Search results for: inverse methods

Authors: Pinho C., Madaleno M.

Abstract:

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined for the entire sample period, revealing some curious features about market evolution, where data fitting performances of the five models are compared. It is shown that variance gamma processes provide relatively better results and that implied volatility shows significant differences through time, having increasingly evolved. Volatility changes for changed uncertainty, or else, increasing futures prices and there is evidence for the need to account for seasonality when modelling both electricity spot/futures prices and volatility.

Keywords: Calibration, Electricity Markets, Implied Volatility, Lévy Models, Options on Futures, Pricing

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, Dynamics, Lagrange, Parallel platform.

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Authors: Ming-Hui Lee, Iau-Teh Wang

Abstract:

The innovative fuzzy estimator is used to estimate the ground motion acceleration of the retaining structure in this study. The Kalman filter without the input term and the fuzzy weighting recursive least square estimator are two main portions of this method. The innovation vector can be produced by the Kalman filter, and be applied to the fuzzy weighting recursive least square estimator to estimate the acceleration input over time. The excellent performance of this estimator is demonstrated by comparing it with the use of difference weighting function, the distinct levels of the measurement noise covariance and the initial process noise covariance. The availability and the precision of the proposed method proposed in this study can be verified by comparing the actual value and the one obtained by numerical simulation.

Keywords: Earthquake, Fuzzy Estimator, Kalman Filter, Recursive Least Square Estimator.

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Authors: Ryosuke Ito, Goro Obinata, Chikara Nagai, Youngwoo Kim

Abstract:

This paper proposes a new parameter identification method based on Linear Fractional Transformation (LFT). It is assumed that the target linear system includes unknown parameters. The parameter deviations are separated from a nominal system via LFT, and identified by organizing I/O signals around the separated deviations of the real system. The purpose of this paper is to apply LFT to simultaneously identify the parameter deviations in systems with fewer outputs than unknown parameters. As a fundamental example, this method is implemented to one degree of freedom vibratory system. Via LFT, all physical parameters were simultaneously identified in this system. Then, numerical simulations were conducted for this system to verify the results. This study shows that all the physical parameters of a system with fewer outputs than unknown parameters can be effectively identified simultaneously using LFT.

Keywords: Identification, Linear Fractional Transformation, Right inverse system

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Authors: Emad Hazbkhah. Abdolreza Zahiri, Hossein Ghorbanizade Kharazi

Abstract:

Reducing river sediments through path correction and preservation of river walls leads to considerable reduction of sedimentation at the pumping stations. Path correction and preservation of walls is not limited to one particular method but, depending on various conditions, a combination of several methods can be employed. In this article, we try to review and evaluate methods for preservation of river banks in order to reduce sediments.

Keywords: Erosion , River Banks , Sediments

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Authors: Jagabondhu Hazra, Avinash Sinha

Abstract:

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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Authors: Sameh H. Ghwanmeh

Abstract:

In this study a clustering technique has been implemented which is K-Means like with hierarchical initial set (HKM). The goal of this study is to prove that clustering document sets do enhancement precision on information retrieval systems, since it was proved by Bellot & El-Beze on French language. A comparison is made between the traditional information retrieval system and the clustered one. Also the effect of increasing number of clusters on precision is studied. The indexing technique is Term Frequency * Inverse Document Frequency (TF * IDF). It has been found that the effect of Hierarchical K-Means Like clustering (HKM) with 3 clusters over 242 Arabic abstract documents from the Saudi Arabian National Computer Conference has significant results compared with traditional information retrieval system without clustering. Additionally it has been found that it is not necessary to increase the number of clusters to improve precision more.

