Search results for: rectangular plates.

Authors: A. Al-Shyyab, A. F. Khadrawi

Abstract:

The hydrodynamics behavior of fluid flow in microconverging plates is investigated analytically. Effects of Knudsen number (
) on the microchannel hydrodynamics behavior and the coefficient of friction are investigated. It is found that as
 increases the slip in the hydrodynamic boundary condition increases. Also, the coefficient of friction decreases as
 increases.

Keywords: Converging plates, hydrodynamic behavior, microplates, microchannel, slip velocity

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Authors: Amin Esmaeilzadeh, Mohammad Sadeghi, Farhad Kolahan

Abstract:

Arc welding is an important joining process widely used in many industrial applications including production of automobile, ships structures and metal tanks. In welding process, the moving electrode causes highly non-uniform temperature distribution that leads to residual stresses and different deviations, especially buckling distortions in thin plates. In order to control the deviations and increase the quality of welded plates, a fixture can be used as a practical and low cost method with high efficiency. In this study, a coupled thermo-mechanical finite element model is coded in the software ANSYS to simulate the behavior of thin plates located by a 3-2-1 positioning system during the welding process. Computational results are compared with recent similar works to validate the finite element models. The agreement between the result of proposed model and other reported data proves that finite element modeling can accurately predict the behavior of welded thin plates.

Keywords: Welding, thin plate, buckling distortion, fixture locators, finite element modelling.

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Authors: Anahita Ghaznavi Jahromi, Farzad Mohajeri, Nooshin Feiz

Abstract:

In this paper a novel structure of metamaterial is proposed in order to miniaturize a rectangular microstrip patch antenna. The metamaterial is composed of two nested split octagons which are located on a 10 mm

Keywords: Metamaterial, miniaturization, patch antenna, sub- wavelength resonance.

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Authors: V. Yu. Shungin, A. V. Popov

Abstract:

The paper gives basic information on application of rotation bending for manufacturing ship hull parts from steel plates and on MGPS machines, employed for this purpose.

Keywords: Roller bending, steel plates, shipbuilding, ship repair.

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Authors: Saravana Kannan Thangavelu

Abstract:

Fuel and oxidant gas delivery plate, or fuel cell plate, is a key component of a Proton Exchange Membrane (PEM) fuel cell. To manufacture low-cost and high performance fuel cell plates, advanced computer modeling and finite element structure analysis are used as virtual prototyping tools for the optimization of the plates at the early design stage. The present study examines thermal stress analysis of the fuel cell plates that are produced using a patented, low-cost fuel cell plate production technique based on screen-printing. Design optimization is applied to minimize the maximum stress within the plate, subject to strain constraint with both geometry and material parameters as design variables. The study reveals the characteristics of the printed plates, and provides guidelines for the structure and material design of the fuel cell plate.

Keywords: Design optimization, FEA, PEM fuel cell, Thermal stress

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Authors: N. Ploysook, R. Rugsaj, C. Suvanjumrat

Abstract:

The characteristic requirement for producing rectangular shape bottles was a uniform thickness of the plastic bottle wall. Die shaping was a good technique which controlled the wall thickness of bottles. An advance technology which was the finite element method (FEM) for blowing parison to be a rectangular shape bottle was conducted to reduce waste plastic from a trial and error method of a die shaping and parison control method. The artificial intelligent (AI) comprised of artificial neural network and genetic algorithm was selected to optimize the die gap shape from the FEM results. The application of AI technique could optimize the suitable die gap shape for the parison blow molding which did not depend on the parison control method to produce rectangular bottles with the uniform wall. Particularly, this application can be used with cheap blow molding machines without a parison controller therefore it will reduce cost of production in the bottle blow molding process.

Keywords: AI, bottle, die shaping, FEM.

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Authors: Homayon Ahmad Panahi, Hossein Sid Kalal, Atyeh Rahimi

Abstract:

A high performance thin layer chromatography system (HPTLC) for the separation of vitamin B2 and B12 has been developed. The separation was successfully using a solvent system of methanol, water, ammonia 7.3.1 (V/V) as mobile phase on HPTLC plates impregnated with boric acid. The effect of other mobile phases on the separation of vitamins was also examined. The method is based on different behavior of investigated compounds in impregnated TLC plates with different amount of boric acid. The Rf values of vitamin B2 and B12 are considered on non impregnated and impregnated silica gel HPTLC plate with boric acid. The effect of boric acid in the mobile phase and on HPTLC plates on the RF values of the vitamins has also been studied.

Keywords: High performance thin layer chromatography, HPTLC, Vitamin B2, Vitamin B12, Separation.

