Search results for: evolutionary equations of electromagnetic theory of time-domain

Authors: Hyeong-Geon Lee, Jae-Young Park, Suk-ki Lee, Jong-Tae Kim

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The LMS adaptive filter has several parameters which can affect their performance. From among these parameters, most papers handle the step size parameter for controlling the performance. In this paper, we approach three parameters: step-size, filter tap-size and filter form. The regression analysis is used for defining the relation between parameters and performance of LMS adaptive filter with using the system level simulation results. The results present that all parameters have performance trends in each own particular form, which can be estimated from equations drawn by regression analysis.

Keywords: System level model, adaptive LMS FIR filter, regression analysis, systemC.

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Authors: Shi Chen, Zi Y. Chen, Jian K. Dan, Jian F. Li

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Evolution of one-dimensional electron system under high-energy-density (HED) conditions is investigated, using the principle of least-action and variational method. In a single-mode modulation model, the amplitude and spatial wavelength of the modulation are chosen to be general coordinates. Equations of motion are derived by considering energy conservation and force balance. Numerical results show that under HED conditions, electron density modulation could exist. Time dependences of amplitude and wavelength are both positively related to the rate of energy input. Besides, initial loading speed has a significant effect on modulation amplitude, while wavelength relies more on loading duration.

Keywords: Electron density modulation, HED, nonlinearevolution, plasmas.

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Authors: Maysam Saidi, Hassan Basirat Tabrizi, Reza Maddahian

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In this paper, numerical simulations are performed to investigate the effect of disturbance block on flow field of the classical square lid-driven cavity. Attentions are focused on vortex formation and studying the effect of block position on its structure. Corner vortices are different upon block position and new vortices are produced because of the block. Finite volume method is used to solve Navier-Stokes equations and PISO algorithm is employed for the linkage of velocity and pressure. Verification and grid independency of results are reported. Stream lines are sketched to visualize vortex structure in different block positions.

Keywords: Disturbance Block, Finite Volume Method, Lid-Driven Cavity

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Authors: H. Mansor, S. B. Mohd Noor

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This paper presents a design method of self-tuning Quantitative Feedback Theory (QFT) by using improved deadbeat control algorithm. QFT is a technique to achieve robust control with pre-defined specifications whereas deadbeat is an algorithm that could bring the output to steady state with minimum step size. Nevertheless, usually there are large peaks in the deadbeat response. By integrating QFT specifications into deadbeat algorithm, the large peaks could be tolerated. On the other hand, emerging QFT with adaptive element will produce a robust controller with wider coverage of uncertainty. By combining QFT-based deadbeat algorithm and adaptive element, superior controller that is called selftuning QFT-based deadbeat controller could be achieved. The output response that is fast, robust and adaptive is expected. Using a grain dryer plant model as a pilot case-study, the performance of the proposed method has been evaluated and analyzed. Grain drying process is very complex with highly nonlinear behaviour, long delay, affected by environmental changes and affected by disturbances. Performance comparisons have been performed between the proposed self-tuning QFT-based deadbeat, standard QFT and standard dead-beat controllers. The efficiency of the self-tuning QFTbased dead-beat controller has been proven from the tests results in terms of controller’s parameters are updated online, less percentage of overshoot and settling time especially when there are variations in the plant.

Keywords: Deadbeat control, quantitative feedback theory (QFT), robust control, self-tuning control.

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Authors: D. Aboutaleb, B. Safi

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In this paper, sodium borosilicates glasses were prepared by melting in air. These heat-resistant transparent glasses have subjected subsequently isothermal treatments at different times, which have transformed them at opaque glass (milky white color). Such changes indicate that these glasses showed clearly phase separation (immiscibility). The immiscibility region in a sodium borosilicate ternary system was investigated in this work, i.e. to determine the regions from which some compositions can show phase separation. For this we went through the conditions of thermodynamic equilibrium, which were translated later by mathematical equations to find an approximate solution. The latter has been translated in a simulation which was established thereafter to find the immiscibility regions in this type of special glasses.

Keywords: Sodium borosilicate, heat-resistant, isothermal treatments, immiscibility, thermodynamics four.

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Authors: Y. Yongli, M. H. Aissa

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The purpose of this paper aims for a geotechnical analysis based on experimental physical and mechanical characteristics of Miocene marl situated at Medea region in Algeria. More than 150 soil samples were taken in the investigation part of the North-South Highway which extends over than 53 km from Chiffa in the North to Berrouaghia in the South of Algeria. The analysis of data in terms of Atterberg limits, plasticity index, and clay content reflects an acceptable correlation justified by a high coefficient of regression which was compared with the previous works in the region. Finally, approximated equations that serve as a guideline for geotechnical design locally have been suggested.

