Search results for: Steady state solution

Authors: Mohammad N. Alanazi, David A. Gustafson

Abstract:

In this article, we introduce a new approach for analyzing UML designs to detect the inconsistencies between multiple state diagrams and sequence diagrams. The Super State Analysis (SSA) identifies the inconsistencies in super states, single step transitions, and sequences. Because SSA considers multiple UML state diagrams, it discovers inconsistencies that cannot be discovered when considering only a single UML state diagram. We have introduced a transition set that captures relationship information that is not specifiable in UML diagrams. The SSA model uses the transition set to link transitions of multiple state diagrams together. The analysis generates three different sets automatically. These sets are compared to the provided sets to detect the inconsistencies. SSA identifies five types of inconsistencies: impossible super states, unreachable super states, illegal transitions, missing transitions, and illegal sequences.

Keywords: Modeling Languages, Object-Oriented Analysis, Sequence Diagrams, Software Models, State Diagrams, UML.

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Authors: Huynh Quyet Thang, Vo Sy Nam

Abstract:

Schema matching plays a key role in many different applications, such as schema integration, data integration, data warehousing, data transformation, E-commerce, peer-to-peer data management, ontology matching and integration, semantic Web, semantic query processing, etc. Manual matching is expensive and error-prone, so it is therefore important to develop techniques to automate the schema matching process. In this paper, we present a solution for XML schema automated matching problem which produces semantic mappings between corresponding schema elements of given source and target schemas. This solution contributed in solving more comprehensively and efficiently XML schema automated matching problem. Our solution based on combining linguistic similarity, data type compatibility and structural similarity of XML schema elements. After describing our solution, we present experimental results that demonstrate the effectiveness of this approach.

Keywords: XML Schema, Schema Matching, SemanticMatching, Automatic XML Schema Matching.

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Authors: R. Mirabdollah Yani, E. Darabi

Abstract:

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.

Keywords: variational iteration method (VIM), cable vibration, closed-form solution

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Authors: A. A. Hossam-Eldin, E. N. Abdallah, M. S. El-Nozahy

Abstract:

Power system state estimation is the process of calculating a reliable estimate of the power system state vector composed of bus voltages' angles and magnitudes from telemetered measurements on the system. This estimate of the state vector provides the description of the system necessary for the operation and security monitoring. Many methods are described in the literature for solving the state estimation problem, the most important of which are the classical weighted least squares method and the nondeterministic genetic based method; however both showed drawbacks. In this paper a modified version of the genetic algorithm power system state estimation is introduced, Sensitivity of the proposed algorithm to genetic operators is discussed, the algorithm is applied to case studies and finally it is compared with the classical weighted least squares method formulation.

Keywords: Genetic algorithms, ill-conditioning, state estimation, weighted least squares.

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Authors: Phongsak Phakamach

Abstract:

A DC servomotor position control system using a Fuzzy Logic Sliding mode Model Following Control or FLSMFC approach is presented. The FLSMFC structure consists of an integrator and variable structure system. The integral control is introduced into it in order to eliminated steady state error due to step and ramp command inputs and improve control precision, while the fuzzy control would maintain the insensitivity to parameter variation and disturbances. The FLSMFC strategy is implemented and applied to a position control of a DC servomotor drives. Experimental results indicated that FLSMFC system performance with respect to the sensitivity to parameter variations is greatly reduced. Also, excellent control effects and avoids the chattering phenomenon.

Keywords: Sliding mode model following control, fuzzy logic, DC servomotor.

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Authors: Adrian T. Plesca

Abstract:

This paper describes a three-dimensional thermal model of the current path included in the low voltage power circuit breakers. The model can be used to analyse the thermal behaviour of the current path during both steady-state and transient conditions. The current path lengthwise temperature distribution and timecurrent characteristic of the terminal connections of the power circuit breaker have been obtained. The influence of the electric current and voltage drop on main electric contact of the circuit breaker has been investigated. To validate the three-dimensional thermal model, some experimental tests have been done. There is a good correlation between experimental and simulation results.

Keywords: Current path, power circuit breakers, temperature distribution, thermal analysis.

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Authors: Sallehan Ismail, Mahyuddin Ramli

Abstract:

This study examined the properties of fresh and hardened concretes as influenced by the moisture state of the coarse recycled concrete aggregates (RCA) after surface treatment. Surface treatment was performed by immersing the coarse RCA in a calcium metasilicate (CM) solution. The treated coarse RCA was maintained in three controlled moisture states, namely, air-dried, oven-dried, and saturated surface-dried (SSD), prior to its use in a concrete mix. The physical properties of coarse RCA were evaluated after surface treatment during the first phase of the experiment to determine the density and the water absorption characteristics of the RCA. The second phase involved the evaluation of the slump, slump loss, density, and compressive strength of the concretes that were prepared with different proportions of natural and treated coarse RCA. Controlling the moisture state of the coarse RCA after surface treatment was found to significantly influence the properties of the fresh and hardened concretes. 

