Search results for: Flow shop scheduling

Authors: Hesham Abdel-Khalek, Sherif M. Hafez, Abdel-Hamid M. el-Lakany, Yasser Abuel-Magd

Abstract:

Investment in a constructed facility represents a cost in the short term that returns benefits only over the long term use of the facility. Thus, the costs occur earlier than the benefits, and the owners of facilities must obtain the capital resources to finance the costs of construction. A project cannot proceed without an adequate financing, and the cost of providing an adequate financing can be quite large. For these reasons, the attention to the project finance is an important aspect of project management. Finance is also a concern to the other organizations involved in a project such as the general contractor and material suppliers. Unless an owner immediately and completely covers the costs incurred by each participant, these organizations face financing problems of their own. At a more general level, the project finance is the only one aspect of the general problem of corporate finance. If numerous projects are considered and financed together, then the net cash flow requirements constitute the corporate financing problem for capital investment. Whether project finance is performed at the project or at the corporate level does not alter the basic financing problem .In this paper, we will first consider facility financing from the owner's perspective, with due consideration for its interaction with other organizations involved in a project. Later, we discuss the problems of construction financing which are crucial to the profitability and solvency of construction contractors. The objective of this paper is to present the steps utilized to determine the best combination of minimum project financing. The proposed model considers financing; schedule and maximum net area .The proposed model is called Project Financing and Schedule Integration using Genetic Algorithms "PFSIGA". This model intended to determine more steps (maximum net area) for any project with a subproject. An illustrative example will demonstrate the feature of this technique. The model verification and testing are put into consideration.

Keywords: Project Management, Large-scale ConstructionProjects, Cash flow, Interest, Investment, Loan, Optimization, Scheduling, Financing and Genetic Algorithms.

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Authors: M. Othman, N. Bhuiyan, G. J. Gouw

Abstract:

In today-s competitive market, most companies develop manufacturing systems that can help in cost reduction and maximum quality. Human issues are an important part of manufacturing systems, yet most companies ignore their effects on production performance. This paper aims to developing an integrated workforce planning system that incorporates the human being. Therefore, a multi-objective mixed integer nonlinear programming model is developed to determine the amount of hiring, firing, training, overtime for each worker type. This paper considers a workforce planning model including human aspects such as skills, training, workers- personalities, capacity, motivation, and learning rates. This model helps to minimize the hiring, firing, training and overtime costs, and maximize the workers- performance. The results indicate that the workers- differences should be considered in workforce scheduling to generate realistic plans with minimum costs. This paper also investigates the effects of human learning rates on the performance of the production systems.

Keywords: Human Factors, Learning Curves, Workers' Differences, Workforce Scheduling

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Authors: Afshin J. Ghajar, Swanand M. Bhagwat

Abstract:

The main purpose of this work is to experimentally investigate the effect of pipe orientation on two phase flow phenomenon. Flow pattern, void fraction and two phase pressure drop is measured in a polycarbonate pipe with an inside diameter of 12.7mm for inclination angles ranging from -20^o to +20^o using air-water fluid combination. The experimental data covers all flow patterns and the entire range of void fraction typically observed in two phase flow. The effect of pipe orientation on void fraction and two phase pressure drop is justified with reference to the change in flow structure and two phase flow behavior. In addition to this, the top performing void fraction and two phase pressure drop correlations available in the literature are presented and their performance is assessed against the experimental data in the present study and that available in the literature.

Keywords: Flow patterns, inclined two phase flow, pressure drop, void fraction.

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Authors: Y. K. Lin, H. T. Hsieh, F. Y. Hsieh

Abstract:

Total weighted tardiness is a measure of customer satisfaction. Minimizing it represents satisfying the general requirement of on-time delivery. In this research, we consider an ant colony optimization (ACO) algorithm to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense. Computational results show that the proposed ACO algorithm is giving promising results compared to other existing algorithms.

Keywords: ant colony optimization, total weighted tardiness, unrelated parallel machines.

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

Abstract:

Hydrocyclones flow field study is conducted by performing a parametric study. Effect of cone angle on deoiling hydrocyclones flow behaviour is studied in this research. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Because of anisotropic behaviour of flow inside hydrocyclones LES is a suitable method to predict the flow field since it resolves large scales and model isotropic small scales. Large eddy simulation is used to predict the flow behavior of three different cone angles. Differences in tangential velocity and pressure distribution are reported in some figures.

