Search results for: Double diffusive convection

Authors: L. Slimani, A. Bousri, A. Hamadouche, H. Ben Hamed

Abstract:

The aim of this experimental and numerical study is to analyze the effects of acoustic streaming generated by 40 kHz ultrasonic waves on heat transfer in forced convection, with and without 40 PPI aluminum metal foam. Preliminary dynamic and thermal studies were done with COMSOL Multiphase, to see heat transfer enhancement degree by inserting a 40PPI metal foam (10 × 2 × 3 cm) on a heat sink, after having determined experimentally its permeability and Forchheimer's coefficient. The results obtained numerically are in accordance with those obtained experimentally, with an enhancement factor of 205% for a velocity of 0.4 m/s compared to an empty channel. The influence of 40 kHz ultrasound on heat transfer was also tested with and without metallic foam. Results show a remarkable increase in Nusselt number in an empty channel with an enhancement factor of 37,5%, while no influence of ultrasound on heat transfer in metal foam presence.

Keywords: Enhancing heat transfer, metal foam, ultrasound, acoustic streaming, laminar flow.

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Authors: S. W. Lo, S.-H. Lu, Y. H. Guo, L.-C. Hsu

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In this paper a novel design of aerostatic thrust bearing is proposed and is analyzed numerically. The capillary restrictor and bearing disk are made of elastomer like silicone and PU. The viscoelasticity of elastomer helps the capillary expand for more air flux and at the same time, allows conicity of the bearing surface to form when the air pressure is enhanced. Therefore the bearing has the better ability of passive compensation. In the present example, as compared with the typical model, the new designs can nearly double the load capability and offer four times static stiffness.

Keywords: Aerostatic, bearing, elastomer, static stiffness.

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Authors: W. Kaowumpai, D. Koolpiruck, K. Viravaidya

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Female breast cancer is the second in frequency after cervical cancer. Surgery is the most common treatment for breast cancer, followed by chemotherapy as a treatment of choice. Although effective, it causes serious side effects. Controlled-release drug delivery is an alternative method to improve the efficacy and safety of the treatment. It can release the dosage of drug between the minimum effect concentration (MEC) and minimum toxic concentration (MTC) within tumor tissue and reduce the damage of normal tissue and the side effect. Because an in vivo experiment of this system can be time-consuming and labor-intensive, a mathematical model is desired to study the effects of important parameters before the experiments are performed. Here, we describe a 3D mathematical model to predict the release of doxorubicin from pluronic gel to treat human breast cancer. This model can, ultimately, be used to effectively design the in vivo experiments.

Keywords: Breast Cancer, Doxorubicin, Controlled ReleaseSystem, Diffusion and Convection Equation.

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Authors: F. Esmaeilzadeh, M. E. Zeighami, J. Fathi

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This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.

Keywords: Hydrate reservoir, numerical modeling, depressurization, thermal stimulation, gas generation.

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Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

Abstract:

The present study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. T0 validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: Inverse method, FLUENT, Plate-fin heat sink, Heat transfer characteristics.

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Authors: Syukri Himran, Rustan Taraka, Anto Duma

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The aim of the study is to improve the understanding of latent and sensible thermal energy storage within a paraffin wax media by an array of cylindrical tubes arranged both in in-line and staggered layouts. An analytical and experimental study is carried out in a horizontal shell-and-tube type system during melting process. Pertamina paraffin-wax was used as a phase change material (PCM), while the tubes are embedded in the PCM. From analytical study we can obtain the useful information in designing a thermal energy storage such as: the motion of interface, amount of material melted at any time in the process, and the heat storage characteristic during melting. The use of staggered tubes is proposed compared to in-line layout in a heat exchanger as thermal storage. The experimental study is used to verify the validity of the analytical predictions. From the comparisons, the analytical and experimental data are in a good agreement.

Keywords: Latent, sensible, paraffin-wax, thermal energy storage, conduction, natural convection.

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Authors: Anirut Luadsong, Nitima Aschariyaphotha

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting upwind schemes for avoiding stability problems and prove that it is consistent to the upwind scheme with same accuracy. The splitting upwind schemes was adopted to split the wave spectral action balance equation into four onedimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-processor computer.