Keywords: Hierarchical K-mean like clustering (HKM), Kmeans, cluster centroids, initial partition, and document distances

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Authors: Seo Young Kim, Toshimitsu Hamasaki

Abstract:

Microarrays have become the effective, broadly used tools in biological and medical research to address a wide range of problems, including classification of disease subtypes and tumors. Many statistical methods are available for analyzing and systematizing these complex data into meaningful information, and one of the main goals in analyzing gene expression data is the detection of samples or genes with similar expression patterns. In this paper, we express and compare the performance of several clustering methods based on data preprocessing including strategies of normalization or noise clearness. We also evaluate each of these clustering methods with validation measures for both simulated data and real gene expression data. Consequently, clustering methods which are common used in microarray data analysis are affected by normalization and degree of noise and clearness for datasets.

Keywords: Gene expression, clustering, data preprocessing.

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Authors: R.Goudarzizadeh, S.H.Mousavi Jahromi, N.Hedayat

Abstract:

This paper analytically investigates the 3D flow pattern at the confluences of two rectangular channels having 900 angles using Navier-Stokes equations based on Reynolds Stress Turbulence Model (RSM). The equations are solved by the Finite- Volume Method (FVM) and the flow is analyzed in terms of steadystate (single-phased) conditions. The Shumate experimental findings were used to test the validity of data. Comparison of the simulation model with the experimental ones indicated a close proximity between the flow patterns of the two sets. Effects of the discharge ratio on separation zone dimensions created in the main-channel downstream of the confluence indicated an inverse relation, where a decrease in discharge ratio, will entail an increase in the length and width of the separation zone. The study also found the model as a powerful analytical tool in the feasibility study of hydraulic engineering projects.

Keywords: 900 confluence angle, flow separation zone, numerical modeling, turbulent flow.

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Authors: R.Goudarzizadeh, N.Hedayat, S.H.Mousavi Jahromi

Abstract:

Channel junctions can be analyzed in two ways of division (lateral intake) and combined flows (confluence). The present paper investigates 3D flow pattern at lateral intake using Navier-Stokes equation and κ -ε (RNG) turbulent model. The equations are solved by Finite-Volume Method (FVM) and results are compared with the experimental data of (Barkdoll, B.D., 1997) to test the validity of the findings. Comparison of the results with the experimental data indicated a close proximity between the two sets of data which suggest a very close simulation. Results further indicated an inverse relation between the effects of discharge ratio ( r Q ) on the length and width of the separation zone. In other words, as the discharge ration increases, the length and width of separation zone decreases.

Keywords: 900 junction, flow division, turbulent flow, numerical modeling, flow separation zone.

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Authors: Manpreet Singh, Parvinder Singh Sandhu, Reet Kamal Kaur

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Protein structure determination and prediction has been a focal research subject in the field of bioinformatics due to the importance of protein structure in understanding the biological and chemical activities of organisms. The experimental methods used by biotechnologists to determine the structures of proteins demand sophisticated equipment and time. A host of computational methods are developed to predict the location of secondary structure elements in proteins for complementing or creating insights into experimental results. However, prediction accuracies of these methods rarely exceed 70%.

Keywords: Protein, Secondary Structure, Prediction, DNA, RNA.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

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Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: Xuewen Yu, Danhui Dan

Abstract:

The identification of impact loads and some hard-to-obtain system parameters is crucial for analysis, validation, and evaluation activities in the engineering field. This paper proposes a method based on 1D-CNN to identify impact loads and partial system parameters from the measured responses. To this end, forward computations are conducted to provide datasets consisting of triples (parameter θ, input u, output y). Two neural networks are then trained: one to learn the mapping from output y to input u and another to learn the mapping from input and output (u, y) to parameter θ. Subsequently, by feeding the measured output response into the trained neural networks, the input impact load and system parameter can be calculated, respectively. The method is tested on two simulated examples and shows sound accuracy in estimating the impact load (waveform and location) and system parameter.

Keywords: Convolutional neural network, impact load identification, system parameter identification, inverse problem.

