Search results for: elliptic equations

Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

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Authors: Sajeda Elbashabsheh, Kamel Al-Khaled

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This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations.

Keywords: approximate solutions, Jaulent-Miodek system, Adomian decomposition method, solitons

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Hemant Upadhyay, Tarun Kumar Kundu

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It is utmost important for a blast furnace operator to understand the mechanisms governing the liquid flow, accumulation, drainage and heat transfer between various phases in blast furnace hearth for a stable and efficient blast furnace operation. Abnormal drainage behavior may lead to high liquid build up in the hearth. Operational problems such as pressurization, low wind intake, and lower material descent rates, normally be encountered if the liquid levels in the hearth exceed a critical limit when Hearth coke and Deadman start to float. Similarly, hot metal temperature is an important parameter to be controlled in the BF operation; it should be kept at an optimal level to obtain desired product quality and a stable BF performance. It is not possible to carry out any direct measurement of above due to the hostile conditions in the hearth with chemically aggressive hot liquids. The objective here is to develop a mathematical model to simulate the variation in hot metal / slag accumulation and temperature during the tapping of the blast furnace based on the computed drainage rate, production rate, mass balance, heat transfer between metal and slag, metal and solids, slag and solids as well as among the various zones of metal and slag itself. For modeling purpose, the BF hearth is considered as a pressurized vessel, filled with solid coke particles. Liquids trickle down in hearth from top and accumulate in voids between the coke particles which are assumed thermally saturated. A set of generic mass balance equations gives the amount of metal and slag intake in hearth. A small drainage (tap hole) is situated at the bottom of the hearth and flow rate of liquids from tap hole is computed taking in account the amount of both the phases accumulated their level in hearth, pressure from gases in the furnace and erosion behaviors of tap hole itself. Heat transfer equations provide the exchange of heat between various layers of liquid metal and slag, and heat loss to cooling system through refractories. Based on all that information a dynamic simulation is carried out which provides real time information of liquids accumulation in hearth before and during tapping, drainage rate and its variation, predicts critical event timings during tapping and expected tapping temperature of metal and slag on preset time intervals. The model is in use at JSPL, India BF-II and its output is regularly cross-checked with actual tapping data, which are in good agreement.

Keywords: blast furnace, hearth, deadman, hotmetal

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Authors: Abdelghafour Galadi

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In this paper, accurate power MOSFET models including quasi-saturation effect are presented. These models have no internal node voltages determined by the circuit simulator and use one JFET or one depletion mode MOSFET transistors controlled by an “effective” gate voltage taking into account the quasi-saturation effect. The proposed models achieve accurate simulation results with an average error percentage less than 9%, which is an improvement of 21 percentage points compared to the commonly used standard power MOSFET model. In addition, the models can be integrated in any available commercial circuit simulators by using their analytical equations. A description of the models will be provided along with the parameter extraction procedure.

Keywords: power MOSFET, drift layer, quasi-saturation effect, SPICE model

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Authors: Fatma Khaled, Khaoula Hidouri, Bechir Chaouachi

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Desalination using solar energy coupled with membrane techniques such as vacuum membrane distillation (VMD) is considered as an interesting alternative for the production of pure water. During this work, a developed model of a polytetrafluoroethylene (PTFE) hollow fiber membrane module of a VMD unit of seawater was carried out. This simulation leads to establishing a comparison between the effects of two different equations of the vaporization latent heat on the membrane surface temperature and on the unit productivity. Besides, in order to study the effect of putting membrane modules in series on the outlet fluid temperature and on the productivity of the process, a simulation was executed.

Keywords: vacuum membrane distillation, membrane module, membrane temperature, productivity

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Authors: N. Targui, H. Kahalerras

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The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy-Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: double pipe heat exchanger, nanofluids, nanoparticles, porous baffles

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Authors: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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Authors: Brahim Mahfoud, Ali Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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Authors: W. Meron Mebrahtu, R. Absi