Keywords: upwind scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Yukinari Minagi , Akinori Kanasugi

Abstract:

This paper describes about dynamic reconfiguration to miniaturize arithmetic circuits in general-purpose processor. Dynamic reconfiguration is a technique to realize required functions by changing hardware construction during operation. The proposed arithmetic circuit performs floating-point arithmetic which is frequently used in science and technology. The data format is floating-point based on IEEE754. The proposed circuit is designed using VHDL, and verified the correct operation by simulations and experiments.

Keywords: dynamic reconfiguration, floating-point arithmetic, double precision, FPGA

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Authors: Jürgen Geiser, Robert Röhle

Abstract:

In this paper we present modeling and simulation for physical vapor deposition for metallic bipolar plates. In the models we discuss the application of different models to simulate the transport of chemical reactions of the gas species in the gas chamber. The so called sputter process is an extremely sensitive process to deposit thin layers to metallic plates. We have taken into account lower order models to obtain first results with respect to the gas fluxes and the kinetics in the chamber. The model equations can be treated analytically in some circumstances and complicated multi-dimensional models are solved numerically with a software-package (UG unstructed grids, see [1]). Because of multi-scaling and multi-physical behavior of the models, we discuss adapted schemes to solve more accurate in the different domains and scales. The results are discussed with physical experiments to give a valid model for the assumed growth of thin layers.

Keywords: Convection-diffusion equations, multi-scale problem, physical vapor deposition, reaction equations, splitting methods.

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Authors: Raveen R. Goundar, Ken-ichi Shiota, Masahiko Toyonaga

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The major building block of most elliptic curve cryptosystems are computation of multi-scalar multiplication. This paper proposes a novel algorithm for simultaneous multi-scalar multiplication, that is by employing addition chains. The previously known methods utilizes double-and-add algorithm with binary representations. In order to accomplish our purpose, an efficient empirical method for finding addition chains for multi-exponents has been proposed.

Keywords: elliptic curve cryptosystems, multi-scalar multiplication, addition chains, Fibonacci sequence.

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Authors: Md. Nasir Uddin, M. A. Alim, M. M. K. Chowdhury

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This analysis is performed to study the momentum, heat and mass transfer characteristics of MHD mixed convective flow past inclined porous plate in porous medium, including the effect of fluid suction. The fluid is assumed to be steady, incompressible and dense. Similarity solution is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically by using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. Numerical results for the various types of parameters entering into the problem for velocity, temperature and concentration distributions are presented graphically and analyzed thereafter. Moreover, expressions for the skin-friction, heat transfer co-efficient and mass transfer co-efficient are discussed with graphs against streamwise distance for various governing parameters.

Keywords: Fluid suction, heat and mass transfer, inclined porous plate, MHD, mixed convection, porous medium.

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Authors: Feyza Eda Akyurek, Bayram Sahin, Kadir Gelis, Eyuphan Manay, Murat Ceylan

Abstract:

Turbulent forced convection heat transfer and pressure drop characteristics of Al₂O₃–water nanofluid flowing through a concentric tube heat exchanger with and without coiled wire turbulators were studied experimentally. The experiments were conducted in the Reynolds number ranging from 4000 to 20000, particle volume concentrations of 0.8 vol.% and 1.6 vol.%. Two turbulators with the pitches of 25 mm and 39 mm were used. The results of nanofluids indicated that average Nusselt number increased much more with increasing Reynolds number compared to that of pure water. Thermal conductivity enhancement by the nanofluids resulted in heat transfer enhancement. Once the pressure drop of the alumina/water nanofluid was analyzed, it was nearly equal to that of pure water at the same Reynolds number range. It was concluded that nanofluids with the volume fractions of 0.8 and 1.6 did not have a significant effect on pressure drop change. However, the use of wire coils in heat exchanger enhanced heat transfer as well as the pressure drop.

Keywords: Turbulators, heat exchanger, nanofluids, heat transfer enhancement.