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Authors: Min Sang Lee, Hee Jae Shin, In Pyo Cha, Sun Ho Ko, Hyun Kyung Yoon, Hong Gun Kim, Lee Ku Kwac

Abstract:

The prepreg process among the CFRP (Carbon Fiber Reinforced Plastic) forming methods is the short term of ‘Pre-impregnation’, which is widely used for aerospace composites that require a high quality property such as a fiber-reinforced woven fabric, in which an epoxy hardening resin is impregnated the reality. However, that this process requires continuous researches and developments for its commercialization because the delamination characteristically develops between the layers when a great weight is loaded from outside to supplement such demerit, three lamination methods among the prepreg lamination methods of CFRP were designed to minimize the delamination between the layers due to external impacts. Further, the newly designed methods and the existing lamination methods were analyzed through a mechanical characteristic test, Interlaminar Shear Strength test. The Interlaminar Shear Strength test result confirmed that the newly proposed three lamination methods, i.e. the Roll, Half and Zigzag laminations, presented more excellent strengths compared to the conventional Ply lamination. The interlaminar shear strength in the roll method with relatively dense fiber distribution was approximately 1.75% higher than that in the existing ply lamination method, and in the half method, it was approximately 0.78% higher.

Keywords: Carbon Fiber Reinforced Plastic (CFRP), Pre-Impregnation, Laminating Method, Interlaminar Shear Strength (ILSS).

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Authors: Kei Kawamorita, Ryouta Kasahara, Yuuki Mochizuki, Kenichiro Noguchi

Abstract:

A separation-kernel-based operating system (OS) has been designed for use in secure embedded systems by applying formal methods to the design of the separation-kernel part. The separation kernel is a small OS kernel that provides an abstract distributed environment on a single CPU. The design of the separation kernel was verified using two formal methods, the B method and the Spin model checker. A newly designed semi-formal method, the extended state transition method, was also applied. An OS comprising the separation-kernel part and additional OS services on top of the separation kernel was prototyped on the Intel IA-32 architecture. Developing and testing of a prototype embedded application, a point-of-sale application, on the prototype OS demonstrated that the proposed architecture and the use of formal methods to design its kernel part are effective for achieving a secure embedded system having a high-assurance separation kernel.

Keywords: B method, embedded systems, extended state transition, formal methods, separation kernel, Spin.

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Authors: Peyman Shadman Heidari, Mohammad Khorasani

Abstract:

The principal purpose of this article is to present a new method based on Adaptive Neural Network Fuzzy Inference System (ANFIS) to generate additional artificial earthquake accelerograms from presented data, which are compatible with specified response spectra. The proposed method uses the learning abilities of ANFIS to develop the knowledge of the inverse mapping from response spectrum to earthquake records. In addition, wavelet packet transform is used to decompose specified earthquake records and then ANFISs are trained to relate the response spectrum of records to their wavelet packet coefficients. Finally, an interpretive example is presented which uses an ensemble of recorded accelerograms to demonstrate the effectiveness of the proposed method.

Keywords: Adaptive Neural Network Fuzzy Inference System, Wavelet Packet Transform, Response Spectrum.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

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Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: Pelin Yildiz

Abstract:

The term interactive education indicates the meaning related with multidisciplinary aspects of distance education following contemporary means around a common basis with different functional requirements. The aim of this paper is to reflect the new techniques in education with the new methods and inventions. These methods are better supplied by interactivity. The integration of interactive facilities in the discipline of education with distance learning is not a new concept but in addition the usage of these methods on design issue is newly being adapted to design education. In this paper the general approach of this method and after the analysis of different samples, the advantages and disadvantages of these approaches are being identified. The method of this paper is to evaluate the related samples and then analyzing the main hypothesis. The main focus is to mention the formation processes of this education. Technological developments in education should be filtered around the necessities of the design education and the structure of the system could then be formed or renewed. The conclusion indicates that interactive methods of education in design issue is a meaning capturing not only technical and computational intelligence aspects but also aesthetical and artistic approaches coming together around the same purpose.

Keywords: Interactive education, distance learning, designeducation, computational intelligence.

