Search results for: transfer matrix method.

Authors: H. Bhowmik, A. Faisal, Ahmed Al Yaarubi, Nabil Al Alawi

Abstract:

Experiments are conducted to analyze the steady-state and the power-on transient natural convection heat transfer from a horizontal cylinder mounted in a vertical up flow circular duct. The heat flux ranges from 177 W/m² to 2426 W/m² and the Rayleigh number ranges from 1×10⁴ to 4.35×10⁴. For natural air flow and constant heat flux condition, the effects of heat transfer around the cylinder under steady-state condition are investigated. The steady-state results compare favorably with that of the available data. The effects of transient heat transfer data on different angular position of the thermocouple (0^o, 90^o, 180^o) are also reported. It is observed that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. In the transient region, the rate of heat transfer obtained at 90^o and 180^o are higher than that of stagnation point (0^o). Finally, the dependence of the average Nusselt number on Rayleigh number for steady and transient natural convection heat transfer are analyzed, and a correlation equation is presented.

Keywords: Steady-state, transient, natural convection, Rayleigh number, Nusselt number, Fourier Number.

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Authors: Ahmed, M., Yasser A., Mahmoud H., Ahmed, A., Abdulla M. S., Nazar, S.

Abstract:

Strut-and-Tie Models (STM) for the design of concrete beams, comprising of struts, ties, nodes as the basic tools, is conceptually simple, but its realization for complex concrete structure is not straightforward and depends on flow of internal forces in the structure. STM technique has won wide acceptance for deep member and shear design. STM technique is a unified approach that considers all load effects (bending, axial, shear, and torsion) simultaneously, not just applicable to shear loading only. The present study is to portray Strut-and-Tie Modeling based on Load-Transfer-Mechanisms as a unified method to analyze, design and detailing for deep and slender concrete beams. Three shear span- effective depth ratio (a/ d) are recommended for the modeling of STM elements corresponding to dominant load paths. The study also discusses the research work conduct on effective stress of concrete, tie end anchorage, and transverse reinforcement demand under different load transfer mechanism. It is also highlighted that to make the STM versatile tool for design of beams applicable to all shear spans, the effective stress of concrete and, transverse reinforcement demand, inclined angle of strut, and anchorage requirements of tie bars is required to be correlated with respect to load transfer mechanism. The country code provisions are to be modified and updated to apply for generalized design of concrete deep and slender member using load transfer mechanism based STM technique. Examples available in literature are reanalyzed with refined STM based on load transfer mechanisms and results are compared. It is concluded from the results that proposed approach will require true reinforcement demand depending on dominant force transfer action in concrete beam.

Keywords: Deep member, Load transfer mechanism, Strut-and-Tie Model, Strut, Truss.

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Authors: Jianmin Xing

Abstract:

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )- bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ =  T M D 0 U N 0 0 V .

Keywords: Generalized module homomorphism, ring homomorphism, isomorphisms, triangular matrix rings.

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

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A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Mohsen Zahraei

Abstract:

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for Є > 0, the notion of Birkhoff-James approximate orthogonality sets for Є−higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: Rank−k numerical range, isometry, numerical range, rectangular matrix polynomials.

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Authors: C. Yesubai Rubavathi, R. Ravi

Abstract:

This paper presents the local mesh co-occurrence patterns (LMCoP) using HSV color space for image retrieval system. HSV color space is used in this method to utilize color, intensity and brightness of images. Local mesh patterns are applied to define the local information of image and gray level co-occurrence is used to obtain the co-occurrence of LMeP pixels. Local mesh co-occurrence pattern extracts the local directional information from local mesh pattern and converts it into a well-mannered feature vector using gray level co-occurrence matrix. The proposed method is tested on three different databases called MIT VisTex, Corel, and STex. Also, this algorithm is compared with existing methods, and results in terms of precision and recall are shown in this paper.

Keywords: Content-based image retrieval system, HSV color space, gray level co-occurrence matrix, local mesh pattern.