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Velocity distribution in turbulent open-channel flows is organized in a complex manner. This is due to the large spatial and temporal variability of fluid motion resulting from the free-surface turbulent flow condition. This phenomenon is complicated further due to the complex geometry of channels and the presence of solids transported. Thus, several efforts were made to understand the phenomenon and obtain accurate mathematical models that are suitable for engineering applications. However, predictions are inaccurate because oversimplified assumptions are involved in modeling this complex phenomenon. Therefore, the aim of this work is to study velocity distribution profiles and obtain simple, more accurate, and predictive mathematical models. Particular focus will be made on the acceptable simplification of the general transport equations and an accurate representation of eddy viscosity. Wide rectangular open-channel seems suitable to begin the study; other assumptions are smooth-wall, and sediment-free flow under steady and uniform flow conditions. These assumptions will allow examining the effect of the bottom wall and the free surface only, which is a necessary step before dealing with more complex flow scenarios. For this flow condition, two ordinary differential equations are obtained for velocity profiles; from the Reynolds-averaged Navier-Stokes (RANS) equation and equilibrium consideration between turbulent kinetic energy (TKE) production and dissipation. Then different analytic models for eddy viscosity, TKE, and mixing length were assessed. Computation results for velocity profiles were compared to experimental data for different flow conditions and the well-known linear, log, and log-wake laws. Results show that the model based on the RANS equation provides more accurate velocity profiles. In the viscous sublayer and buffer layer, the method based on Prandtl’s eddy viscosity model and Van Driest mixing length give a more precise result. For the log layer and outer region, a mixing length equation derived from Von Karman’s similarity hypothesis provides the best agreement with measured data except near the free surface where an additional correction based on a damping function for eddy viscosity is used. This method allows more accurate velocity profiles with the same value of the damping coefficient that is valid under different flow conditions. This work continues with investigating narrow channels, complex geometries, and the effect of solids transported in sewers.

Keywords: accuracy, eddy viscosity, sewers, velocity profile

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Sanjeet Patra, Soham Roychowdhury

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In recent times, functionally graded dielectric elastomer (FGDE) has gained significant attention within the realm of soft actuation due to its dual capacity to exert highly localized stresses while maintaining its compliant characteristics on application of electro-mechanical loading. Nevertheless, the full potential of dielectric elastomer (DE) has not been fully explored due to their susceptibility to instabilities when subjected to electro-mechanical loads. As a result, study and analysis of such instabilities becomes crucial for the design and realization of dielectric actuators. Prismatic bifurcation is a type of instability that has been recognized in a DE tube. Though several studies have reported on the analysis for prismatic bifurcation in an isotropic DE tube, there is an insufficiency in studies related to prismatic bifurcation of FGDE tubes. Therefore, this paper aims to determine the onset of prismatic bifurcations on an incompressible FGDE tube when subjected to electrical loading across the thickness of the tube and internal pressurization. The analysis has been conducted by imposing two axial boundary conditions on the tube, specifically axially free ends and axially clamped ends. Additionally, the rigidity modulus of the tube has been linearly graded in the direction of thickness where the inner surface of the tube has a lower stiffness than the outer surface. The static equilibrium equations for deformation of the axisymmetric tube are derived and solved using numerical technique. The condition for prismatic bifurcation of the axisymmetric static equilibrium solutions has been obtained by using the linearized incremental constitutive equations. Two modes of bifurcations, corresponding to two different non-circular cross-sectional geometries, have been explored in this study. The outcomes reveal that the FGDE tubes experiences prismatic bifurcation before the Hessian criterion of failure is satisfied. It is observed that the lower mode of bifurcation can be triggered at a lower critical voltage as compared to the higher mode of bifurcation. Furthermore, the tubes with larger stiffness gradient require higher critical voltages for triggering the bifurcation. Moreover, with the increase in stiffness gradient, a linear variation of the critical voltage is observed with the thickness of the tube. It has been found that on applying internal pressure to a tube with low thickness, the tube becomes less susceptible to bifurcations. A thicker tube with axially free end is found to be more stable than the axially clamped end tube at higher mode of bifurcation.

Keywords: critical voltage, functionally graded dielectric elastomer, linearized incremental approach, modulus of rigidity, prismatic bifurcation

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Authors: V. Benedico, C. Anacleto, A. Bearzi, L. Brice, V. Delahaye

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The aim in present paper is to construct an affordable and reliable commodity prices based on a recalculation of its cost through time which allows visualize the potential risks and thus, take more appropriate decisions regarding forecasts. Here attention has been focused on Levy model, more reliable and realistic than classical random Gaussian one as it takes into consideration observed abrupt jumps in case of sudden price variation. In application to Energy Trading sector where it has never been used before, equations corresponding to Levy model have been written for electricity pricing in European market. Parameters have been set in order to predict and simulate the price and its evolution through time to remarkable accuracy. As predicted by Levy model, the results show significant spikes which reach unconventional levels contrary to currently used Brownian model.