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Authors: Ali Reza Tahavvor, Saeed Hosseini, Afshin Karimzadeh Fard

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In this paper the effect of wall waviness of side walls in a two-dimensional wavy enclosure is numerically investigated. Two vertical wavy walls and straight top wall are kept isothermal and the bottom wall temperature is higher and spatially varying with cosinusoidal temperature distribution. A computational code based on Finite-volume approach is used to solve governing equations and SIMPLE method is used for pressure velocity coupling. Test is performed for several different numbers of undulations. The Prandtl number was kept constant and the Ra number denotes that the flow is laminar. Temperature and velocity fields are determined. Therefore, according to the obtained results a correlation is proposed for average Nusselt number as a function of number of side wall waves. The results indicate that the Nusselt number is highly affected by number of waves and increasing it decreases the wavy walls Nusselt number; although the Nusselt number is not highly affected by surface waviness when the number of undulations is below one.

Keywords: Cavity, natural convection, Nusselt number, wavy wall.

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Authors: Md. Nasir Uddin, M. A. Alim, M. M. K. Chowdhury

Abstract:

The effect of mass transfer on MHD mixed convective flow along inclined porous plate with thermodiffusion have been analyzed on the basis of boundary layer approximations. The fluid is assumed to be incompressible and dense, and a uniform magnetic field is applied normal to the direction of the flow. A Similarity transformation is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. The behavior of velocity, temperature, concentration, local skin-friction, local Nusselt number and local Sherwood number for different values of parameters have been computed and the results are presented graphically, and analyzed thereafter. The validity of the numerical methodology and the results are questioned by comparing the findings obtained for some specific cases with those available in the literature, and a comparatively good agreement is reached.

Keywords: Mass transfer, inclined porous plate, MHD, mixed convection, thermodiffusion.

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Authors: D Bhargavi, J. Sharath Kumar Reddy

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The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γ_p on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: Porous material, channel partially filled with a porous material, axial conduction, viscous dissipation.

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Authors: Chang Liu, Zishu He

Abstract:

Adaptive echo cancellers with two-path algorithm are applied to avoid the false adaptation during the double-talk situation. In the two-path algorithm, several transfer logic solutions have been proposed to control the filter update. This paper presents an improved transfer logic solution. It improves the convergence speed of the two-path algorithm, and allows the reduction of the memory elements and computational complexity. Results of simulations show the improved performance of the proposed solution.

Keywords: Acoustic echo cancellation, Echo return lossenhancement (ERLE), Two-path algorithm, Transfer logic

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Authors: S. H. Anilkumar, Ghulam Jilani

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The objective of the present work is to conduct investigations leading to a more complete explanation of single phase natural convective heat transfer in an enclosure with fin utilizing nano fluids. The nano fluid used, which is composed of Aluminum oxide nano particles in suspension of Ethylene glycol, is provided at various volume fractions. The study is carried out numerically for a range of Rayleigh numbers, fin heights and aspect ratio. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions are identified as symmetry of sections. One half of such a rectangular region is chosen as the computational domain taking into account the symmetry about the fin. Transport equations are modeled by a stream functionvorticity formulation and are solved numerically by finite-difference schemes. Comparisons with previously published works on the basis of special cases are done. Results are presented in the form of streamline, vector and isotherm plots as well as the variation of local Nusselt number along the fin under different conditions.

Keywords: Fin height, Nano fluid, natural convection, Rayleigh number.

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Authors: D. Zabala, Y. Cárdenas, G. Núñez

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In this work the numerical simulation of transient heat transfer in a cylindrical probe is done. An experiment was conducted introducing a steel cylinder in a heating chamber and registering its surface temperature along the time during one hour. In parallel, a mathematical model was solved for one dimension transient heat transfer in cylindrical coordinates, considering the boundary conditions of the test. The model was solved using finite difference method, because the thermal conductivity in the cylindrical steel bar and the convection heat transfer coefficient used in the model are considered temperature dependant functions, and both conditions prevent the use of the analytical solution. The comparison between theoretical and experimental results showed the average deviation is below 2%. It was concluded that numerical methods are useful in order to solve engineering complex problems. For constant k and h, the experimental methodology used here can be used as a tool for teaching heat transfer in mechanical engineering, using mathematical simplified models with analytical solutions.