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Authors: Xuguang Leng

Abstract:

The theory of tectonic plate asteroid driver provides that comet and asteroid collisions have ample energy to fracture, move, and deform tectonic plate. The enormous kinetic energy of an asteroid collision is dissipated through the fracture and violent movement of the tectonic plates, and stored in the plate deformations. The stored energy will be released in the future through plate slow movement. The reflection of plate edge upwards upon collision impact causes the plate to sit on top of adjacent plate and creates the subduction plate. Higher probability and higher energy of asteroid collision in the equator area provides the net energy to drive heavier land plates to higher latitudes, offsetting the tidal and self spin forces, creating a more random land plates distribution. The trend of asteroid collisions is less frequency and intensity as loose objects are merging into the planets and Jupiter is taking ever larger shares of collisions. As overall energy input from asteroid collision decreases, plate movement is slowing down and eventually land plates will congregate towards equator area. The current trajectory of plate movements is the cumulative effect of past asteroid collisions, and can be altered, new plates be created, by future collisions.

Keywords: Tectonic plate, Earth, asteroid, comet.

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Authors: Y.Bakhshan, H.Ashoori

Abstract:

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Keywords: Rectangular Cavity, magneto-hydrodynamic, free convection, simulation

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Authors: Zhao Cai-qi, Ma Jun

Abstract:

Twin steel plates-concrete composite shear walls are composed of a pair of steel plate layers and a concrete layer sandwiched between them, which have the characteristics of both reinforced concrete shear walls and steel plate shear walls. Twin steel plates-composite shear walls contain very high ultimsate bearing capacity and ductility, which have great potential to be applied in the super high-rise buildings and special structures. In this paper, we analyzed the basic characteristics and stress mechanism of the twin steel plates-composite shear walls. Specifically, we analyzed the effects of the steel plate thickness, wall thickness and concrete strength on the bearing capacity of the twin steel plates-composite shear walls. The analysis results indicate that: (1) the initial shear stiffness and ultimate shear-carrying capacity is not significantly affected by the thickness of concrete wall but by the class of concrete, (2) both factors significantly impact the shear distribution of the shear walls in ultimate shear-carrying capacity. The technique of twin steel plates-composite shear walls has been successfully applied in the construction of an 88-meter Huge Statue of Buddha located in Hunan Province, China. The analysis results and engineering experiences showed that the twin steel plates-composite shear walls have great potential for future research and applications.

Keywords: Twin steel plates-concrete composite shear wall, huge statue of Buddha, shear capacity, initial lateral stiffness, overturning moment bearing.

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Authors: Nur Irmawati, H.A. Mohammed

Abstract:

In the present study, mixed convection in a horizontal rectangular duct using Al2O3 is numerically investigated. The effects of different Rayleigh number, Reynolds number and radiation on flow and heat transfer characteristics are studied in detail. This study covers Rayleigh number in the range of 2 × 10^6 ≤ Ra ≤ 2 × 10^7 and Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that the Nusselt number increases as Reynolds and Rayleigh numbers increase. It is also found that the dimensionless temperature distribution increases as Rayleigh number increases.

Keywords: Numerical simulation, Mixed convection, Horizontal rectangular duct, Nanofluids.

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Authors: Radouane Elbahjaoui, Hamid El Qarnia

Abstract:

The present work aims to investigate numerically the thermal and flow characteristics of a rectangular latent heat storage unit (LHSU) during the melting process of a phase change material (PCM). The LHSU consists of a number of vertical and identical plates of PCM separated by rectangular channels. The melting process is initiated when the LHSU is heated by a heat transfer fluid (HTF: water) flowing in channels in a downward or upward direction. The proposed study is motivated by the need to optimize the thermal performance of the LHSU by accelerating the charging process. A mathematical model is developed and a fixed-grid enthalpy formulation is adopted for modeling the melting process coupling with convection-conduction heat transfer. The finite volume method was used for discretization. The obtained numerical results are compared with experimental, analytical and numerical ones found in the literature and reasonable agreement is obtained. Thereafter, the numerical investigations were carried out to highlight the effects of the HTF flow direction and the aspect ratio of the PCM slabs on the heat transfer characteristics and thermal performance enhancement of the LHSU.

Keywords: Phase change material, thermal energy storage, latent heat storage unit, melting.

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Authors: Priyadarsini P.L.K, Hemalatha T.