Keywords: Correlation, geotechnical properties, Miocene marl, north-south highway.

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Authors: Mohammad Shanbghazani, Vahid Heidarpour, Iraj Mirzaee

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In this study a two dimensional axisymmetric, steady state and incompressible laminar flow in a rotating single disk is numerically investigated. The finite volume method is used for solving the momentum equations. The numerical model and results are validated by comparing it to previously reported experimental data for velocities, angles and moment coefficients. It is demonstrated that increasing the axial distance increases the value of axial velocity and vice versa for tangential and total velocities. However, the maximum value of nondimensional radial velocity occurs near the disk wall. It is also found that with increase rotational Reynolds number, moment coefficient decreases.

Keywords: Rotating disk, Laminar flow, Numerical, Momentum

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Authors: C. Ardil

Abstract:

This paper presents an original application of multiple criteria decision making analysis theory to the evaluation of aircraft selection problem. The selection of an optimal, efficient and reliable fleet, network and operations planning policy is one of the most important factors in aircraft selection problem. Given that decision making in aircraft selection involves the consideration of a number of opposite criteria and possible solutions, such a selection can be considered as a multiple criteria decision making analysis problem. This study presents a new integrated approach to decision making by considering the multiple criteria utility theory and the maximal regret minimization theory methods as well as aircraft technical, economical, and environmental aspects. Multiple criteria decision making analysis method uses different normalization techniques to allow criteria to be aggregated with qualitative and quantitative data of the decision problem. Therefore, selecting a suitable normalization technique for the model is also a challenge to provide data aggregation for the aircraft selection problem. To compare the impact of different normalization techniques on the decision problem, the vector, linear (sum), linear (max), and linear (max-min) data normalization techniques were identified to evaluate aircraft selection problem. As a logical implication of the proposed approach, it enhances the decision making process through enabling the decision maker to: (i) use higher level knowledge regarding the selection of criteria weights and the proposed technique, (ii) estimate the ranking of an alternative, under different data normalization techniques and integrated criteria weights after a posteriori analysis of the final rankings of alternatives. A set of commercial passenger aircraft were considered in order to illustrate the proposed approach. The obtained results of the proposed approach were compared using Spearman's rho tests. An analysis of the final rank stability with respect to the changes in criteria weights was also performed so as to assess the sensitivity of the alternative rankings obtained by the application of different data normalization techniques and the proposed approach.

Keywords: Normalization Techniques, Aircraft Selection, Multiple Criteria Decision Making, Multiple Criteria Decision Making Analysis, MCDMA

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Authors: H. Sadjadian , H.D. Taghirad Member, A. Fatehi

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In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

Keywords: Forward Kinematics, Neural Networks, Numerical Solution, Parallel Manipulators.

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Authors: Yoichi Hikino, Mutsuto Kawahara

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The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wavebeam both in elevation and azimuth. In this paper a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Ali Mchirgui, Nejib Hidouri, Mourad Magherbi, Ammar Ben Brahim

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The paper provides a numerical investigation of the entropy generation analysis due to natural convection in an inclined square porous cavity. The coupled equations of mass, momentum, energy and species conservation are solved using the Control Volume Finite-Element Method. Effect of medium permeability and inclination angle on entropy generation is analysed. It was found that according to the Darcy number and the porous thermal Raleigh number values, the entropy generation could be mainly due to heat transfer or to fluid friction irreversibility and that entropy generation reaches extremum values for specific inclination angles.

Keywords: Porous media, entropy generation, convection, numerical method.

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Authors: Cheika Jahangeer, Naushad Mamode Khan, Maleika Heenaye-Mamode Khan

Abstract:

Exclusive breastfeeding is the feeding of a baby on no other milk apart from breast milk. Exclusive breastfeeding during the first 6 months of life is of fundamental importance because it supports optimal growth and development during infancy and reduces the risk of obliterating diseases and problems. Moreover, in developed countries, exclusive breastfeeding has decreased the incidence and/or severity of diarrhea, lower respiratory infection and urinary tract infection. In this paper, we study the factors that influence exclusive breastfeeding and use the Generalized Poisson regression model to analyze the practices of exclusive breastfeeding in Mauritius. We develop two sets of quasi-likelihood equations (QLE)to estimate the parameters.