Keywords: Heat transfer experiment, thermal conductivity, finite difference, engineering education.

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Authors: S. Fawzia, M. A. Karim

Abstract:

The use of externally bonded Carbon Fiber Reinforced Polymer (CFRP) reinforcement has proven to be an effective technique to strengthen steel structures. An experimental study on CFRP bonded steel plate with double strap joint has been conducted and specimens are tested under tensile loadings. An empirical model has been developed using stress-based approach to predict ultimate capacity of the CFRP bonded steel structure. The results from the model are comparable with the experimental result with a reasonable accuracy.

Keywords: Carbon fibre reinforced polymer, shear stress, slip, effective bond, steel structure.

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Authors: Gianluca Cornetta, Abdellah Touhafi, David J. Santos, Jose Manuel Vazquez

Abstract:

A direct downconversion receiver implemented in 0.13 μm 1P8M process is presented. The circuit is formed by a single-end LNA, an active balun for conversion into balanced mode, a quadrature double-balanced passive switch mixer and a quadrature voltage-controlled oscillator. The receiver operates in the 2.4 GHz ISM band and complies with IEEE 802.15.4 (ZigBee) specifications. The circuit exhibits a very low noise figure of only 2.27 dB and dissipates only 14.6 mW with a 1.2 V supply voltage and is hence suitable for low-power applications.

Keywords: LNA, Active Balun, Passive Mixer, VCO, IEEE 802.15.4(ZigBee).

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Authors: C. A. Cortes-Quiroz, A. Azarbadegan, E. Moeendarbary

Abstract:

A new design of a planar passive T-micromixer with fin-shaped baffles in the mixing channel is presented. The mixing efficiency and the level of pressure loss in the channel have been investigated by numerical simulations in the range of Reynolds number (Re) 1 to 50. A Mixing index (Mi) has been defined to quantify the mixing efficiency, which results over 85% at both ends of the Re range, what demonstrates the micromixer can enhance mixing using the mechanisms of diffusion (lower Re) and convection (higher Re). Three geometric dimensions: radius of baffle, baffles pitch and height of the channel define the design parameters, and the mixing index and pressure loss are the performance parameters used to optimize the micromixer geometry with a multi-criteria optimization method. The Pareto front of designs with the optimum trade-offs, maximum mixing index with minimum pressure loss, is obtained. Experiments for qualitative and quantitative validation have been implemented.

Keywords: Computational fluids dynamics, fin-shaped baffle, mixing strategies, multi-objective optimization, passive micromixer.

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Authors: Kavita H. Dhanawade, Hanamant S. Dhanawade

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Heat transfer enhancement objects like extended surfaces, fins etc. are chosen for their thermal performance as well as for other design parameters depending on various applications. The present paper is on experimental study to investigate the heat transfer enhancement through wire mesh fin arrays equipped with horizontal base plate. The data used in performance analysis were obtained experimentally for the material (mild steel) for different heat inputs such as 40, 60, 80, 100 and 120 watt, by varying wire mesh diameter, fin height and spacing between two fin arrays. Using the Taguchi experimental design method, optimum design parameters and their levels were investigated. Average heat transfer coefficient was considered as a performance characteristic parameter. An L₉ (3³) orthogonal array was selected as an experimental plan. Optimum results were found by experimenting. It is observed that the wire mesh diameter and fin height have a higher impact on heat transfer coefficient as compared to spacing between two fin arrays.

Keywords: Heat transfer enhancement, finned surface, wire mesh diameter, natural convection.

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Authors: J. Geiser, R. Röhle

Abstract:

In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

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Authors: Wisam K. Hussam, Ali Alfeeli, Gergory J. Sheard