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Authors: Hiroyuki Ohsaki, Makoto Imase

Abstract:

In Grid computing, a data transfer protocol called GridFTP has been widely used for efficiently transferring a large volume of data. Currently, two versions of GridFTP protocols, GridFTP version 1 (GridFTP v1) and GridFTP version 2 (GridFTP v2), have been proposed in the GGF. GridFTP v2 supports several advanced features such as data streaming, dynamic resource allocation, and checksum transfer, by defining a transfer mode called X-block mode. However, in the literature, effectiveness of GridFTP v2 has not been fully investigated. In this paper, we therefore quantitatively evaluate performance of GridFTP v1 and GridFTP v2 using mathematical analysis and simulation experiments. We reveal the performance limitation of GridFTP v1, and quantitatively show effectiveness of GridFTP v2. Through several numerical examples, we show that by utilizing the data streaming feature, the average file transfer time of GridFTP v2 is significantly smaller than that of GridFTP v1.

Keywords: Grid Computing, GridFTP, Performance Evaluation, Queuing Theory.

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Authors: Jiashang Jiang, Yongxin Yuan

Abstract:

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords: Model updating, damped gyroscopic system, partially prescribed spectral information.

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Authors: A.S.N.Murti, D.R.V.S.R.K. Sastry, P.K. Kameswaran, T. Poorna Kantha

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In this paper, the effects of radiation, chemical reaction and double dispersion on mixed convection heat and mass transfer along a semi vertical plate are considered. The plate is embedded in a Newtonian fluid saturated non - Darcy (Forchheimer flow model) porous medium. The Forchheimer extension and first order chemical reaction are considered in the flow equations. The governing sets of partial differential equations are nondimensionalized and reduced to a set of ordinary differential equations which are then solved numerically by Fourth order Runge– Kutta method. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) against various parameters are presented in graphs. The obtained results are checked against previously published work for special cases of the problem and are found to be in good agreement.

Keywords: Radiation, Chemical reaction, Double dispersion, Mixed convection, Heat and Mass transfer

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Authors: K. Khelil, H. Ammar, K. Saouchi

Abstract:

Fiber Bragg Grating (FBG) structure is an periodically modulated optical fiber. It acts as a selective filter of wavelength whose reflected peak is called Bragg wavelength and it depends on the period of the fiber and the refractive index. The simulation of FBG is based on solving the Coupled Mode Theory equation by using the Transfer Matrix Method which is carried out using MATLAB. It is found that spectral reflectivity is shifted when the change of temperature and strain is uniform. Under non-uniform temperature or strain perturbation, the spectrum is both shifted and destroyed. In case of transverse loading, reflectivity spectrum is split into two peaks, the first is specific to X axis, and the second belongs to Y axis. FBGs are used in civil engineering to detect perturbations applied to buildings.

Keywords: Bragg wavelength, coupled mode theory, optical fiber, temperature measurement.

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Authors: Michal Spilacek, Martin Lisy, Marek Balas, Zdenek Skala

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This article is trying to determine the status of flue gas that is entering the KWH heat exchanger from combustion chamber in order to calculate the heat transfer ratio of the heat exchanger. Combination of measurement, calculation and computer simulation was used to create a useful way to approximate the heat transfer rate. The measurements were taken by a number of sensors that are mounted on the experimental device and by a thermal imaging camera. The results of the numerical calculation are in a good correspondence with the real power output of the experimental device. That result shows that the research has a good direction and can be used to propose changes in the construction of the heat exchanger, but still needs enhancements.

Keywords: Heat exchanger, heat transfer rate, numerical calculation, thermal images.