Keywords: commodity pricing, Lévy Model, price spikes, electricity market

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

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The analytical bright two soliton solution of the 3-coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: optical soliton, soliton interaction, soliton switching, WDM

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Authors: Haseen Siddiqui, Sanjay M. Mahajani

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Various important reactions in chemical and metallurgical industries fall in the category of gas-solid reactions. These reactions can be categorized as catalytic and non-catalytic gas-solid reactions. In gas-solid reaction systems, heat and mass transfer limitations put an appreciable influence on the rate of the reaction. The consequences can be unavoidable for overlooking such effects while collecting the reaction rate data for the design of the reactor. Pyrolysis reaction comes in this category that involves the production of gases due to the interaction of heat and solid substance. Pyrolysis is also an important step in the gasification process and therefore, the gasification reactivity majorly influenced by the pyrolysis process that produces the char, as a feed for the gasification process. Therefore, in the present study, a non-isothermal transient 1-D model is developed for a single biomass pellet to investigate the effect of heat and mass transfer limitations on the rate of pyrolysis reaction. The obtained set of partial differential equations are firstly discretized using the concept of ‘method of lines’ to obtain a set of ordinary differential equation with respect to time. These equations are solved, then, using MATLAB ode solver ode15s. The model is capable of incorporating structural changes, porosity variation, variation in various thermal properties and various pellet shapes. The model is used to analyze the effectiveness factor for different values of Lewis number and heat of reaction (G factor). Lewis number includes the effect of thermal conductivity of the solid pellet. Higher the Lewis number, the higher will be the thermal conductivity of the solid. The effectiveness factor was found to be decreasing with decreasing Lewis number due to the fact that smaller Lewis numbers retard the rate of heat transfer inside the pellet owing to a lower rate of pyrolysis reaction. G factor includes the effect of the heat of reaction. Since the pyrolysis reaction is endothermic in nature, the G factor takes negative values. The more the negative value higher will be endothermic nature of the pyrolysis reaction. The effectiveness factor was found to be decreasing with more negative values of the G factor. This behavior can be attributed to the fact that more negative value of G factor would result in more energy consumption by the reaction owing to a larger temperature gradient inside the pellet. Further, the analytical expressions are also derived for gas and solid concentrations and effectiveness factor for two limiting cases of the general model developed. The two limiting cases of the model are categorized as the homogeneous model and unreacted shrinking core model.

Keywords: effectiveness factor, G-factor, homogeneous model, lewis number, non-catalytic, shrinking core model

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Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi

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This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

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Authors: Ekaterina Artiukhina, Panagiotis Grammelis

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Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion and co-firing applications. In the course of torrefaction the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The non-stationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: torrefaction, biomass pellets, model, heat, mass transfer

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Authors: Utsav Bhardwaj, Shyama Prasad Das

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To meet the extensive requirements of thermal management of the circuit card assemblies (CCAs), satellites, PCBs, microprocessors, any other electronic circuitry, pulsating heat pipes (PHPs) have emerged in the recent past as one of the best solutions technically. But industrial application of PHPs is still unexplored up to a large extent due to their poor reliability. There are several systems as well as operational parameters which not only affect the performance of an operating PHP, but also decide whether the PHP can operate sustainably or not. Functioning may completely be halted for some particular combinations of the values of system and operational parameters. Among the system parameters, adiabatic length is one of the important ones. In the present work, a simplest single branch PHP system with an adiabatic section has been considered. It is assumed to have only one vapour bubble and one liquid plug. First, the system has been mathematically modeled using film evaporation/condensation model, followed by the steps of recognition of equilibrium zone, non-dimensionalization and linearization. Then proceeding with a periodical solution of the linearized and reduced differential equations, stability analysis has been performed. Slow and fast variables have been identified, and averaging approach has been used for the slow ones. Ultimately, temporal evolution of the PHP is predicted by numerically solving the averaged equations, to know whether the oscillations are likely to sustain/decay temporally. Stability threshold has also been determined in terms of some non-dimensional numbers formed by different groupings of system and operational parameters. A combined analytical and numerical approach has been used, and it has been found that for each combination of all other parameters, there exists a maximum length of the adiabatic section beyond which the PHP cannot function at all. This length has been called as “Critical Adiabatic Length (L_ac)”. For adiabatic lengths greater than “L_ac”, oscillations are found to be always decaying sooner or later. Dependence of “L_ac” on some other parameters has also been checked and correlated at certain evaporator & condenser section temperatures. “L_ac” has been found to be linearly increasing with increase in evaporator section length (L_e), whereas the condenser section length (L_c) has been found to have almost no effect on it upto a certain limit. But at considerably large condenser section lengths, “L_ac” is expected to decrease with increase in “L_c” due to increased wall friction. Rise in static pressure (p_r) exerted by the working fluid reservoir makes “L_ac” rise exponentially whereas it increases cubically with increase in the inner diameter (d) of PHP. Physics of all such variations has been given a good insight too. Thus, a methodology for quantification of the critical adiabatic length for any possible set of all other parameters of PHP has been established.