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Authors: L. Melecký

Abstract:

Measurement of competitiveness between countries or regions is an important topic of many economic analysis and scientific papers. In European Union (EU), there is no mainstream approach of competitiveness evaluation and measuring. There are many opinions and methods of measurement and evaluation of competitiveness between states or regions at national and European level. The methods differ in structure of using the indicators of competitiveness and ways of their processing. The aim of the paper is to analyze main sources of competitive potential of the EU Member States with the help of Factor analysis (FA) and to classify the EU Member States to homogeneous units (clusters) according to the similarity of selected indicators of competitiveness factors by Cluster analysis (CA) in reference years 2000 and 2011. The theoretical part of the paper is devoted to the fundamental bases of competitiveness and the methodology of FA and CA methods. The empirical part of the paper deals with the evaluation of competitiveness factors in the EU Member States and cluster comparison of evaluated countries by cluster analysis. 

Keywords: Competitiveness, cluster analysis, EU, factor analysis, multivariate methods.

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Authors: Guy Rosman, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel

Abstract:

We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.

Keywords: Dimensionality reduction, manifold learning, multidimensional scaling, geodesic distance, boundary detection.

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Authors: Arkady Bolotin

Abstract:

One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way function. The assumption implies that at the macroscopic level the Schrödinger equation becomes unfeasible to compute. This unfeasibility plays a role of limit of the validity of the linear Schrödinger equation.

Keywords: One-way functions, P versus NP problem, quantummeasurements.

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Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Renáta Iváncsy, Sándor Juhász

Abstract:

Web usage mining has become a popular research area, as a huge amount of data is available online. These data can be used for several purposes, such as web personalization, web structure enhancement, web navigation prediction etc. However, the raw log files are not directly usable; they have to be preprocessed in order to transform them into a suitable format for different data mining tasks. One of the key issues in the preprocessing phase is to identify web users. Identifying users based on web log files is not a straightforward problem, thus various methods have been developed. There are several difficulties that have to be overcome, such as client side caching, changing and shared IP addresses and so on. This paper presents three different methods for identifying web users. Two of them are the most commonly used methods in web log mining systems, whereas the third on is our novel approach that uses a complex cookie-based method to identify web users. Furthermore we also take steps towards identifying the individuals behind the impersonal web users. To demonstrate the efficiency of the new method we developed an implementation called Web Activity Tracking (WAT) system that aims at a more precise distinction of web users based on log data. We present some statistical analysis created by the WAT on real data about the behavior of the Hungarian web users and a comprehensive analysis and comparison of the three methods

Keywords: Data preparation, Tracking individuals, Web useridentification, Web usage mining

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: R. Manaffar, R. Maleki, S. Zare, N. Agh, S. Soltanian, B. Sehatnia, P. Sorgeloos, P. Bossier, G. Van Stappen

Abstract:

Artemia is one of the most conspicuous invertebrates associated with aquaculture. It can be considered as a model organism, offering numerous advantages for comprehensive and multidisciplinary studies using morphologic or molecular methods. Since DNA extraction is an important step of any molecular experiment, a new and a rapid method of DNA extraction from adult Artemia was described in this study. Besides, the efficiency of this technique was compared with two widely used alternative techniques, namely Chelex® 100 resin and SDS-chloroform methods. Data analysis revealed that the new method is the easiest and the most cost effective method among the other methods which allows a quick and efficient extraction of DNA from the adult animal.

Keywords: APD, Artemia, DNA extraction, Molecularexperiments

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Authors: M. S. Khurram, S. A. Memon, S. Khan

Abstract:

Bed voidage behavior among different flow regimes for Geldart A, B, and D particles (fluid catalytic cracking catalyst (FCC), particle A and glass beads) of diameter range 57-872 μm, apparent density 1470-3092 kg/m³, and bulk density range 890-1773 kg/m³ were investigated in a gas-solid circulating fluidized bed of 0.1 m-i.d. and 2.56 m-height of plexi-glass. Effects of variables (gas velocity, particle properties, and static bed height) were analyzed on bed voidage. The axial voidage profile showed a typical trend along the riser: a dense bed at the lower part followed by a transition in the splash zone and a lean phase in the freeboard. Bed expansion and dense bed voidage increased with an increase of gas velocity as usual. From experimental results, a generalized model relationship based on inverse fluidization number for dense bed voidage from bubbling to fast fluidization regimes was presented.