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Authors: Mohammad R. Salimpour, Amir Dehshiri

Abstract:

In the present article, we investigate experimental laminar forced convective heat transfer specifications of TiO2/water nanofluids through conduits with different cross sections. we check the effects of different parameters such as cross sectional shape, Reynolds number and concentration of nanoparticles in stable suspension on increasing convective heat transfer by designing and assembling of an experimental apparatus. The results demonstrate adding a little amount of nanoparticles to the base fluid, improves heat transfer behavior in conduits. Moreover, conduit with circular cross-section has better performance compared to the square and triangular cross sections. However, conduits with square and triangular cross sections have more relative heat transfer enchantment than conduit with circular cross section.

Keywords: Nanofluid, cross-sectional shape, TiO2, convection.

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Authors: Jing Meng, Peiyong Zhu, Houbiao Li

Abstract:

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices. To remedy this situation, we enforce the collinearity condition on the shifted system and propose shift implicitly restarted global GMRES. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solution for the shifted systems using only as many matrix vector multiplications as the solution of the seed system requires. In addition, some numerical experiments also confirm the effectiveness of our method.

Keywords: Shifted linear systems, global Krylov subspace, GLGMRESIR, GLGMRESIRsh, harmonic Ritz matrix, harmonic Ritz vector.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

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Authors: Fatiha Teklal, Bachir Kacimi, Arezki Djebbar

Abstract:

The study and application of composite materials are a truly interdisciplinary endeavor that has been enriched by contributions from chemistry, physics, materials science, mechanics and manufacturing engineering. The understanding of the interface (or interphase) in composites is the central point of this interdisciplinary effort. From the early development of composite materials of various nature, the optimization of the interface has been of major importance. Even more important, the ideas linking the properties of composites to the interface structure are still emerging. In our study, we need a direct characterization of the interface; the micromechanical tests we are addressing seem to meet this objective and we chose to use two complementary tests simultaneously. The microindentation test that can be applied to real composites and the drop test, preferred to the pull-out because of the theoretical possibility of studying systems with high adhesion (which is a priori the case with our systems). These two tests are complementary because of the principle of the model specimen used for both the first "compression indentation" and the second whose fiber is subjected to tensile stress called the drop test. Comparing the results obtained by the two methods can therefore be rewarding.

Keywords: Interface, micromechanics, pull-out, composite, fiber, matrix.

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Authors: Kavita H. Dhanawade, Hanamant S. Dhanawade, Ajay Kashikar, Shweta Matey, Mahesh Bhadane, Sunny Sarraf

Abstract:

Extended surfaces are commonly used in practice to enhance heat transfer. Most of the engineering problems require high performance heat transfer components with light weight, volumes, accommodating shapes, costs and reliability depending on industrial applications. This paper reports an experimental analysis to investigate heat transfer enhancement by forced convection using different sizes of pin-fin with rectangular slots at the center. The cross sectional area of the oblong duct was 200 mm x 80 mm. The info utilized in performance analysis was obtained experimentally for material, aluminum at 200 Watts heat input varying velocity 1 m/s to 5 m/s. Using the Taguchi experimental design method, optimum design parameters and their levels were analysed. Nusselt number and friction factor were considered as a performance characteristic parameter. An An L₉ (3³) orthogonal array was designated as an experimental proposal. Optimum results were found by experimenting. It is observed that pin-fins with different slots sizes have a better impact on Nusselt Number.

Keywords: Heat transfer coefficient, Nusselt Number, pin-fin, forced convection.

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Authors: Xia Zhou, Shouming Zhong

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

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Authors: Jiri Plocek, Petr Holec, Simona Kubickova, Barbara Pacakova, Irena Matulkova, Alice Mantlikova, Ivan Nemec, Daniel Niznansky, Jana Vejpravova

Abstract:

This article presents summary on preparation and characterization of zinc, copper, cadmium and cobalt chromite nanocrystals, embedded in an amorphous silica matrix. The ZnCr2O4/SiO2, CuCr2O4/SiO2, CdCr2O4/SiO2 and CoCr2O4/SiO2 nanocomposites were prepared by a conventional sol-gel method under acid catalysis. Final heat treatment of the samples was carried out at temperatures in the range of 900−1200 ◦C to adjust the phase composition and the crystallite size, respectively. The resulting samples were characterized by Powder X-ray diffraction (PXRD), High Resolution Transmission Electron Microscopy (HRTEM), Raman/FTIR spectroscopy and magnetic measurements. Formation of the spinel phase was confirmed in all samples. The average size of the nanocrystals was determined from the PXRD data and by direct particle size observation on HRTEM; both results were correlated. The mean particle size (reviewed by HRTEM) was in the range from ∼4 to 46 nm. The results showed that the sol-gel method can be effectively used for preparation of the spinel chromite nanoparticles embedded in the silica matrix and the particle size is driven by the type of the cation A2+ in the spinel structure and the temperature of the final heat treatment. Magnetic properties of the nanocrystals were found to be just moderately modified in comparison to the bulk phases.

Keywords: Chromite, Fourier transform infrared spectroscopy, agnetic properties, nanocomposites, Raman spectroscopy, Rietveld refinement, sol-gel method, spinel.

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Authors: N.S. Tomer, Phool Singh, Manoj Kumar

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The flow and heat transfer characteristics for natural convection along an inclined plate in a saturated porous medium with an applied magnetic field have been studied. The fluid viscosity has been assumed to be an inverse function of temperature. Assuming temperature vary as a power function of distance. The transformed ordinary differential equations have solved by numerical integration using Runge-Kutta method. The velocity and temperature profile components on the plate are computed and discussed in detail for various values of the variable viscosity parameter, inclination angle, magnetic field parameter, and real constant (λ). The results have also been interpreted with the aid of tables and graphs. The numerical values of Nusselt number have been calculated for the mentioned parameters.

Keywords: Heat Transfer, Magnetic Field, Porosity, Viscosity

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Authors: Ahmad Amiri, Hamed K. Arzani, S. N. Kazi, B. T. Chew

Abstract:

Since graphene nanoplatelet (GNP) is a promising material due to desirable thermal properties, this paper is related to the thermophysical and heat transfer performance of covalently functionalized GNP-based water/ethylene glycol nanofluid through an annular channel. After experimentally measuring thermophysical properties of prepared samples, a computational fluid dynamics study has been carried out to examine the heat transfer and pressure drop of well-dispersed and stabilized nanofluids. The effect of concentration of GNP and Reynolds number at constant wall temperature boundary condition under turbulent flow regime on convective heat transfer coefficient has been investigated. Based on the results, for different Reynolds numbers, the convective heat transfer coefficient of the prepared nanofluid is higher than that of the base fluid. Also, the enhancement of convective heat transfer coefficient and thermal conductivity increase with the increase of GNP concentration in base-fluid. Based on the results of this investigation, there is a significant enhancement on the heat transfer rate associated with loading well-dispersed GNP in base-fluid.

Keywords: Nanofluid, turbulent flow, forced convection flow, graphene, annular, annulus.

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Authors: Jason P. Michaud, Connor P. Speer, David A. Miller, David S. Nobes

Abstract:

An experimental study on finned-tube radiators has been conducted. Three radiators found in desktop computers sized for 120 mm fans were tested in steady and pulsatile flows of ambient air over a Reynolds number range of  50 < Re < 900. Water at 60 °C was circulated through the radiators to maintain a constant fin temperature during the tests. For steady flow, it was found that the heat transfer rate increased linearly with the mass flow rate of air. The pulsatile flow experiments showed that frequency of pulsation had a negligible effect on the heat transfer rate for the range of frequencies tested (0.5 Hz – 2.5 Hz). For all three radiators, the heat transfer rate was decreased in the case of pulsatile flow. Linear heat transfer correlations for steady and pulsatile flow were calculated in terms of Reynolds number and Nusselt number.

Keywords: Finned-tube heat exchangers, radiators, heat transfer correlations, pulsatile flow, computer radiators.