Abstract:

In the Top Right Access point Minimum Length Corridor (TRA-MLC) problem [1], a rectangular boundary partitioned into rectilinear polygons is given and the problem is to find a corridor of least total length and it must include the top right corner of the outer rectangular boundary. A corridor is a tree containing a set of line segments lying along the outer rectangular boundary and/or on the boundary of the rectilinear polygons. The corridor must contain at least one point from the boundaries of the outer rectangle and also the rectilinear polygons. Gutierrez and Gonzalez [1] proved that the MLC problem, along with some of its restricted versions and variants, are NP-complete. In this paper, we give a shorter proof of NP-Completeness of TRA-MLC by findig the reduction in the following way.

Keywords: NP-complete, 2-connected planar graph, Grid embedding of a plane graph.

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Authors: Ceren Ince, Berkay Z. Erdem, Shahram Derogar, Nabi Yuzer

Abstract:

Fibre cement plates, often used in construction, generally are made using quartz as an inert material, cement as a binder and cellulose as a fibre. This paper, first of all, investigates the mechanical properties and durability of fibre cement plates when quartz is both partly and fully replaced with diatomite. Diatomite does not only have lower density compared to quartz but also has high pozzolanic activity. The main objective of this paper is the investigation of the effects of supplementary cementing materials (SCMs) on the short and long term mechanical properties and durability characteristics of fibre cement plates prepared using diatomite. Supplementary cementing materials such as ground granulated blast furnace slug (GGBS) and fly ash (FA) are used in this study. Volume proportions of 10, 20, 30 and 40% of GGBS and FA are used as partial replacement materials to cement. Short and long term mechanical properties such as compressive and flexural strengths as well as sorptivity characteristics and mass were investigated. Consistency and setting time at each replacement levels of SCMs were also recorded. The effects of using supplementary cementing materials on the carbonation and sulphate resistance of fibre cement plates were then experimented. The results, first of all, show that the use of diatomite as a full or partial replacement to quartz resulted in a systematic decrease in total mass of the fibre cement plates. The reduction of mass was largely due to the lower density and finer particle size of diatomite compared to quartz. The use of diatomite did not only reduce the mass of these plates but also increased the compressive strength significantly as a result of its high pozzolanic activity. The replacement levels of both GGBS and FA resulted in a systematic decrease in short term compressive strength with increasing replacement levels. This was essentially expected as the total rate of hydration is much lower in GGBS and FA than that of cement. Long term results however, indicated that the compressive strength of fibre cement plates prepared using both GGBS and FA increases with time and hence the compressive strength of plates prepared using SCMs is either equivalent or more than the compressive strength of plates prepared using cement alone. Durability characteristics of fibre cement plates prepared using SCMs were enhanced significantly. Measurements of sopritivty characteristics were also indicated that the plates prepared using SCMs has much lower water absorption capacities compared to plates prepared cement alone. Much higher resistance to carbonation and sulphate attach were observed with plates prepared using SCMs. The results presented in this paper show that the use of SCMs does not only support the production of more sustainable construction materials but also enhances the mechanical properties and durability characteristics of fibre cement plates.

Keywords: Diatomite, fibre, strength, supplementary cementing materials.

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Authors: Seungyeong Choi, Namkyu Lee, Dong Il Shim, Young Mun Lee, Yong-Ki Park, Hyung Hee Cho

Abstract:

Effect of the cross-sectional geometry on heat transfer and particle motion of circulating fluidized bed riser for CO₂ capture was investigated. Numerical simulation using Eulerian-eulerian method with kinetic theory of granular flow was adopted to analyze gas-solid flow consisting in circulating fluidized bed riser. Circular, square, and rectangular cross-sectional geometry cases of the same area were carried out. Rectangular cross-sectional geometries were analyzed having aspect ratios of 1: 2, 1: 4, 1: 8, and 1:16. The cross-sectional geometry significantly influenced the particle motion and heat transfer. The downward flow pattern of solid particles near the wall was changed. The gas-solid mixing degree of the riser with the rectangular cross section of the high aspect ratio was the lowest. There were differences in bed-to-wall heat transfer coefficient according to rectangular geometry with different aspect ratios.

Keywords: Bed geometry, computational fluid dynamics, circulating fluidized bed riser, heat transfer.

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Authors: C. S. Tsai, Yung-Chang Lin

Abstract:

In order to upgrade the seismic resistibility of structures and enhance the functionality of an isolator, a new base isolator called the multiple trench friction pendulum system (MTFPS) is proposed in this study. The proposed MTFPS isolator is composed of a trench concave surface and several intermediate sliding plates in two orthogonal directions. Mathematical formulations have been derived to examine the characteristics of the proposed MTFPS isolator possessing multiple intermediate sliding plates. By means of mathematical formulations, it can be inferred that the natural period and damping effect of the MTFPS isolator with several intermediate sliding plates can be altered continually and controllably during earthquakes. Furthermore, results obtained from shaking table tests demonstrate that the proposed isolator provides good protection to structures for prevention of damage from strong earthquakes.

