Search results for: Combined conduction and radiation

Authors: J. Mlýnek, R. Srb

Abstract:

This article is focused on the calculation of heat radiation intensity and its optimization on an aluminum mould surface. The inside of the mould is sprinkled with a special powder and its outside is heated by infra heaters located above the mould surface, up to a temperature of 250°C. By this way artificial leathers in the car industry are produced (e. g. the artificial leather on a car dashboard). A mathematical model of heat radiation of infra heaters on a mould surface is described in this paper. This model allows us to calculate a heat-intensity radiation on the mould surface for the concrete location of infra heaters above the mould surface. It is necessary to ensure approximately the same heat intensity radiation on the mould surface by finding a suitable location for the infra heaters, and in this way the same material structure and color of artificial leather. In the model we have used a genetic algorithm to optimize the radiation intensity on the mould surface. Experimental measured values for the heat radiation intensity by a sensor in the surroundings of an infra heater are used for the calculation procedures. A computational procedure was programmed in language Matlab.

Keywords: Genetic algorithm, mathematical model of heat radiation, optimization of radiation intensity, software implementation

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Authors: M. Ebrahimi Shohani, S. M. Taheri, S. M. Golgoun

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Environmental radiation dosimeter is a kind of detector that measures the dose of the radiation area. Dosimeter registers the radiation and converts it to the dose according to the calibration parameters. The limit of a dose is different at each radiation area and this limit should be notified and reported to the user and health physics department. The stochastic nature of radiation is the reason for the fluctuation of any gamma detector dosimetry. In this research we investigated Geiger-Muller type of dosimeter and tried to improve the dose measurement. Geiger-Muller dosimeter is a counter that converts registered radiation to the dose. Therefore, for better data analysis, it is necessary to apply an algorithm to smooth statistical variations of registered radiation. We proposed a method to smooth these fluctuations much more and also proposed a dynamic way to trace rapid changes of radiations. Results show that our method is fast and reliable method in comparison the traditional method.

Keywords: Geiger-Muller, radiation detection, smoothing algorithms, dosimeter, dose calculation.

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Authors: A. Kamath, Z. X. Chen, C. J. Gu, F. Zheng, X. P. Wang, N. Singh, G-Q. Lo

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In this paper we use low frequency noise analysis to understand and map the current conduction path in a multi gate junctionless FinFET.  The device used in this study behaves as a gated resistor and shows excellent short channel effect suppression due to its multi gate structure. Generally for a bulk conduction device like the junctionless device studied in this work, the low frequency noise can be modelled using the mobility fluctuation model; however for this device we can also see the effect of carrier fluctuations on the LFN characteristic. The noise characteristic at different gate bias and also the possible location of the traps is explained.

Keywords: LFN analysis, junctionless, Current conduction path, FinFET.

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Authors: Pei-Ju Chao, Tsair-Fwu Lee, Wei-Luen Huang, Long-Chang Chen, Te-Jen Su, Wen-Ping Chen

Abstract:

The main goal in this paper is to quantify the quality of different techniques for radiation treatment plans, a back-propagation artificial neural network (ANN) combined with biomedicine theory was used to model thirteen dosimetric parameters and to calculate two dosimetric indices. The correlations between dosimetric indices and quality of life were extracted as the features and used in the ANN model to make decisions in the clinic. The simulation results show that a trained multilayer back-propagation neural network model can help a doctor accept or reject a plan efficiently. In addition, the models are flexible and whenever a new treatment technique enters the market, the feature variables simply need to be imported and the model re-trained for it to be ready for use.

Keywords: neural network, dosimetric index, radiation treatment, tumor

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Authors: Ramamurthy S, Ranjan P V, Raghavendiran T A

Abstract:

Reduced switching loss favours Pulse Skipping Modulation mode of switching dc-to-dc converters at light loads. Under certain conditions the converter operates in discontinuous conduction mode (DCM). Inductor current starts from zero in each switching cycle as the switching frequency is constant and not adequately high. A DC-to-DC buck converter is modelled and simulated in this paper under DCM. Effect of ESR of the filter capacitor in input current frequency components is studied. The converter is studied for its operation under input voltage and load variation. The operating frequency is selected to be close to and above audio range.