Keywords: Deoiling hydrocyclones, Flow field, Hydrocyclone cone angle, Large Eddy Simulation, Pressure distribution

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Authors: Indar Chaerah Gunadin, Adi Soeprijanto, Ontoseno Penangsang

Abstract:

This paper will discuss about an active power generator scheduling method in order to increase the limit level of steady state systems. Some power generator optimization methods such as Langrange, PLN (Indonesian electricity company) Operation, and the proposed Z-Thevenin-based method will be studied and compared in respect of their steady state aspects. A method proposed in this paper is built upon the thevenin equivalent impedance values between each load respected to each generator. The steady state stability index obtained with the REI DIMO method. This research will review the 500kV-Jawa-Bali interconnection system. The simulation results show that the proposed method has the highest limit level of steady state stability compared to other optimization techniques such as Lagrange, and PLN operation. Thus, the proposed method can be used to create the steady state stability limit of the system especially in the peak load condition.

Keywords: generation scheduling, steady-state stability limit, REI Dimo, margin stability

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Authors: A. A. Shafie, Fadhlan Hafiz, M. H. Ali

Abstract:

Motion detection is very important in image processing. One way of detecting motion is using optical flow. Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. The method used for finding the optical flow in this project is assuming that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. This technique is later used in developing software for motion detection which has the capability to carry out four types of motion detection. The motion detection software presented in this project also can highlight motion region, count motion level as well as counting object numbers. Many objects such as vehicles and human from video streams can be recognized by applying optical flow technique.

Keywords: Background modeling, Motion detection, Optical flow, Velocity smoothness constant, motion trajectories.

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Authors: Morteza Mirhosseini, Amir B. Khoshnevis

Abstract:

The boundary layer separation and new active flow control of a NACA 0025 airfoil were studied experimentally. This new flow control is sometimes known as a co-flow jet (cfj) airfoil. This paper presents the fluctuating velocity in a wall jet over the co-flow jet airfoil subjected to an adverse pressure gradient and a curved surface. In these results, the fluctuating velocity at the inner part increasing by increased the angle of attack up to 12^o and this has due to the jet energized, while the angle of attack 20^o has different. The airfoil cord based Reynolds number has 10⁵.

Keywords: Adverse pressure gradient, fluctuating velocity, wall jet, co-flow jet airfoil.

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Authors: P. Sawitri, S. Cdr. Sittha, T. Kritsana

Abstract:

Flow forming is widely used in many industries, especially in defence technology industries. Pressure vessels requirements are high precision, light weight, seamless and optimum strength. For large pressure vessels, flow forming by 3 rollers machine were used. In case of long range rocket motor case flow forming and welding of pressure vessels have been used for manufacturing. Due to complication of welding process, researchers had developed 4 meters length pressure vessels without weldment by 4 rollers flow forming machine. Design and preparation of preform work pieces are performed. The optimization of flow forming parameter such as feed rate, spindle speed and depth of cut will be discussed. The experimental result shown relation of flow forming parameters to quality of flow formed tube and prototype pressure vessels have been made.

Keywords: Flow forming, Pressure vessel, four rollers, feed rate, spindle speed, cold work.

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Authors: M. Sumida

Abstract:

The flow of suspensions of wood pulp fibers in circular pipes has been investigated experimentally. The flow characteristics of pulp suspensions are discussed with regard to five flow regimes designated by the author. In particular, the effects of the shear stress at the pipe wall on the disruption and dispersion of networks of pulp fibers are examined. The values of the disruptive and dispersive shear stresses are formulated as simple expressions depending on only the fiber concentration. Furthermore, the flow properties of the suspensions are described using the yield shear stress.

Keywords: Fiber Concentration, Flow Properties, Pulp Suspension, Yield Shear Stress.

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Authors: S.A. Alqallaf, S.A. Al-Mawsawi, A. Haider

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In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, Decoupled model, Load flow.

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Authors: Mohammad Taghi Shervani Tabar, Zahra Poursharifi

Abstract:

The interaction of the blade tip with the casing boundary layer and the leakage flow may lead to a kind of cavitation namely tip vortex cavitation. In this study, the onset of tip vortex cavitation was experimentally investigated in an axial flow pump. For a constant speed and a fixed angle of attack and by changing the flow rate, the pump head, input power, output power and efficiency were calculated and the pump characteristic curves were obtained. The cavitation phenomenon was observed with a camera and a stroboscope. Finally, the critical flow region, which tip vortex cavitation might have occurred, was identified. The results show that just by adjusting the flow rate, out of the specified region, the possibility of occurring tip vortex cavitation, decreases to a great extent.

Keywords: Axial flow pump, Gap cavitation, Leakage vortex, Tip vortex cavitation.

