Search results for: Boussinesq's approximation and Mean Nusselt number.

Authors: Le Hieu Giang, Truong Nguyen Luan Vu, Le Linh

Abstract:

In this paper, the analytical tuning rules of IMC-PID controller are presented for the multivariable Smith predictor that involved the ideal decoupling. Accordingly, the decoupler is first introduced into the multivariable Smith predictor control system by a well-known approach of ideal decoupling, which is compactly extended for general nxn multivariable processes and the multivariable Smith predictor controller is then obtained in terms of the multiple single-loop Smith predictor controllers. The tuning rules of PID controller in series with filter are found by using Maclaurin approximation. Many multivariable industrial processes are employed to demonstrate the simplicity and effectiveness of the presented method. The simulation results show the superior performances of presented method in compared with the other methods.

Keywords: Ideal decoupler, IMC-PID controller, multivariable Smith predictor, Maclaurin approximation.

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Authors: Sudhakar G

Abstract:

In this paper a new concept of partial complement of a graph G is introduced and using the same a new graph parameter, called completion number of a graph G, denoted by c(G) is defined. Some basic properties of graph parameter, completion number, are studied and upperbounds for completion number of classes of graphs are obtained , the paper includes the characterization also.

Keywords: Completion Number, Maximum Independent subset, Partial complements, Partial self complementary

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Authors: Yongxin Yuan

Abstract:

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Keywords: Partially prescribed spectral information, symmetric arrow-head matrix, inverse problem, optimal approximation.

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Authors: Airoldi G., Bumby J. R., Dominy C., G.L. Ingram, Lim C. H., Mahkamov K., N. L. Brown, A. Mebarki, M. Shanel

Abstract:

Axial Flux Permanent Magnet (AFPM) Machines require effective cooling due to their high power density. The detrimental effects of overheating such as degradation of the insulation materials, magnets demagnetization, and increase of Joule losses are well known. This paper describes the CFD simulations performed on a test rig model of an air cooled Axial Flux Permanent Magnet (AFPM) generator built at Durham University to identify the temperatures and heat transfer coefficient on the stator. The Reynolds Averaged Navier-Stokes and the Energy equations are solved and the flow pattern and heat transfer developing inside the machine are described. The Nusselt number on the stator surfaces has been found. The dependency of the heat transfer on the flow field is described temperature field obtained. Tests on an experimental are undergoing in order to validate the CFD results.

Keywords: Axial flux permanent magnet machines, thermal modeling, CFD.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

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The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.

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Authors: Kemalettin Erbatur, Özer Koca, Evrim Taşkıran, Metin Yılmaz, Utku Seven

Abstract:

Recent fifteen years witnessed fast improvements in the field of humanoid robotics. The human-like robot structure is more suitable to human environment with its supreme obstacle avoidance properties when compared with wheeled service robots. However, the walking control for bipedal robots is a challenging task due to their complex dynamics. Stable reference generation plays a very important role in control. Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable walking reference generation of biped walking robots. This paper follows this main approach too. We propose a natural and continuous ZMP reference trajectory for a stable and human-like walk. The ZMP reference trajectories move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass trajectory is obtained from predefined ZMP reference trajectories by a Fourier series approximation method. The Gibbs phenomenon problem common with Fourier approximations of discontinuous functions is avoided by employing continuous ZMP references. Also, these ZMP reference trajectories possess pre-assigned single and double support phases, which are very useful in experimental tuning work. The ZMP based reference generation strategy is tested via threedimensional full-dynamics simulations of a 12-degrees-of-freedom biped robot model. Simulation results indicate that the proposed reference trajectory generation technique is successful.

Keywords: Biped robot, Linear Inverted Pendulum Model, Zero Moment Point, Fourier series approximation.

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Authors: H.Y. Lai, S. C. Chang, W. L. Chen

Abstract:

The hydrodynamic and thermal lattice Boltzmann methods are applied to investigate the turbulent convective heat transfer in the wavy channel flows. In this study, the turbulent phenomena are modeling by large-eddy simulations with the Smagorinsky model. As a benchmark, the laminar and turbulent backward-facing step flows are simulated first. The results give good agreement with other numerical and experimental data. For wavy channel flows, the distribution of Nusselt number and the skin-friction coefficients are calculated to evaluate the heat transfer effect and the drag force. It indicates that the vortices at the trough would affect the magnitude of drag and weaken the heat convection effects on the wavy surface. In turbulent cases, if the amplitude of the wavy boundary is large enough, the secondary vortices would be generated at troughs and contribute to the heat convection. Finally, the effects of different Re on the turbulent transport phenomena are discussed.

Keywords: Heat transfer, lattice Boltzmann method, turbulence, wavy channel.

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

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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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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: M-J. Huang, C-J. Huang, L-C. Chen

Abstract:

In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.

Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.

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Authors: Marina Franulovic, Robert Basan, Bozidar Krizan

Abstract:

Constitutive modeling of material behavior is becoming increasingly important in prediction of possible failures in highly loaded engineering components, and consequently, optimization of their design. In order to account for large number of phenomena that occur in the material during operation, such as kinematic hardening effect in low cycle fatigue behavior of steels, complex nonlinear material models are used ever more frequently, despite of the complexity of determination of their parameters. As a method for the determination of these parameters, genetic algorithm is good choice because of its capability to provide very good approximation of the solution in systems with large number of unknown variables. For the application of genetic algorithm to parameter identification, inverse analysis must be primarily defined. It is used as a tool to fine-tune calculated stress-strain values with experimental ones. In order to choose proper objective function for inverse analysis among already existent and newly developed functions, the research is performed to investigate its influence on material behavior modeling.

Keywords: Genetic algorithm, kinematic hardening, material model, objective function

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Authors: Li Long, Thomas Ortlepp

Abstract:

The transport properties of carriers in polycrystalline silicon film affect the performance of polycrystalline silicon-based devices. They depend strongly on the grain structure, grain boundary trap properties and doping concentration, which in turn are determined by the film deposition and processing conditions. Based on the properties of charge carriers, phonons, grain boundaries and their interactions, the thermoelectric properties of polycrystalline silicon are analyzed with the relaxation time approximation of the Boltzmann transport equation. With this approach, thermal conductivity, electrical conductivity and Seebeck coefficient as a function of grain size, trap properties and doping concentration can be determined. Experiment on heavily doped polycrystalline silicon is carried out and measurement results are compared with the model.

Keywords: Conductivity, polycrystalline silicon, relaxation time approximation, Seebeck coefficient, thermoelectric property.

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Authors: Edlira Donefski, Tina Donefski, Lorenc Ekonomi

Abstract:

Edgeworth Approximation, Bootstrap and Monte Carlo Simulations have a considerable impact on the achieving certain results related to different problems taken into study. In our paper, we have treated a financial case related to the effect that have the components of a Cash-Flow of one of the most successful businesses in the world, as the financial activity, operational activity and investing activity to the cash and cash equivalents at the end of the three-months period. To have a better view of this case we have created a Vector Autoregression model, and after that we have generated the impulse responses in the terms of Asymptotic Analysis (Edgeworth Approximation), Monte Carlo Simulations and Residual Bootstrap based on the standard errors of every series created. The generated results consisted of the common tendencies for the three methods applied, that consequently verified the advantage of the three methods in the optimization of the model that contains many variants.

Keywords: Autoregression, Bootstrap, Edgeworth Expansion, Monte Carlo Method.

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Authors: Anam Rafique, Syed Sohail Ahmed

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One of the essential components of much of DSP application is noise cancellation. Changes in real time signals are quite rapid and swift. In noise cancellation, a reference signal which is an approximation of noise signal (that corrupts the original information signal) is obtained and then subtracted from the noise bearing signal to obtain a noise free signal. This approximation of noise signal is obtained through adaptive filters which are self adjusting. As the changes in real time signals are abrupt, this needs adaptive algorithm that converges fast and is stable. Least mean square (LMS) and normalized LMS (NLMS) are two widely used algorithms because of their plainness in calculations and implementation. But their convergence rates are small. Adaptive averaging filters (AFA) are also used because they have high convergence, but they are less stable. This paper provides the comparative study of LMS and Normalized NLMS, AFA and new enhanced average adaptive (Average NLMS-ANLMS) filters for noise cancelling application using speech signals.

Keywords: AFA, ANLMS, LMS, NLMS.

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Authors: S. Boria

Abstract:

In the last years, the crashworthiness of an automotive body structure can be improved, since the beginning of the design stage, thanks to the development of specific optimization tools. It is well known how the finite element codes can help the designer to investigate the crashing performance of structures under dynamic impact. Therefore, by coupling nonlinear mathematical programming procedure and statistical techniques with FE simulations, it is possible to optimize the design with reduced number of analytical evaluations. In engineering applications, many optimization methods which are based on statistical techniques and utilize estimated models, called meta-models, are quickly spreading. A meta-model is an approximation of a detailed simulation model based on a dataset of input, identified by the design of experiments (DOE); the number of simulations needed to build it depends on the number of variables. Among the various types of meta-modeling techniques, Kriging method seems to be excellent in accuracy, robustness and efficiency compared to other ones when applied to crashworthiness optimization. Therefore the application of such meta-model was used in this work, in order to improve the structural optimization of a bumper for a racing car in composite material subjected to frontal impact. The specific energy absorption represents the objective function to maximize and the geometrical parameters subjected to some design constraints are the design variables. LS-DYNA codes were interfaced with LS-OPT tool in order to find the optimized solution, through the use of a domain reduction strategy. With the use of the Kriging meta-model the crashworthiness characteristic of the composite bumper was improved.