Keywords: Buck converter, Discontinuous conduction mode, Electromagnetic Interference, Pulse Skipping Modulation.

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Authors: Thanh-Duoc Phan, Saden H. Zahiri, S. H. Masood, Mahnaz Jahedi

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In this article, using finite element analysis (FEA) and an X-ray diffractometer (XRD), cold-sprayed titanium particles on a steel substrate is investigated in term of cooling time and the development of residual strains. Three cooling-down models of sprayed particles after deposition stage are simulated and discussed: the first model (m1) considers conduction effect to the substrate only, the second model (m2) considers both conduction as well as convection effect to the environment, and the third model (m3) which is the same as the second model but with the substrate heated to a near particle temperature before spraying. Thereafter, residual strains developed in the third model is compared with the experimental measurement of residual strains, which involved a Bruker D8 Advance Diffractometer using CuKa radiation (40kV, 40mA) monochromatised with a graphite sample monochromator. For deposition conditions of this study, a good correlation was found to exist between the FEA results and XRD measurements of residual strains.

Keywords: cold gas dynamic spray, X-ray diffraction, explicit finite element analysis, residual strain, titanium, particle impact, deformation behavior.

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Authors: Sajjad A. Memon, Sadaf T. Qureshi, Naeem A. Laghari, Noor M. Khuhro

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The present study represents the occupational radiation doses received by selected workers of Nuclear Institute of Medicine and Radiotherapy (NIMRA) Jamshoro Pakistan and conducted to discuss about how we be careful and try to avoid make ourselves overconscious. Film badges with unique identification number were issued to radiation worker to detect occupational radiation doses. In this study, only 08 workers with high radiation doses were assessed amongst 35 radiation workers during the period of January 2012 to December 2012. The selected radiation workers’ occupational doses were according to designated work areas and in the range of 1.21 to 7.78 mSv (mili Sieveret) out of the annual dose limit of 20 mSv. By the comparison of different studies and earth’s HNBR (High Natural Background Radiation) locations’ doses, it is concluded that the worker’s high doses are of magnitude of HNBR Regions and were in the acceptable range of National and International regulatory bodies so we must not to show any type of overconsciousness but be careful in handling the radioactive sources.

Keywords: Natural background radiation, Occupational dose, Overconscious, Personal monitoring.

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Authors: Lenka Markovičová, Viera Zatkalíková, Tomasz Garbacz

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The development of composite materials and the related design and manufacturing technologies is one of the most important advances in the history of materials. Composites are multifunctional materials having unprecedented mechanical and physical properties that can be tailored to meet the requirements of a particular application. Some composites also exhibit great resistance to high-temperature corrosion, oxidation, and wear. Polymers are widely used indoors and outdoors, therefore they are exposed to a chemical environment which may include atmospheric oxygen, acidic fumes, acidic rain, moisture heat and thermal shock, ultra-violet light, high energy radiation, etc. Different polymers are affected differently by these factors even though the amorphous polymers are more sensitive. Ageing is also important and it is defined as the process of deterioration of engineering materials resulting from the combined effects of atmospheric radiation, heat, oxygen, water, microorganisms and other atmospheric factors.

Keywords: Composites with glass fibres, mechanical properties, polyamides, UV degradation.

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: Analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction.

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Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

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In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: Heat transfer, Radiation effect, Shrinking sheet Unsteady flow.

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Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: P. Amatachaya, P. Khantikomol, R. Sangchot, B. Krittacom

Abstract:

The steady-state temperature for one-dimensional transpiration cooling system has been conducted experimentally and numerically to investigate the heat transfer characteristics of combined convection and radiation. The Nickel –Chrome (Ni-Cr) open-cellular porous material having porosity of 0.93 and pores per inch (PPI) of 21.5 was examined. The upper surface of porous plate was heated by the heat flux of incoming radiation varying from 7.7 - 16.6 kW/m2 whereas air injection velocity fed into the lower surface was varied from 0.36 - 1.27 m/s, and was then rearranged as Reynolds number (Re). For the report of the results in the present study, two efficiencies including of temperature and conversion efficiency were presented. Temperature efficiency indicating how close the mean temperature of a porous heat plate to that of inlet air, and increased rapidly with the air injection velocity (Re). It was then saturated and had a constant value at Re higher than 10. The conversion efficiency, which was regarded as the ability of porous material in transferring energy by convection after absorbed from heat radiation, decreased with increasing of the heat flux and air injection velocity. In addition, it was then asymptotic to a constant value at the Re higher than 10. The numerical predictions also agreed with experimental data very well.