Keywords: Friction Pendulum System, Multiple Friction Pendulum System, Base Isolation, Earthquake Engineering

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Authors: Ben Mohamed Ahemed Mohamed, Yassine Adnan

Abstract:

The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins. This article treats the case of objects with a free orientation of 90Ôùª. We propose an approach of resolution combining optimization by colony of ants (ACO) and the heuristic method IMA to resolve this NP-Hard problem.

Keywords: Ant colony algorithm, bin-packing problem, heuristics methods.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Rectangular and circular membranes, propagation matrix, reflection matrix, vibration analysis.

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Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

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Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla

Abstract:

The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.

Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs

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Authors: Azli Abd. Razak, Yusli Yaakob, Mohd Nazir Ramli

Abstract:

This study comprehensively simulate the use of k-ε model for predicting flow and heat transfer with measured flow field data in a stationary duct with elucidates on the detailed physics encountered in the fully developed flow region, and the sharp 180° bend region. Among the major flow features predicted with accuracy are flow transition at the entrance of the duct, the distribution of mean and turbulent quantities in the developing, fully developed, and sharp 180° bend, the development of secondary flows in the duct cross-section and the sharp 180° bend, and heat transfer augmentation. Turbulence intensities in the sharp 180° bend are found to reach high values and local heat transfer comparisons show that the heat transfer augmentation shifts towards the wall and along the duct. Therefore, understanding of the unsteady heat transfer in sharp 180° bends is important. The design and simulation are related to concept of fluid mechanics, heat transfer and thermodynamics. Simulation study has been conducted on the response of turbulent flow in a rectangular duct in order to evaluate the heat transfer rate along the small scale multiple rectangular duct

Keywords: Heat transfer, turbulence, rectangular duct, simulation.

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Authors: Hari Mohan Kushwaha, Santosh K. Sahu

Abstract:

In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen Number, Modified Brinkman Number, Slip Flow, Velocity Slip.

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Authors: Y. Lu, X. S. Qin

Abstract:

Extensive rainfall disaggregation approaches have been developed and applied in climate change impact studies such as flood risk assessment and urban storm water management.In this study, five rainfall models that were capable ofdisaggregating daily rainfall data into hourly one were investigated for the rainfall record in theChangi Airport, Singapore. The objectives of this study were (i) to study the temporal characteristics of hourly rainfall in Singapore, and (ii) to evaluate the performance of variousdisaggregation models. The used models included: (i) Rectangular pulse Poisson model (RPPM), (ii) Bartlett-Lewis Rectangular pulse model (BLRPM), (iii) Bartlett-Lewis model with 2 cell types (BL2C), (iv) Bartlett-Lewis Rectangular with cell depth distribution dependent on duration (BLRD), and (v) Neyman-Scott Rectangular pulse model (NSRPM). All of these models werefitted using hourly rainfall data ranging from 1980 to 2005 (which was obtained from Changimeteorological station).The study results indicated that the weight scheme of inversely proportional variance could deliver more accurateoutputs for fitting rainfall patterns in tropical areas, and BLRPM performedrelatively better than other disaggregation models.

Keywords: Rainfall disaggregation, statistical properties, poisson processed, Bartlett-Lewis model, Neyman-Scott model.

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Authors: S. Kulsri, M. Jaroensutasinee, K. Jaroensutasinee

Abstract:

We developed a new method based on quasimolecular modeling to simulate the cavity flow in three cavity shapes: rectangular, half-circular and bucket beer in cgs units. Each quasi-molecule was a group of particles that interacted in a fashion entirely analogous to classical Newtonian molecular interactions. When a cavity flow was simulated, the instantaneous velocity vector fields were obtained by using an inverse distance weighted interpolation method. In all three cavity shapes, fluid motion was rotated counter-clockwise. The velocity vector fields of the three cavity shapes showed a primary vortex located near the upstream corners at time t ~ 0.500 s, t ~ 0.450 s and t ~ 0.350 s, respectively. The configurational kinetic energy of the cavities increased as time increased until the kinetic energy reached a maximum at time t ~ 0.02 s and, then, the kinetic energy decreased as time increased. The rectangular cavity system showed the lowest kinetic energy, while the half-circular cavity system showed the highest kinetic energy. The kinetic energy of rectangular, beer bucket and half-circular cavities fluctuated about stable average values 35.62 x 103, 38.04 x 103 and 40.80 x 103 ergs/particle, respectively. This indicated that the half-circular shapes were the most suitable shape for a shrimp pond because the water in shrimp pond flows best when we compared with rectangular and beer bucket shape.