Keywords: Composite material, crashworthiness, finite element analysis, optimization.

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Authors: V. T. S. Dao, T. G. Etoh, C. Vo Le, H. D. Nguyen, K. Takehara, T. Akino, K. Nishi

Abstract:

We present an explicit expression to estimate driving voltage attenuation through RC networks representation of an ultrahigh- speed image sensor. Elmore delay metric for a fundamental RC chain is employed as the first-order approximation. By application of dimensional analysis to SPICE simulation data, we found a simple expression that significantly improves the accuracy of the approximation. Estimation error of the resultant expression for uniform RC networks is less than 2%. Similarly, another simple closed-form model to estimate 50 % delay through fundamental RC networks is also derived with sufficient accuracy. The framework of this analysis can be extended to address delay or attenuation issues of other VLSI structures.

Keywords: Dimensional Analysis, Elmore model, RC network, Signal Attenuation, Ultra-High-Speed Image Sensor.

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Authors: S. Khali, R. Nebbali, K. Bouhadef

Abstract:

A numerical investigation is performed for non Newtonian fluids flow between two concentric cylinders. The D2Q9 lattice Boltzmann model developed from the Bhatangar-Gross-Krook (LBGK) approximation is used to obtain the flow field for fluids obeying to the power-law model. The inner and outer cylinders rotate in the same and the opposite direction while the end walls are maintained at rest. The combined effects of the Reynolds number (Re) of the inner and outer cylinders, the radius ratio (η) as well as the power-law index (n) on the flow characteristics are analyzed for an annular space of a finite aspect ratio (Γ). Two flow modes are obtained: a primary mode (laminar stable regime) and a secondary mode (laminar unstable regime). The so obtained flow structures are different from one mode to another. The transition critical Reynolds number Re_c from the primary to the secondary mode is analyzed for the co-courant and counter-courant flows. This critical value increases as n increases. The prediction of the swirling flow of non Newtonians fluids in axisymmetric geometries is shown in the present work.

Keywords: Taylor-Couette flows, non Newtonian fluid, Lattice Boltzmann method.

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Authors: Perumal Kumar, Rajamohan Ganesan

Abstract:

Addition of milli or micro sized particles to the heat transfer fluid is one of the many techniques employed for improving heat transfer rate. Though this looks simple, this method has practical problems such as high pressure loss, clogging and erosion of the material of construction. These problems can be overcome by using nanofluids, which is a dispersion of nanosized particles in a base fluid. Nanoparticles increase the thermal conductivity of the base fluid manifold which in turn increases the heat transfer rate. Nanoparticles also increase the viscosity of the basefluid resulting in higher pressure drop for the nanofluid compared to the base fluid. So it is imperative that the Reynolds number (Re) and the volume fraction have to be optimum for better thermal hydraulic effectiveness. In this work, the heat transfer enhancement using aluminium oxide nanofluid using low and high volume fraction nanofluids in turbulent pipe flow with constant wall temperature has been studied by computational fluid dynamic modeling of the nanofluid flow adopting the single phase approach. Nanofluid, up till a volume fraction of 1% is found to be an effective heat transfer enhancement technique. The Nusselt number (Nu) and friction factor predictions for the low volume fractions (i.e. 0.02%, 0.1 and 0.5%) agree very well with the experimental values of Sundar and Sharma (2010). While, predictions for the high volume fraction nanofluids (i.e. 1%, 4% and 6%) are found to have reasonable agreement with both experimental and numerical results available in the literature. So the computationally inexpensive single phase approach can be used for heat transfer and pressure drop prediction of new nanofluids.

Keywords: Heat transfer intensification, nanofluid, CFD, friction factor

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Authors: Shuhua Lai, Kairui Chen

Abstract:

In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: Coarsening, mesh clustering, shape approximation, mesh simplification.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: Multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, Importance sampling, approximate posterior distribution, Marginal likelihood evidence.

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Authors: Abdullah Y. Al-Hossain

Abstract:

This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley.s approximation to compute the Bayes estimates. Another Bayes estimator has been obtained based on continuous-discrete joint prior for the unknown parameters. An example with the real data is discussed to illustrate the proposed method. Finally, we made comparisons between these estimators and the maximum likelihood estimators using a Monte Carlo simulation study.

Keywords: Progressive type II censoring, compound Rayleigh failure time distribution, maximum likelihood estimation, Bayes estimation, Lindley's approximation method, Monte Carlo simulation.