Keywords: Convection, open-cellular, radiation, transpiration cooling, Reynolds number.

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Authors: Z. C. Chang, S. C. Liang

Abstract:

RF magnetron sputtering is used on the ceramic targets, each of which contains zinc oxide (ZnO), zinc oxide doped with aluminum (AZO) and zinc oxide doped with gallium (GZO). The electric conduction mechanism of the AZO and GZO films came mainly from the Al and Ga, the oxygen vacancies, Zn interstitial atoms, and Al and/or Ga interstitial atoms. AZO and GZO films achieved higher conduction than did ZnO film, it being ion vacant and nonstoichiometric. The XRD analysis showed a preferred orientation along the (002) plane for ZnO, AZO, and GZO films.

Keywords: ZnO, AZO, GZO, Doped, Sputtering

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Authors: Lai Xuejiang, Huang Li, Yang Yi

Abstract:

To study the potential hazards of the sudden emergency relief of flare stack, the thermal radiation and noise calculation of flare stack is carried out by using Flaresim program 2.0. Thermal radiation and noise analysis should be considered as the sudden emergency relief takes place. According to the Flaresim software simulation results, the thermal radiation and noise meet the requirement.

Keywords: Flare stack, thermal radiation, noise, safety assessment.

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Authors: Muhammad Waqar, Touqir Ahmad Afridi, Quratulain Soomro

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Radiation is a ghost causing unimaginable physical damage, but its harm is not inevitable. The panic created by previously reported worst-case scenarios i.e., Three Mile Island, Fukushima, Chernobyl, has adversely affected the attitude of radiation workers towards the profession. The psychological effect of radiation-related catastrophes creates an invisible barrier that reduces the efficiency of radiation workers. Careful handling and proper monitoring of radiation decreases the hazards of radiation and proves that the psychological impairment of radiation is myriad fold adverse than its physiological damage. Thermoluminescent Dosimeter (TLD) badges with unique identity numbers were provided to 36 radiation workers for a period of one year (2021). TLDs were read quarterly, and doses were recorded for every radiation worker. Annual doses were recorded and compared with national and international standards. Moreover, the period for which an individual worker is expected to reach one year limit of 20 mSv was also calculated. The highest radiation dose for the radiation worker in 2021 was found at 3.2 mSv, which was 16% of the permissible annual dose limit. The average occupational radiation doses ranged from 1.0 mSv to 3.20 mSv. 64% of the employees did not exceed the 10% of the annual limit, receiving less than 2 mSv. The least time for 20 mSv completion was found 6.25 years for the hot-lab technician. As a whole, the 20 mSv completion period ranged from 6.25 to 20 years. We concluded that the annual professional radiation doses were well within the permissible limits of Pakistan Nuclear Regulatory Authority (PNRA) and International Commission on Radiological Protection (ICRP). The fear of radiation is unnecessary and it creates reluctance towards performing their assigned duties and it is also not favorable for the institute. It must be abolished through education and training sessions.