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Authors: Hideki Yoshikawa, Masahiro Kaminaga, Arimitsu Shikoda, Toshinori Suzuki

Abstract:

Round addition differential fault analysis using operation skipping for lightweight block ciphers with on-the-fly key scheduling is presented. For 64-bit KLEIN, it is shown that only a pair of correct and faulty ciphertexts can be used to derive the secret master key. For PRESENT, one correct ciphertext and two faulty ciphertexts are required to reconstruct the secret key. Furthermore, secret key extraction is demonstrated for the LBlock Feistel-type lightweight block cipher.

Keywords: Differential Fault Analysis (DFA), round addition, block cipher, on-the-fly key schedule.

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

Abstract:

The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability.

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Authors: Irina Eglite, Andrei A. Kolyshkin

Abstract:

The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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Authors: V. K. Bansal

Abstract:

Geographic Information System (GIS) is a computerbased tool used extensively to solve various engineering problems related to spatial data. In spite of growing popularity of GIS, its complete potential to construction industry has not been realized. In this paper, the summary of up-to-date work on spatial applications of GIS technologies in construction industry is presented. GIS technologies have the potential to solve space related problems of construction industry involving complex visualization, integration of information, route planning, E-commerce, cost estimation, etc. GISbased methodology to handle time and space issues of construction projects scheduling is developed and discussed in this paper.

Keywords: Construction, GIS in construction, Scheduling, Project Management.

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Authors: Václav Dvořák, Petra Dančová

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The article deals with pneumatic and hot wire anemometry measurement on subsonic axi-symmetric air ejector. Performances of the ejector with and without pulsations of primary flow are compared, measuring of characteristic pressures and mass flow rates are performed and ejector efficiency is evaluated. The pulsations of primary flow are produced by a synthetic jet generator, which is placed in the supply line of the primary flow just in front of the primary nozzle. The aim of the pulsation is to intensify the mixing process. In the article we present: Pressure measuring of pulsation on the mixing chamber wall, behind the mixing chamber and behind the diffuser measured by fast pressure transducers and results of hot wire anemometry measurement. It was found out that using of primary flow pulsations yields higher back pressure behind the ejector and higher efficiency. The processes in this ejector and influences of primary flow pulsations on the mixing processes are described.

Keywords: Air ejector, pulsation flow

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Authors: Sangsuree Vasupongayya

Abstract:

To provide a better understanding of fair share policies supported by current production schedulers and their impact on scheduling performance, A relative fair share policy supported in four well-known production job schedulers is evaluated in this study. The experimental results show that fair share indeed reduces heavy-demand users from dominating the system resources. However, the detailed per-user performance analysis show that some types of users may suffer unfairness under fair share, possibly due to priority mechanisms used by the current production schedulers. These users typically are not heavy-demands users but they have mixture of jobs that do not spread out.

Keywords: Fair share, Parallel job scheduler, Backfill, Measures

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Authors: Y. Galerkin, O. Solovieva

Abstract:

Parameters of flow are calculated in vaneless diffusers with relative width 0,014–0,10. Inlet angles of flow and similarity criteria were varied. There is information on flow separation, boundary layer development, configuration of streamlines. Polytrophic efficiency, loss coefficient and recovery coefficient are used to compare effectiveness of diffusers. The sample of optimization of narrow diffuser with conical walls is presented. Three wide diffusers with narrowing walls are compared. The work is made in the R&D laboratory “Gas dynamics of turbo machines” of the TU SPb.

Keywords: Vaneless diffuser, relative width, flow angle, flow separation, loss coefficient, similarity criteria.

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Authors: László Lengyel, Tihamér Levendovszky, Hassan Charaf

Abstract:

This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations out of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This work discusses the termination properties of VCFL and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual Model Transformation, OCL, Termination Properties, UML.

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Authors: Imen Sfaihi, Noureddine Hamdi

Abstract:

In this paper, we investigate the study of techniques for scheduling users for resource allocation in the case of multiple input and multiple output (MIMO) packet transmission systems. In these systems, transmit antennas are assigned to one user or dynamically to different users using spatial multiplexing. The allocation of all transmit antennas to one user cannot take full advantages of multi-user diversity. Therefore, we developed the case when resources are allocated dynamically. At each time slot users have to feed back their channel information on an uplink feedback channel. Channel information considered available in the schedulers is the zero forcing (ZF) post detection signal to interference plus noise ratio. Our analysis study concerns the round robin and the opportunistic schemes. In this paper, we present an overview and a complete capacity analysis of these schemes. The main results in our study are to give an analytical form of system capacity using the ZF receiver at the user terminal. Simulations have been carried out to validate all proposed analytical solutions and to compare the performance of these schemes.