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Authors: Alexander B. Bichkov, Alla A. Mityureva, Valery V. Smirnov

Abstract:

In present work are considered the scheme of evaluation the transition probability in quantum system. It is based on path integral representation of transition probability amplitude and its evaluation by means of a saddle point method, applied to the part of integration variables. The whole integration process is reduced to initial value problem solutions of Hamilton equations with a random initial phase point. The scheme is related to the semiclassical initial value representation approaches using great number of trajectories. In contrast to them from total set of generated phase paths only one path for each initial coordinate value is selected in Monte Karlo process.

Keywords: Path integral, saddle point method, semiclassical approximation, transition probability

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Authors: Schehrazad Selmane

Abstract:

According to Hermite there exists only a finite number of number fields having a given degree, and a given value of the discriminant, nevertheless this number is not known generally. The determination of a maximum number of number fields of degree 10 having a given discriminant that contain a subfield of degree 5 having a fixed class number, narrow class number and Galois group is the purpose of this work. The constructed lists of the first coincidences of 52 (resp. 50, 40, 48, 22, 6) nonisomorphic number fields with same discriminant of degree 10 of signature (6,2) (resp. (4,3), (8,1), (2,4), (0,5), (10,0)) containing a quintic field. For each field in the lists, we indicate its discriminant, the discriminant of its subfield, a relative polynomial generating the field over its quintic field and its relative discriminant, the corresponding polynomial over Q and its Galois closure are presented with concluding remarks.

Keywords: Discriminant, nonisomorphic fields, quintic fields, relative quadratic extensions.

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Authors: Jianguo Tang, Kun She, William Zhu

Abstract:

Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a covering-based rough sets is an important issue. In this paper, two concepts, determinate elements and indeterminate elements in a universe, are proposed and given precise definitions respectively. This research makes a reasonable refinement of the covering-element from a new viewpoint. And the refinement may generate better approximations of covering-based rough sets models. To prove the theory above, it is applied to eight major coveringbased rough sets models which are adapted from other literature. The result is, in all these models, the lower approximation increases effectively. Correspondingly, in all models, the upper approximation decreases with exceptions of two models in some special situations. Therefore, the roughness of recognizing objects is reduced. This research provides a new approach to the study and application of covering-based rough sets.

Keywords: Determinate element, indeterminate element, refinementof covering-element, refinement of covering, covering-basedrough sets.

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Authors: Rama Bhargava, Mania Goyal

Abstract:

The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Keywords: Viscoelastic nanofluid, partial slip, stretching sheet, heat generation/absorption, MHD flow, FEM.

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Authors: S. Sukparungsee

Abstract:

Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: Number of defects, Exponentially Weighted Moving Average, Average Run Length, Square root transformations.

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Authors: J. Zamastil, V. Patkos

Abstract:

Recent progress in calculation of the one-loop selfenergy of the electron bound in the Coulomb field is summarized. The relativistic multipole expansion is introduced. This expansion is based on a single assumption: except for the part of the time component of the electron four-momentum corresponding to the electron rest mass, the exchange of four-momentum between the virtual electron and photon can be treated perturbatively. For non Sstates and normalized difference n3
En −
E1 of the S-states this itself yields very accurate results after taking the method to the third order. For the ground state the perturbation treatment of the electron virtual states with very high three-momentum is to be avoided. For these states one can always rearrange the pertinent expression in such a way that free-particle approximation is allowed. Combination of the relativistic multipole expansion and free-particle approximation yields very accurate result after taking the method to the ninth order. These results are in very good agreement with the previous results obtained by the partial wave expansion and definitely exclude the possibility that the uncertainity in determination of the proton radius comes from the uncertainity in the calculation of the one-loop selfenergy.

Keywords: Hydrogen-like atoms, self-energy.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: Integral differential equations, American options, jump–diffusion model, rational approximation.

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

Abstract:

In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: Heat Transfer, Nanofluid, Shrinking Surface, Stability Analysis, Three-Dimensional Flow.

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Authors: Y. Outaleb, K. Bouhadef, O. Rahli

Abstract:

Double-diffusive steady convection in a partially porous cavity with partially permeable walls and under the combined buoyancy effects of thermal and mass diffusion was analysed numerically using finite volume method. The top wall is well insulated and impermeable while the bottom surface is partially well insulated and impermeable and partially submitted to constant temperature T1 and concentration C1. Constant equal temperature T2 and concentration C2 are imposed along the vertical surfaces of the enclosure. Mass suction/injection and injection/suction are respectively considered at the bottom of the porous centred partition and at one of the vertical walls. Heat and mass transfer characteristics as streamlines and average Nusselt numbers and Sherwood numbers were discussed for different values of buoyancy ratio, Rayleigh number, and injection/suction coefficient. It is especially noted that increasing the injection factor disadvantages the exchanges in the case of the injection while the transfer is augmented in case of suction. On the other hand, a critical value of the buoyancy ratio was highlighted for which heat and mass transfers are minimized.

Keywords: Double diffusive convection, Injection/Extraction, Partially porous cavity

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