Keywords: Axial voidage, circulating fluidized bed, splash zone, static bed.

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Authors: Gholamreza Ghodrati Amiri, Mojtaba Jafarian Abyaneh, Ali Zare Hosseinzadeh

Abstract:

This paper presents an effective model updating strategy for damage localization and quantification in frames by defining damage detection problem as an optimization issue. A generalized version of the Modal Residual Force (MRF) is employed for presenting a new damage-sensitive cost function. Then, Grey Wolf Optimization (GWO) algorithm is utilized for solving suggested inverse problem and the global extremums are reported as damage detection results. The applicability of the presented method is investigated by studying different damage patterns on the benchmark problem of the IASC-ASCE, as well as a planar shear frame structure. The obtained results emphasize good performance of the method not only in free-noise cases, but also when the input data are contaminated with different levels of noises.

Keywords: Frame, grey wolf optimization algorithm, modal residual force, structural damage detection.

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Authors: Nan-Chyuan Tsai, Sheng-Liang Hsu

Abstract:

An innovative tri-axes micro-power receiver is proposed. The tri-axes micro-power receiver consists of two sets 3-D micro-solenoids and one set planar micro-coils in which iron core is embedded. The three sets of micro-coils are designed to be orthogonal to each other. Therefore, no matter which direction the flux is present along, the magnetic energy can be harvested and transformed into electric power. Not only dead space of receiving power is mostly reduced, but also transformation efficiency of electromagnetic energy to electric power can be efficiently raised. By employing commercial software, Ansoft Maxwell, the preliminary simulation results verify that the proposed micro-power receiver can efficiently pick up the energy transmitted by magnetic power source. As to the fabrication process, the isotropic etching technique is employed to micro-machine the inverse-trapezoid fillister so that the copper wire can be successfully electroplated. The adhesion between micro-coils and fillister is much enhanced.

Keywords: Wireless Power Transmission, Magnetic Flux, Tri-axes Micro-power Receiver

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Authors: Jörg Lassig, Stefanie Thiem

Abstract:

The objective of this paper is the introduction to a unified optimization framework for research and education. The OPTILIB framework implements different general purpose algorithms for combinatorial optimization and minimum search on standard continuous test functions. The preferences of this library are the straightforward integration of new optimization algorithms and problems as well as the visualization of the optimization process of different methods exploring the search space exclusively or for the real time visualization of different methods in parallel. Further the usage of several implemented methods is presented on the basis of two use cases, where the focus is especially on the algorithm visualization. First it is demonstrated how different methods can be compared conveniently using OPTILIB on the example of different iterative improvement schemes for the TRAVELING SALESMAN PROBLEM. A second study emphasizes how the framework can be used to find global minima in the continuous domain.

Keywords: Global Optimization Heuristics, Particle Swarm Optimization, Ensemble Based Threshold Accepting, Ruin and Recreate

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Authors: M. Norouzi, M. H. Kayhani, M. R. H. Nobari, M. Karimi Demneh

Abstract:

In this paper, fully developed flow and heat transfer of viscoelastic materials in curved ducts with square cross section under constant heat flux have been investigated. Here, staggered mesh is used as computational grids and flow and heat transfer parameters have been allocated in this mesh with marker and cell method. Numerical solution of governing equations has being performed with FTCS finite difference method. Furthermore, Criminale-Eriksen- Filbey (CEF) constitutive equation has being used as viscoelastic model. CEF constitutive equation is a suitable model for studying steady shear flow of viscoelastic materials which is able to model both effects of the first and second normal stress differences. Here, it is shown that the first and second normal stresses differences have noticeable and inverse effect on secondary flows intensity and mean Nusselt number which is the main novelty of current research.

Keywords: Viscoelastic, fluid flow, heat convection, CEF model, curved duct, square cross section.

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