Keywords: MIMO, scheduling, ZF receiver, spatial multiplexing, round robin scheduling, opportunistic.

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Authors: Xiaoming Jiang, Jinqiao Shi, Qingfeng Tan, Wentao Zhang, Xuebin Wang, Muqian Chen

Abstract:

Nowadays, big companies such as Google, Microsoft, which have adequate proxy servers, have perfectly implemented their web crawlers for a certain website in parallel. But due to lack of expensive proxy servers, it is still a puzzle for researchers to crawl large amounts of information from a single website in parallel. In this case, it is a good choice for researchers to use free public proxy servers which are crawled from the Internet. In order to improve efficiency of web crawler, the following two issues should be considered primarily: (1) Tasks may fail owing to the instability of free proxy servers; (2) A proxy server will be blocked if it visits a single website frequently. In this paper, we propose Proxisch, an optimization approach of large-scale unstable proxy servers scheduling, which allow anyone with extremely low cost to run a web crawler efficiently. Proxisch is designed to work efficiently by making maximum use of reliable proxy servers. To solve second problem, it establishes a frequency control mechanism which can ensure the visiting frequency of any chosen proxy server below the website’s limit. The results show that our approach performs better than the other scheduling algorithms.

Keywords: Proxy server, priority queue, optimization approach, distributed web crawling.

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Authors: A. Moussouni, L. Mouzai, M. Bouhadef

Abstract:

The purpose of this investigation is to relate the rain power and the overland flow power to soil erodibility to assess the effects of both parameters on soil erosion using variable rainfall intensity on remoulded agricultural soil. Six rainfall intensities were used to simulate the natural rainfall and are as follows: 12.4mm/h, 20.3mm/h, 28.6mm/h, 52mm/h, 73.5mm/h and 103mm/h. The results have shown that the relationship between overland flow power and rain power is best represented by a linear function (R2=0.99). As regards the relationships between soil erodibility factor and rain and overland flow powers, the evolution of both parameters with the erodibility factor follow a polynomial function with high coefficient of determination. From their coefficients of determination (R2=0.95) for rain power and (R2=0.96) for overland flow power, we can conclude that the flow has more power to detach particles than rain. This could be explained by the fact that the presence of particles, already detached by rain and transported by the flow, give the flow more weight and then contribute to the detachment of particles by collision.

Keywords: Laboratory experiments, soil erosion, flow power, erodibility, rainfall intensity.

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Authors: A. Esmael, A. El Shrif

Abstract:

In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

Keywords: Hydrodynamic Instability, Modified Taylor-Couette Flow, Turbulence, Taylor vortices.

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Authors: Liu-Chao Qiu

Abstract:

The damage caused by surge waves generated in water bodies by flow-like landslides can be very high in terms of human lives and economic losses. The complicated phenomena occurred in this highly unsteady process are difficult to model because three interacting phases: air, water and sediment are involved. The problem therefore is challenging since the effects of non-Newtonian fluid describing the rheology of the flow-like landslides, multi-phase flow and free surface have to be included in the simulation. In this work, the commercial computational fluid dynamics (CFD) package FLUENT is used to model the surge waves due to flow-like landslides. The comparison between the numerical results and experimental data reported in the literature confirms the accuracy of the method.

Keywords: Flow-like landslide, surge wave, VOF, non-Newtonian fluids, multi-phase flows, free surface flow.

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Authors: Suwimon Saneewong Na Ayuttaya, Chainarong Chaktranond, Phadungsak Rattanadecho

Abstract:

This study numerically investigates the effects of Electrohydrodynamic on flow patterns and heat transfer enhancement within a cavity which is on the lower wall of channel. In this simulation, effects of using ground wire and ground plate on the flow patterns are compared. Moreover, the positions of electrode wire respecting with ground are tested in the range of angles θ = 0 - 180^o. High electrical voltage exposes to air is 20 kV. Bulk mean velocity and temperature of inlet air are controlled at 0.1 m/s and 60 ^OC, respectively. The result shows when electric field is applied, swirling flow is appeared in the channel. In addition, swirling flow patterns in the main flow of using ground plate are widely spreader than that of using ground wire. Moreover, direction of swirling flow also affects the flow pattern and heat transfer in a cavity. These cause the using ground wire to give the maximum temperature and heat transfer higher than using ground plate. Furthermore, when the angle is at θ = 60^o, high shear flow effect is obtained. This results show high strength of swirling flow and effective heat transfer enhancement.