Keywords: Exclusive breastfeeding, Regression model, Quasilikelihood.

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Authors: I. Naeem, R. Naz

Abstract:

The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.

Keywords: Two-dimensional jets, radial jets, group invariant solution.

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Authors: Ji-Hye Lee, Jongdeok Kim

Abstract:

This research investigates the use of digital technology namely interactive multimedia in effective art education provided by museum. Several multimedia experience examples created for art education are study case subjected to assistance audiences- learning within the context of existing theory in the field of interactive multimedia.

Keywords: E-learning, Fine Arts, Interactivity, Multimedia

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Authors: Amir Alani, Mojtaba Mahmoodian, Anna Romanova, Asaad Faramarzi

Abstract:

Pipelines are extensively used engineering structures which convey fluid from one place to another. Most of the time, pipelines are placed underground and are encumbered by soil weight and traffic loads. Corrosion of pipe material is the most common form of pipeline deterioration and should be considered in both the strength and serviceability analysis of pipes. The study in this research focuses on concrete pipes in sewage systems (concrete sewers). This research firstly investigates how to involve the effect of corrosion as a time dependent process of deterioration in the structural and failure analysis of this type of pipe. Then three probabilistic time dependent reliability analysis methods including the first passage probability theory, the gamma distributed degradation model and the Monte Carlo simulation technique are discussed and developed. Sensitivity analysis indexes which can be used to identify the most important parameters that affect pipe failure are also discussed. The reliability analysis methods developed in this paper contribute as rational tools for decision makers with regard to the strengthening and rehabilitation of existing pipelines. The results can be used to obtain a cost-effective strategy for the management of the sewer system.

Keywords: Reliability analysis, service life prediction, Monte Carlo simulation method, first passage probability theory, gamma distributed degradation model.

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Authors: Hosein Shokohmand, Mahmood Hosein Zare, Abdorreza Qolibeik

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In this paper, the effects of thermodynamic, hydrodynamic and geometric of an air cooled condenser on COP of vapor compression cycle are investigated for a fixed condenser facing surface area. The system is utilized with a scroll compressor, modeled based on thermodynamic and heat transfer equations employing Matlab software. The working refrigerant is R134a whose thermodynamic properties are called from Engineering Equation Software. This simulation shows that vapor compression cycle can be designed by different configurations and COPs, economical and optimum working condition can be obtained via considering these parameters.

Keywords: Vapor compression cycle, air cooled condenser, COP, heat exchanger, thermal modeling.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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Authors: S. Jungsuttiwong, R. Tarsang, S. Pansay, T. Yakhantip, V. Promarak, T. Sudyoadsuk, T. Kaewin, S. Saengsuwan, S. Namuangrak

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In this paper, four carbazole-based D-D-π-A organic dyes code as CCT2A, CCT3A, CCT1PA and CCT2PA were reported. A series of these organic dyes containing identical donor and acceptor group but different π-system. The effect of replacing of thiophene by phenyl thiophene as π-system on the physical properties has been focused. The structural, energetic properties and absorption spectra were theoretically investigated by means of Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT). The results show that nonplanar conformation due to steric hindrance in donor part (cabazolecarbazole unit) of dye molecule can prevent unfavorable dye aggregation. By means of the TD-DFT method, the absorption spectra were calculated by B3LYP and BHandHLYP to study the affect of hybrid functional on the excitation energy (Eg). The results revealed the increasing of thiophene units not only resulted in decreasing of Eg, but also found the shifting of absorption spectra to higher wavelength. TD-DFT/BHandHLYP calculated results are more strongly agreed with the experimental data than B3LYP functions. Furthermore, the adsorptions of CCT2A and CCT3A on the TiO2 anatase (101) surface were carried out by mean of the chemical periodic calculation. The result exhibit the strong adsorption energy. The calculated results provide our new organic dyes can be effectively used as dye for Dye Sensitized Solar Cell (DSC).

Keywords: Dye-Sensitized Solar cell, Carbarzole, TD-DFT, D-D-π-A organic dye

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Authors: Qiang Niu, Linzhang Lu

Abstract:

Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.

Keywords: Arnoldi process, GMRES, Krylov subspace, systems of linear equations.