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Authors: Samindi Samarakoon, Ørjan Sletbakk Vie, Remi Kleiven Fjelldal

Abstract:

White concrete facade elements are widely used in construction industry. It is challenging to achieve the desired workability in casting of white concrete elements. Particle Matrix model was used for proportioning the self-compacting white concrete (SCWC) to control segregation and bleeding and to improve workability. The paper presents how to reach the target slump flow while controlling bleeding and segregation in SCWC. The amount of aggregates, binders and mixing water, as well as type and dosage of superplasticizer (SP) to be used are the major factors influencing the properties of SCWC. Slump flow and compressive strength tests were carried out to examine the performance of SCWC, and the results indicate that the particle matrix model could produce successfully SCWC controlling segregation and bleeding.

Keywords: Mix design, particle, matrix model, white concrete.

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Authors: S.G.Venkatesh, S.K.Ayyaswamy, G.Hariharan

Abstract:

In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

Keywords: Haar wavelet method, Bratu's problem, boundary value problems, initial value problems, adomain decomposition method.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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Authors: Jeong Hyun Kim, Gyo Woo Lee

Abstract:

In this study, heat release performances of the three extruded-type heat sinks can be used in inverter for solar power generation were evaluated. Numbers of fins in the heat sinks (namely E-38, E-47 and E-76) were 38, 47 and 76, respectively. Heat transfer areas of them were 1.8, 1.9 and 2.8m². The heat release performances of E-38, E-47 and E-76 heat sinks were measured as 79.6, 81.6 and 83.2%, respectively. The results of heat release performance show that the larger amount of heat transfer area the higher heat release rate. While on the other, in this experiment, variations of mass flow rates caused by different cross sectional areas of the three heat sinks may not be the major parameter of the heat release. Despite the 47.4% increment of heat transfer area of E-76 heat sink than that of E-47 one, its heat release rate was higher by only 2.0%; this suggests that its heat transfer area need to be optimized.

Keywords: Solar Inverter, Heat Sink, Forced Convection, Heat Transfer, Performance Evaluation.

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Authors: Yue-Tzu Yang, Shu-Ching Liao

Abstract:

This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm² ≦q"≦ 40W/cm². The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.

Keywords: Microchannel heat sinks, Conjugate heat transfer, Optimization, Genetic algorithm method.

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Authors: Mehran Yazdi, Kazem Gheysari

Abstract:

In this paper, we propose an approach for the classification of fingerprint databases. It is based on the fact that a fingerprint image is composed of regular texture regions that can be successfully represented by co-occurrence matrices. So, we first extract the features based on certain characteristics of the cooccurrence matrix and then we use these features to train a neural network for classifying fingerprints into four common classes. The obtained results compared with the existing approaches demonstrate the superior performance of our proposed approach.

Keywords: Biometrics, fingerprint classification, gray level cooccurrence matrix, regular texture representation.

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Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: A. D. Parekh, P. R. Tailor, Tejendra Patel

Abstract:

Capacity and efficiency of any refrigerating system diminish rapidly as the difference between the evaporating and condensing temperature is increased by a reduction in the evaporator temperature. The single stage vapour compression refrigeration system using various refrigerants are limited to an evaporator temperature of -40 0C. Below temperature of -40 0C the either cascade refrigeration system or multi stage vapour compression system is employed. Present work describes thermal design of condenser (HTS), cascade condenser and evaporator (LTS) of R404A-R508B and R410A-R23 cascade refrigeration system. Heat transfer area of condenser, cascade condenser and evaporator for both systems are compared and the effect of condenser and evaporator temperature on heat-transfer area for both systems is studied under same operating condition. The results shows that the required heat-transfer area of condenser and cascade condenser for R410A-R23 cascade system is lower than the R404A-R508B cascade system but heat transfer area of evaporator is similar for both the system. The heat transfer area of condenser and cascade condenser decreases with increase in condenser temperature (Tc), whereas the heat transfer area of cascade condenser and evaporator increases with increase in evaporator temperature (Te).

Keywords: Heat-transfer area, R410A, R404A, R508B, R23, Refrigeration system, Thermal design

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