Keywords: TLD, thermoluminescent dosimeter, psychological impact, radiation dose, annual dose limit, PNRA, ICRP, IAEA.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: Yusuff Idowu Moshood, Sanni Mohammed

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Natural radiations such as ultraviolet (UV) radiation sourced from sun are known to be the main causes of skin cancer, sunburn, eye damage, premature aging of skin and other skin related diseases. Its percentage of radiation reaching the earth populace and its impacts are not well known. Its variability in near-surface relating to its impacts on populace depends on some atmospheric parameters. Hence, this work was embarked on to determine the variability in near-surface UV radiation and its dependency on some atmospheric parameters at different time of the day in Offa, Nigeria. The variability was determined using the data obtained from meteorological garden, Science Laboratory Technology Department, Federal Polytechnic Offa, Nigeria. The data obtained were solar UV radiation, solar radiation, temperature, humidity and pressure at 30 minutes interval. Relationships were determined and correlations were derived using SPSS Pearson Correlation tool. The results showed a significant level of correlation with p-value of 0.01 and 0.05 levels. Thus, the results revealed some good relationships between the solar UV radiation and other atmospheric parameters with significance level less than p-value obtained. Inferentially, interdependent relationships were found to exist. Therefore, the nature of relationship obtained could be a yardstick for decision making in short term environmental planning on solar UV radiation depending of some atmospheric parameters within Offa locality.

Keywords: Correlation, inferential, radiation, yardstick.

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Authors: Yu-Ching Yang, Haw-Long Lee, Win-Jin Chang

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The present work numerically analyzes the transient heat transfer in the absorber plates of a flat-plate solar collector based on the dual-phase-lag (DPL) heat conduction model. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods is used to solve the linear hyperbolic heat conduction equation. This work also examines the effect of different medium parameters on the behavior of heat transfer. Results show that, while the heat-flux phase lag induces thermal waves in the medium, the temperature-gradient phase lag smoothens the thermal waves by promoting non-Fourier diffusion-like conduction into the medium.

Keywords: Absorber plates, dual-phase-lag, non-Fourier, solar collector.

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Authors: Meiling Yang, Shuguo Xie, Yilong Zhu

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Nowadays, due to diverse electric products and complex electromagnetic environment, the localization and troubleshooting of the electromagnetic radiation source is urgent and necessary especially on the condition of far field. However, based on the existing DOA positioning method, the system or devices are complex, bulky and expensive. To address this issue, this paper proposes a single antenna radiation source localization method. A single antenna moves to form a virtual antenna array combined with DOA and MUSIC algorithm to position accurately, meanwhile reducing the cost and simplify the equipment. As shown in the results of simulations and experiments, the virtual antenna array DOA estimation modeling is correct and its positioning is credible.

Keywords: Virtual antenna array, DOA, localization, far field.

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Authors: J. Y. Jang, Y. W. Lee, C. N. Lin, C. H. Wang

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The reheating furnace is used to reheat the steel slabs before the hot-rolling process. The supported system includes the stationary/moving beams, and the skid buttons which block some thermal radiation transmitted to the bottom of the slabs. Therefore, it is important to analyze the steel slab temperature distribution during the heating period. A three-dimensional mathematical transient heat transfer model for the prediction of temperature distribution within the slab has been developed. The effects of different skid button height (H=60mm, 90mm, and 120mm) and different gap distance between two slabs (S=50mm, 75mm, and 100mm) on the slab skid mark formation and temperature profiles are investigated. Comparison with the in-situ experimental data from Steel Company in Taiwan shows that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace. It is found that the skid mark severity decreases with an increase in the skid button height. The effect of gap distance is important only for the slab edge planes, while it is insignificant for the slab central planes.

Keywords: 3-D, slab, transient heat conduction, reheating furnace, thermal radiation.

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Authors: N. Todorovic, I. Bikit, J. Nikolov, S. Forkapic, D. Mrdja, S. Todorovic

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Interventional cardiologists are at greater risk from radiation exposure as a result of the procedures they undertake than most other medical specialists. A study was performed to evaluate operator dose during interventional cardiology procedures and to establish methods of operator dose reduction with a radiation protective device. Different procedure technique and use of protective tools can explain big difference in the annual equivalent dose received by the professionals. Strategies to prevent and monitor radiation exposure, advanced protective shielding and effective radiation monitoring methods should be applied.

Keywords: absorbed dose rate measurements, annualequivalent dose, protective device.

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Authors: Isao Tomita

Abstract:

Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ~I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction.

Keywords: Electrical Conduction, Electron Phase Coherence, Polycrystalline Metal, Magnetic Field.