Keywords: critical adiabatic length, evaporation/condensation, pulsating heat pipe (PHP), thermal management

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Authors: Saima Q. Memon, Mazhar I. Khaskheli

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The aim of present study was to investigate the efficiency of mulberry leaves for the removal of both arsenic (III) and arsenic (V) from aqueous medium. Batch equilibrium studies were carried out to optimize various parameters such as pH of metal ion solution, volume of sorbate, sorbent doze, and agitation speed and agitation time. Maximum sorption efficiency of mulberry leaves for As (III) and As (V) at optimum conditions were 2818 μg.g-1 and 4930 μg.g-1, respectively. The experimental data was a good fit to Freundlich and D-R adsorption isotherm. Energy of adsorption was found to be in the range of 3-6 KJ/mole suggesting the physical nature of process. Kinetic data followed the first order rate, Morris-Weber equations. Developed method was applied to remove arsenic from real water samples.

Keywords: arsenic removal, mulberry, adsorption isotherms, kinetics of adsorption

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Authors: Jurij Tasinkiewicz

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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 wave beam 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, piezoelectric layer

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Danilo López, Nelson Vera, Luis Pedraza

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This paper analyzes fundamental ideas and concepts related to neural networks, which provide the reader a theoretical explanation of Long Short-Term Memory (LSTM) networks operation classified as Deep Learning Systems, and to explicitly present the mathematical development of Backward Pass equations of the LSTM network model. This mathematical modeling associated with software development will provide the necessary tools to develop an intelligent system capable of predicting the behavior of licensed users in wireless cognitive radio networks.

Keywords: neural networks, multilayer perceptron, long short-term memory, recurrent neuronal network, mathematical analysis

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Authors: A. Ja, J. Belabid, A. Cheddadi

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This paper reports the numerical simulation of double diffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: natural convection, double-diffusion, porous medium, annular geometry, finite differences

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Authors: Azzedine Abdedou, Khedidja Bouhadef

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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, porous media, oriented confined jet, fluid mechanics

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Authors: Maryamosadat Ghasemi, Reza Amrollahi

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Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be able to support this plasma equilibrium geometry. In this work the prepared numerical code based on radial basis functions are presented and used to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of tokamak plasma. The radial basis functions (RBFs) which is a kind of numerical meshfree method (MFM) for solving partial differential equations (PDEs) has appeared in the last decade and is developing significantly in the last few years. This technique is applied in this study to obtain the equilibrium configuration for Alborz Tokamak. The behavior of numerical solution convergences show the validation of this calculations.

Keywords: equilibrium, grad–shafranov, radial basis functions, Alborz Tokamak

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Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality, normal forms, universal unfolding instability, structural stability

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Authors: Farhad Aalizadeh, Ali Moosavi

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When a blood vessel is injured, the cells of your blood bond together to form a blood clot. The blood clot helps you stop bleeding. Blood clots are made of a combination of blood cells, platelets(small sticky cells that speed up the clot-making process), and fibrin (protein that forms a thread-like mesh to trap cells). Doctors call this kind of blood clot a “thrombus.”We study the effects of different parameters on the deposition of Nanoparticles on the surface of a bump in the blood vessels by the magnetic field. The Maxwell and the flow equations are solved for this purpose. It is assumed that the blood is non-Newtonian and the number of particles has been considered enough to rely on the results statistically. Using MHD and its property it is possible to control the flow velocity, remove the fouling on the walls and return the system to its original form.

Keywords: MHD, fouling, in-vivo, blood clots, simulation

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Authors: Ishak Hashim, Ammar Alsabery

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The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating.

Keywords: conjugate free convection, square cavity, nanofluid, spatial temperature

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