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Solar panels that use photovoltaic (PV) cells are popular for converting solar radiation into electricity. One of the major problems impacting the performance of PV panels is the overheating caused by excessive solar radiation and high ambient temperatures, which degrades the efficiency of the PV panels remarkably. To overcome this issue, an aluminum heat sink was used to dissipate unwanted heat from PV cells. The dimensions of the heat sink were determined considering the optimal fin spacing that fulfils hot climatic conditions. In this study, the effects of cooling on the efficiency and power output of a PV panel were studied experimentally. Two PV modules were used: one without and one with a heat sink. The experiments ran for 11 hours from 6:00 a.m. to 5:30 p.m. where temperature readings in the rear and front of both PV modules were recorded at an interval of 15 minutes using sensors and an Arduino microprocessor. Results are recorded for both panels simultaneously for analysis, temperate comparison, and for power and efficiency calculations. A maximum increase in the solar to electrical conversion efficiency of 35% and almost 55% in the power output were achieved with the use of a heat sink, while temperatures at the front and back of the panel were reduced by 9% and 11%, respectively.

Keywords: Photovoltaic cell, natural convection, heat sink, efficiency.

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Authors: Jatinderdeep Kaur

Abstract:

In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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Authors: Mohamed Ali

Abstract:

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. The surface temperature is assumed to vary inversely with the vertical direction x for n = -1. The skin friction at the surface scales as (x-1/2) at m = 0. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as the buoyancy parameter λ and the suction/injection parameter fw for air (Pr = 0.72) are studied. The choice of n and m ensures that the used similarity solutions are x independent. The results show that, assisting flow (λ > 0) enhancing the heat transfer coefficient along the surface for any constant value of fw. Furthermore, injection increases the heat transfer coefficient but suction reduces it at constant λ.

Keywords: Stretching surface, Boundary layers, Prescribed skin friction, Suction or injection, similarity solutions, buoyancy effects.

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Authors: Farid Arya, Trevor Hyde

Abstract:

The development of vacuum glazing represents a significant advancement in the area of low heat loss glazing systems with the potential to substantially reduce building heating and cooling loads. Vacuum glazing consists of two or more glass panes hermetically sealed together around the edge with a vacuum gap between the panes. To avoid the glass panes from collapsing and touching each other under the influence of atmospheric pressure an array of support pillars is provided between the glass panes. A high level of thermal insulation is achieved by evacuating the spaces between the glass panes to a very low pressure which greatly reduces conduction and convection within the space; therefore heat transfer through this kind of glazing is significantly lower when compared with conventional insulating glazing. However, vacuum glazing is subject to inherent stresses due to atmospheric pressure and temperature differentials which can lead to fracture of the glass panes and failure of the edge seal. A flexible edge seal has been proposed to minimise the impact of these issues. In this paper, vacuum glazing system with rigid and flexible edge seals is theoretically studied and their advantages and disadvantages are discussed.

Keywords: Flexible edge seal, stress, support pillar, vacuum glazing.

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Authors: J. B. Seo, K. J. Kim, S. W. Nam

Abstract:

In this paper, a nonlinear acoustic echo cancellation (AEC) system is proposed, whereby 3rd order Volterra filtering is utilized along with a variable step-size Gauss-Seidel pseudo affine projection (VSSGS-PAP) algorithm. In particular, the proposed nonlinear AEC system is developed by considering a double-talk situation with near-end signal variation. Simulation results demonstrate that the proposed approach yields better nonlinear AEC performance than conventional approaches.

Keywords: Acoustic echo cancellation (AEC), Volterra filtering, variable step-size, GS-PAP.

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Authors: Loralee P. Potter, Peter J. Schubert

Abstract:

Solid-state hydrogen storage using catalytically-modified porous silicon can be rapidly charged at moderate pressures (8 bar) without exothermic runaway. Discharge requires temperatures of approximately 110oC, so for larger storage vessels a means is required for thermal energy to penetrate bulk storage media. This can be realized with low-density metal foams, such as Celmet™. This study explores several material and dimensional choices of the metal foam to produce rapid heating of bulk silicon particulates. Experiments run under vacuum and in a pressurized hydrogen environment bracket conditions of empty and full hydrogen storage vessels, respectively. Curve-fitting of the heating profiles at various distances from an external heat source is used to derive both a time delay and a characteristic time constant. System performance metrics of a hydrogen storage subsystem are derived from the experimental results. A techno-economic analysis of the silicon and metal foam provides comparison with other methods of storing hydrogen for mobile and portable applications. 

Keywords: conduction, convection, kinetics, fuel cell

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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