Keywords: Quasi-molecular modelling, particle modelling, lid driven cavity flow.

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Authors: Jefri Marzal, Hong Xie, Chun Che Fung

Abstract:

Visibility problems are central to many computational geometry applications. One of the typical visibility problems is computing the view from a given point. In this paper, a linear time procedure is proposed to compute the visibility subsets from a corner of a rectangular prism in an orthogonal polyhedron. The proposed algorithm could be useful to solve classic 3D problems.

Keywords: Visibility, rectangular prism, orthogonal polyhedron.

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Authors: Kargarnovin M.H., Faghidian S. A, Arghavani J.

Abstract:

The limit load carrying capacity of functionally graded materials (FGM) circular plates subjected to an arbitrary rotationally symmetric loading has been computed. It is provided that the plate material behaves rigid perfectly plastic and obeys either the Square or the Tresca yield criterion. To this end the upper and lower bound principles of limit analysis are employed to determine the exact value for the limiting load. The correctness of the result are verified and finally limiting loads for two examples namely; through radius and through thickness FGM circular plates with simply supported edges are calculated, respectively and moreover, the values of critical loading factor are determined.

Keywords: Circular plate, FGM circular plate, Limit analysis, Lower and Upper bound theorems.

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Authors: D. Zabala, N. Sánchez, J. Pinto

Abstract:

A transient heat transfer mathematical model for the prediction of temperature distribution in the car body during primer baking has been developed by considering the thermal radiation and convection in the furnace chamber and transient heat conduction governing equations in the car framework. The car cockpit is considered like a structure with six flat plates, four vertical plates representing the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transient heat conduction in each flat plate is modeled by the lumped capacitance method. Comparison with the experimental data shows that the heat transfer model works well for the prediction of thermal behavior of the car body in the curing furnace, with deviations below 5%.

Keywords: Transient heat transfer, car body, lumpedcapacitance, primer baking.

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Authors: S. Kampeephat, P. Krachodnok, R. Wongsan

Abstract:

The conventional rectangular horn has been used for microwave antenna a long time. Its gain can be increased by enlarging the construction of horn to flare exponentially. This paper presents a study of the shaped woodpile Electromagnetic Band Gap (EBG) to improve its gain for conventional horn without construction enlargement. The gain enhancement synthesis method for shaped woodpile EBG that has to transfer the electromagnetic fields from aperture of a horn antenna through woodpile EBG is presented by using the variety of shaped woodpile EBGs such as planar, triangular, quadratic, circular, gaussian, cosine, and squared cosine structures. The proposed technique has the advantages of low profile, low cost for fabrication and light weight. The antenna characteristics such as reflection coefficient (S₁₁), radiation patterns and gain are simulated by utilized A Computer Simulation Technology (CST) software. With the proposed concept, an antenna prototype was fabricated and experimented. The S₁₁ and radiation patterns obtained from measurements show a good impedance matching and a gain enhancement of the proposed antenna. The gain at dominant frequency of 10 GHz is 25.6 dB, application for X- and Ku-Band Radar, that higher than the gain of the basic rectangular horn antenna around 8 dB with adding only one appropriated EBG structures.

Keywords: Conventional Rectangular Horn Antenna, Electromagnetic Band Gap, Gain Enhancement, X- and Ku-Band Radar.

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Authors: Thomas Jin-Chee Liu, Yu-Shen Chen

Abstract:

Using the numerical and experimental methods, this paper discusses some primary studies on the vibration and cooling performances of the piezoelectric cooling fan with the rectangular blade. When the fan works at its natural frequency, the vibrating displacement is largest and the cooling performance is best. Due to the vibration behavior, the cooling performance is affected by the geometry, material property, and working frequency of the piezoelectric cooling fan. 

Keywords: Piezoelectric cooling fan, finite element, vibration, natural frequency.

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Authors: El Kaak Rachid, El Bikri Khalid, Benamar Rhali

Abstract:

In the present study, the problem of geometrically nonlinear free vibrations of functionally graded circular plates (FGCP) resting on Pasternak elastic foundation with immovable ends was studied. The material properties of the functionally graded composites examined were assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the classical Plate theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results dealing with the problem of functionally graded plates. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the FGCP has been studied. The effect of the linear and shearing foundations is to decrease the frequency ratio, where it increases with the effect of the nonlinear foundation stiffness. 

Keywords: Non-linear vibrations, Circular plates, Pasternak foundation, functionally graded materials.

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