analysis of the data on materials and technical knowledge. The assistance that cannot be overestimated **in** this situation are computer systems for decision support **in** specific areas. This study is related with one of the components of a hybrid decision support system CAPCAST, implemented under a research project conducted by WIMIIP AGH. It is a model of knowledge representation about materials **in** the form of a relational database, designed to allow the trans- formation of its records into a rule-based knowledge base.

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ABSTRACT: **In** many studies worldwide the use of treated sewage effluents (TSE) as water and nutrient sources **in** agricultural irrigation have been introduced as a viable alternative for wastewater destination **in** the environment. Considering agronomic and environmental aspects the objectives of this review were: (i) to present an overview of TSE irrigation on different agro-systems (annual crops, orchards, forests and forages); and (ii) to show the principal changes on chemical, physical and microbiological soil characteristics after TSE application. Various studies have revealed that the nutrient supply only by TSE irrigation was not sufficient to meet plant nutrient requirements resulting **in** yield decreases. The problem could be solved by an adapted effluent/fertilizer management. Moreover, TSE could generally substitute efficiently freshwater for irrigation. Regarding soil quality conditions, TSE irrigation affected mainly: (i) total soil carbon and nitrogen, and mineral nitrogen **in** soil **solution**; (ii) microbial activity, composition of microbial communities and their function; (iii) exchangeable calcium and magnesium; (iv) salinity, sodicity, clay dispersion and hydraulic conductivity. Other soil parameters considered **in** this review (e.g. heavy metals) did not present significant changes over short and medium terms. Due to the often observed accumulation of sodium and nitrogen losses (leaching, volatilization and denitrification) after TSE irrigation, the monitoring of these components is of crucial importance for a sustainable use. Finally, further studies on the technical-economical-environmental viability of TSE irrigation are required to establish reliable recommendations for TSE use particularly **in** Brazilian agro-systems.

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Numerical solutions for heat transfer problems are usually obtained using an algorithm implemented **in** a sequential programming language. Despite a powerful set of tools that can be useful **in** many heat transfer problems, electronic spreadsheets have not been used **in** these sorts of problems, except for less complex issues. That is partially due to the dificulty **in** simulate loop iterations **in** electronic spreadsheets. **In** the present work a relatively complex phase change **transient** heat transfer problem is solved by coupling the spreadsheet iteration facility with the time increase required by the problem’s physics. Besides, the energy conservation equation is written based on an enthalpy formulation and the **finite** volume method is used for the discretization of the corresponding differential equation.

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When exposed to high temperatures, such as **in** a fire situation, the physical and resistance characteristics of the materials employed **in** the structure deteriorate as the temperature increases. This fact promotes a considerable loss **in** the bearing capacity and stiffness of the structural system. The verification of a structure exposed to fire depends primarily and principally on the thermal analysis of the cross section of the structural element. This analysis permits determination of the temperature variation or temperature range **in** the element from the boundary conditions provided by the fire model adopted. As such, this study had the objective of performing a thermal analysis **in** a **transient** regime by means of a **finite** element method on steel-concrete composite cross sections that are employed **in** civil construction through use of the Computational Sys- tem for Advanced Structural Analysis/Fire Analysis (CS-ASA/FA). **Two** cross sections are analyzed and the results obtained were satisfactory. **In** addition, different iterative **solution** processes were adopted **in** the analysis. Parametric studies were also performed related to the mesh variation of the **finite** elements and time increase. From the results, it was possible to conclude that CS-ASA/FA can supply the necessary information when a thermo-structural analysis is performed for the evaluation of strength and stiffness losses of the structural material when exposed to fire.

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Richardson with SOR, Chebyshev with Gauss-Seidel and Chebyshev with SOR. The iterative schemes were applied to Banded system, Tridiagonal systems and SPD system with varying dimensions. The Krylov subspace methods: GMRES, QMR, MINRES and BiCGSTAB converged to an approximate solutions less than or equal to the dimension of the coefficient matrix for each identified systems of linear equations. Again, Chebyshev and Richardson acceleration methods were the fastest convergence methods **in** terms of number of iterations. Again, Residual smoothing and the accelerated gradient schemes should be used for large and sparse systems of linear equations. The acceleration processes were very efficient when solving large and sparse systems of linear equation and therefore useful especially for systems resulting from the **solution** of partial differential equations.

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se of excreta on arable land secures valuable fertilisers for crop production and limits the negative impact on water bodies [29,13, 6]. The environmental impact of excreta disposal usage would always be less than that of the direct use of water bodies as the primary recipient of excreta and greywater [29]. To preserve its fertility, arable land needs to be compensated for the plant nutrients removed. Today, chemical fertilisers produced by fossil resources do mostly this. **In** the long-term perspective the world cannot securely rely on fossil resources, as the recycling of plant nutrients. Another way of compensating soil fertility is from human excreta’s direct application to arable land [18]. Urine has been used as a valuable plant food for centuries **in** many parts of the world, particularly **in** the Far East. It is surprising, therefore, that nearly all the urine produced **in** the West and **in** Africa goes to waste and is lost to agriculture [16]. Urine is known to contribute the major proportion of the nutrients (N, P and K) **in** domestic wastewater as compared to faeces which even poses a greater health risk when used [9]. Thus, separating the urine which accounts for about 1% of the total wastewater flow, and using it as fertilizer makes it possible to utilize most of the nutrient content of wastewater [10]. Urine is usually collected **in** a source separating toilet [20], and nitrogen

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