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Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

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The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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Authors: Ren Jian, Yang Shulin

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In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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Authors: Rehab I. Abdul Rahman, Mazhar B. Tayel

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This paper presents a method of hardening the 8051 micro-controller, able to assure reliable operation in the presence of bit flips caused by radiation. Aiming at avoiding such faults in the 8051 micro-controller, Hamming code protection was used in its SRAM memory and registers. A VHDL code has been used for this hamming code protection.

Keywords: Radiation, hardening, bitflip, hamming code.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: S. N. Ekbote, G. K. Padam, Manju Arora

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Electron spin resonance (ESR) spectroscopic investigations of (Bi, Pb)2Sr2Ca2Cu3O10-x (Bi-2223) bulk samples were carried out in both the normal and superconducting states. A broad asymmetric resonance signal with side signals is obtained in the normal state, and all of them disappear in the superconducting state. The temperature and angular orientation effects on these signals suggest that the broad asymmetric signal arises from electron spin resonance of conduction electrons (CESR) and the side signals from exchange interactions as Platzman-Wolff type spin waves. The disappearance of CESR and spin waves in a superconducting state demonstrates the role of exchange interactions in Cooper pair formation.

Keywords: Bi-2223 superconductor, electron spin resonance of conduction electrons, electron spin resonance, Exchange interactions, spin waves.

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Authors: T. Zalabsky, P. Bezousek, T. Shejbal

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The paper describes new concept of the ribbon beam antenna for RFID technology. Antenna is located near to railway lines to monitor tags situated on trains. Antenna works at 2.45 GHz and it is fabricated by microstrip technology. Antenna contains two same mirrored parts having the same radiation patterns. Each part consists of three dielectric layers. The first layer has on one side radiation elements. The second layer is only for mechanical construction and it sets optimal electromagnetic field for each radiating elements. The third layer has on its top side a ground plane and on the bottom side a microstrip circuit used for individual radiation elements feeding.

Keywords: RFID, cosecant radiation pattern, ribbon beam, patch antenna, microstrip.

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Authors: B. I. Lee, S. I. Kim, D. H. Suh, J. I. Kim, Y. K. Lim

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A total of 33,680 nuclear power plants (NPPs) workers were monitored and recorded from 1990 to 2007. According to the record, the average individual radiation dose has been decreasing continually from it 3.20 mSv/man in 1990 to 1.12 mSv/man at the end of 2007. After the International Commission on Radiological Protection (ICRP) 60 recommendation was generalized in South Korea, no nuclear power plant workers received above 20 mSv radiation, and the numbers of relatively highly exposed workers have been decreasing continuously. The age distribution of radiation workers in nuclear power plants was composed of mainly 20-30- year-olds (83%) for 1990 ~ 1994 and 30-40-year-olds (75%) for 2003 ~ 2007. The difference in individual average dose by age was not significant. Most (77%) of NPP radiation exposures from 1990 to 2007 occurred mostly during the refueling period. With regard to exposure type, the majority of exposures were external exposures, representing 95% of the total exposures, while internal exposures represented only 5%. External effective dose was affected mainly by gamma radiation exposure, with an insignificant amount of neutron exposure. As for internal effective dose, tritium (3H) in the pressurized heavy water reactor (PHWR) was the biggest cause of exposure.

Keywords: Dose distribution, External exposure, Nuclear powerplant, Occupational radiation dose

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Authors: Kai-Long Hsiao

Abstract:

In this study, an analysis has been performed for free convection with radiation effect over a thermal forming nonlinearly stretching sheet. Parameters n, k0, Pr, G represent the dominance of the nonlinearly effect, radiation effect, heat transfer and free convection effects which have been presented in governing equations, respectively. The similarity transformation and the finite-difference methods have been used to analyze the present problem. From the results, we find that the effects of parameters n, k0, Pr, Ec and G to the nonlinearly stretching sheet. The increase of Prandtl number Pr, free convection parameter G or radiation parameter k0 resulting in the increase of heat transfer effects, but increase of the viscous dissipation number Ec will decrease of heat transfer effect.

Keywords: Nonlinearly stretching sheet, Free convection, Finite-difference, Radiation effect.

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