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Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

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

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

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

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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Authors: Hefin Gwilym

Abstract:

This paper will explore the political biographies of social workers in a neoliberal era. The findings are based on a research project for a successfully completed professional doctorate in social work. The methodology deployed for the research is a combination of constructivist grounded theory and biographical inquiry. The paper will present findings from 14 biographical interviews and will focus on one case study of a participant whose life story is richly informed by political social work. The 14 participants reflect different genders, ethnic identities, cultural and linguistic identities, age and length of social work careers. The participants also reflect different forms of political engagement, such as, as political activists and members of political parties, including parliamentarians. The findings demonstrate how deeply ingrained the social work identity is amongst the participants and how their political identity has remained strongly social democratic in nature despite the many changes in the social work profession since the rise of neoliberalism as a thought collective and policy package. The individual case study will explore the early roots of political identity in the childhood and nurturing years and the interface with subsequent social work and political careers. It will also explore the evolution of the participant’s political identity in the social work career. The case study will also present findings on how the participant has contributed to the political field with policy involvement and initiatives. The presentation will conclude with a discussion on how this particular group of social workers can best contribute to the future direction of the social work profession.

Keywords: Political social work, political biographies, neoliberal, grounded theory.

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Authors: Gilberto Gonzalez-A, Ignacio Rodríguez- A., Dunia Nuñez-P

Abstract:

A bond graph model of a two degrees of freedom PUMA is described. System inversion gives the system input required to generate a given system output. In order to get the system inversion of the PUMA manipulator, a linearization of the nonlinear bond graph is obtained. Hence, the bicausality of the linearized bond graph of the PUMA manipulator is applied. Thus, the bicausal bond graph provides a systematic way of generating the equations of the system inversion. Simulation results to verify the calculated input for a given output are shown.

Keywords: Bond graph, system inversion, bicausality, PUMA manipulator

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Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

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Authors: Diako Azizi, Ahmad Gholami, Vahid Abbasi

Abstract:

High voltage generators are being subject to higher voltage rating and are being designed to operate in harsh conditions. Stator windings are the main component of generators in which Electrical, magnetically and thermal stresses remain major failures for insulation degradation accelerated aging. A large number of generators failed due to stator winding problems, mainly insulation deterioration. Insulation degradation assessment plays vital role in the asset life management. Mostly the stator failure is catastrophic causing significant damage to the plant. Other than generation loss, stator failure involves heavy repair or replacement cost. Electro thermal analysis is the main characteristic for improvement design of stator slot-s insulation. Dielectric parameters such as insulation thickness, spacing, material types, geometry of winding and slot are major design consideration. A very powerful method available to analyze electro thermal performance is Finite Element Method (FEM) which is used in this paper. The analysis of various stator coil and slot configurations are used to design the better dielectric system to reduce electrical and thermal stresses in order to increase the power of generator in the same volume of core. This paper describes the process used to perform classical design and improvement analysis of stator slot-s insulation.

Keywords: Electromagnetic field, field distribution, insulation, winding, finite element method

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Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Chaiwat Waree

Abstract:

This research aims at development of the Multiple Intelligences Measurement of Elementary Students. The structural accuracy test and normality establishment are based on the Multiple Intelligences Theory of Gardner. This theory consists of eight aspects namely linguistics, logic and mathematics, visual-spatial relations, body and movement, music, human relations, self-realization/selfunderstanding and nature. The sample used in this research consists of elementary school students (aged between 5-11 years). The size of the sample group was determined by Yamane Table. The group has 2,504 students. Multistage Sampling was used. Basic statistical analysis and construct validity testing were done using confirmatory factor analysis. The research can be summarized as follows; 1. Multiple Intelligences Measurement consisting of 120 items is content-accurate. Internal consistent reliability according to the method of Kuder-Richardson of the whole Multiple Intelligences Measurement equals .91. The difficulty of the measurement test is between .39-.83. Discrimination is between .21-.85. 2). The Multiple Intelligences Measurement has construct validity in a good range, that is 8 components and all 120 test items have statistical significance level at .01. Chi-square value equals 4357.7; p=.00 at the degree of freedom of 244 and Goodness of Fit Index equals 1.00. Adjusted Goodness of Fit Index equals .92. Comparative Fit Index (CFI) equals .68. Root Mean Squared Residual (RMR) equals 0.064 and Root Mean Square Error of Approximation equals 0.82. 3). The normality of the Multiple Intelligences Measurement is categorized into 3 levels. Those with high intelligence are those with percentiles of more than 78. Those with moderate/medium intelligence are those with percentiles between 24 and 77.9. Those with low intelligence are those with percentiles from 23.9 downwards.

Keywords: Multiple Intelligences, Measurement, Elementary Students.

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Authors: Y.Bakhshan, H.Ashoori

Abstract:

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

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

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