Keywords: Swirling Flow, Heat Transfer, Electrohydrodynamic, Numerical Analysis.

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Authors: P. Keerthika, P. Suresh

Abstract:

Grid is an environment with millions of resources which are dynamic and heterogeneous in nature. A computational grid is one in which the resources are computing nodes and is meant for applications that involves larger computations. A scheduling algorithm is said to be efficient if and only if it performs better resource allocation even in case of resource failure. Resource allocation is a tedious issue since it has to consider several requirements such as system load, processing cost and time, user’s deadline and resource failure. This work attempts in designing a resource allocation algorithm which is cost-effective and also targets at load balancing, fault tolerance and user satisfaction by considering the above requirements. The proposed Budget Constrained Load Balancing Fault Tolerant algorithm with user satisfaction (BLBFT) reduces the schedule makespan, schedule cost and task failure rate and improves resource utilization. Evaluation of the proposed BLBFT algorithm is done using Gridsim toolkit and the results are compared with the algorithms which separately concentrates on all these factors. The comparison results ensure that the proposed algorithm works better than its counterparts.

Keywords: Grid Scheduling, Load Balancing, fault tolerance, makespan, cost, resource utilization.

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Authors: V.D. Hatamipour, M.A. Akhavan-Behabadi

Abstract:

Evaporator is an important and widely used heat exchanger in air conditioning and refrigeration industries. Different methods have been used by investigators to increase the heat transfer rates in evaporators. One of the passive techniques to enhance heat transfer coefficient is the application of microfin tubes. The mechanism of heat transfer augmentation in microfin tubes is dependent on the flow regime of two-phase flow. Therefore many investigations of the flow patterns for in-tube evaporation have been reported in literatures. The gravitational force, surface tension and the vapor-liquid interfacial shear stress are known as three dominant factors controlling the vapor and liquid distribution inside the tube. A review of the existing literature reveals that the previous investigations were concerned with the two-phase flow pattern for flow boiling in horizontal tubes [12], [9]. Therefore, the objective of the present investigation is to obtain information about the two-phase flow patterns for evaporation of R-134a inside horizontal smooth and microfin tubes. Also Investigation of heat transfer during flow boiling of R-134a inside horizontal microfin and smooth tube have been carried out experimentally The heat transfer coefficients for annular flow in the smooth tube is shown to agree well with Gungor and Winterton-s correlation [4]. All the flow patterns occurred in the test can be divided into three dominant regimes, i.e., stratified-wavy flow, wavy-annular flow and annular flow. Experimental data are plotted in two kinds of flow maps, i.e., Weber number for the vapor versus weber number for the liquid flow map and mass flux versus vapor quality flow map. The transition from wavy-annular flow to annular or stratified-wavy flow is identified in the flow maps.

Keywords: Flow boiling, Flow pattern, Heat transfer, Horizontal, Smooth tube, Microfin tube.

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Authors: U. P. L. Wijayarathne, K. C. Wasalathilake

Abstract:

This work presents the modelling and simulation of saponification of ethyl acetate in the presence of sodium hydroxide in a plug flow reactor using Aspen Plus simulation software. Plug flow reactors are widely used in the industry due to the non-mixing property. The use of plug flow reactors becomes significant when there is a need for continuous large scale reaction or fast reaction. Plug flow reactors have a high volumetric unit conversion as the occurrence for side reactions is minimum. In this research Aspen Plus V8.0 has been successfully used to simulate the plug flow reactor. In order to simulate the process as accurately as possible HYSYS Peng- Robinson EOS package was used as the property method. The results obtained from the simulation were verified by the experiment carried out in the EDIBON plug flow reactor module. The correlation coefficient (r2) was 0.98 and it proved that simulation results satisfactorily fit for the experimental model. The developed model can be used as a guide for understanding the reaction kinetics of a plug flow reactor.

Keywords: Aspen Plus, Modelling, Plug Flow Reactor, Simulation.

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Authors: Yu-Jen Chang, Shih-Chieh Chen, Yu-Wei Kuo

Abstract:

In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the reworked products. In this paper, we formulate a mathematical model for the ELSP with reworks using the basic period approach. In order to solve this problem, we propose a search algorithm to find the cyclic multiplier ki of each product that can be cyclically produced for every ki basic periods. This research also uses two heuristics to search for the optimal production sequence of all lots and the optimal time length of the basic period so as to minimize the average total cost. This research uses a numerical example to show the effectiveness of our approach.

Keywords: Economic lot, reworks, inventory, basic period.

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