Keywords: Moisture state, recycled concrete aggregate, surface treatment.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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Authors: Amela Ajanovic

Abstract:

Electric vehicles are considered as technology which can significantly reduce the problems related to road transport such as increasing GHG emissions, air pollutions and energy import dependency. The core objective of this paper is to analyze the current energetic, ecological and economic characteristics of different types of electric vehicles. The major conclusions of this analysis are: The high investments cost are the major barrier for broad market breakthrough of battery electric vehicles and fuel cell vehicles. For battery electric vehicles also the limited driving range states a key obstacle. The analyzed hybrids could in principle serve as a bridging technology. However, due to their tank-to-wheel emissions they cannot state a proper solution for urban areas. Finally, the most important perception is that also battery electric vehicles and fuel cell vehicles are environmentally benign solution if the primary fuel source is renewable.

Keywords: Costs, fuel intensity, electric vehicles, emissions.

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Authors: Satean Tunyasrirut, Tianchai Suksri, Arjin Numsomran, Supan Gulpanich, Kitti Tirasesth

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This paper presents the approach to design the Auto- Tuning PID controller for interactive Water Level Process using integral step response. The Integral Step Response (ISR) is the method to model a dynamic process which can be done easily, conveniently and very efficiently. Therefore this method is advantage for design the auto tune PID controller. Our scheme uses the root locus technique to design PID controller. In this paper MATLAB is used for modeling and testing of the control system. The experimental results of the interacting water level process can be satisfyingly illustrated the transient response and the steady state response.

Keywords: Coupled-Tank, Interacting water level process, PIDController, Auto-tuning.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

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In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: T. Thompson, E. F. Zegeye

Abstract:

Bacterial Cellulose (BC) is a structural organic compound produced in the anaerobic process. This material can be a useful eco-friendly substitute for commercial textiles that are used in industries today. BC is easily and sustainably produced and has the capabilities to be used as a replacement in textiles. However, BC is extremely fragile when it completely dries. This research was conducted to improve the mechanical properties of the BC by reinforcing with an organic polymer and exfoliated graphite (EG). The BC films were grown over a period of weeks in a green tea and kombucha solution at 30 °C, then cleaned and added to an enhancing solution. The enhancing solutions were a mixture of 2.5 wt% polymer and 2.5 wt% latex solution, a 5 wt% polymer solution, a 0.20 wt% graphite solution and were each allowed to sit in a furnace for 48 h at 50 °C. Tensile test samples were prepared and tested until fracture at a strain rate of 8 mm/min. From the research with the addition of a 5 wt% polymer solution, the flexibility of the BC has significantly improved with the maximum strain significantly larger than that of the base sample. The addition of EG has also increased the modulus of elasticity of the BC by about 25%.

Keywords: Bacterial cellulose, exfoliated graphite, kombucha scoby, tensile test.

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Authors: Qiaozhen Song

Abstract:

Based on the feature of model disturbances and uncertainty being compensated dynamically in auto – disturbances-rejection-controller (ADRC), a new method using ADRC is proposed for the decoupling control of dispenser longitudinal movement in big flight envelope. Developed from nonlinear model directly, ADRC is especially suitable for dynamic model that has big disturbances. Furthermore, without changing the structure and parameters of the controller in big flight envelope, this scheme can simplify the design of flight control system. The simulation results in big flight envelope show that the system achieves high dynamic performance, steady state performance and the controller has strong robustness.

Keywords: ADRC, ESO, nonlinear system

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Authors: Gabi Nehme

Abstract:

The relationship between different types of Molybdenum disulfide greases under extreme pressure loading and different speed situations have been studied using Design of Experiment (DOE) under 1200rpm steady state rotational speed and cyclic frequencies between 2400 and 1200rpm using a Plint machine software to set up the different rotational speed situations.  Research described here is aimed at providing good friction and wear performance while optimizing cyclic frequencies and MoS2 concentration due to the recent concern about grease behavior in extreme pressure applications. Extreme load of 785 Newton was used in conjunction with different cyclic frequencies (2400rpm -3.75min, 1200rpm -7.5min, 2400rpm -3.75min, 1200rpm -7.5min), to examine lithium based grease with and without MoS2 for equal number of revolutions, and a total run of 36000 revolutions; then compared to 1200rpm steady speed for the same total number of revolutions. 4 Ball wear tester was utilized to run large number of experiments randomly selected by the DOE software. The grease was combined with fine grade MoS2 or technical grade then heated to 750C and the wear scar width was collected at the end of each test. DOE model validation results verify that the data were very significant and can be applied to a wide range of extreme pressure applications. Based on simulation results and Scanning Electron images (SEM), it has been found that wear was largely dependent on the cyclic frequency condition. It is believed that technical grade MoS2 greases under faster cyclic speeds perform better and provides antiwear film that can resist extreme pressure loadings. Figures showed reduced wear scars width and improved frictional values.

 

Keywords: MoS2 grease, wear, friction, extreme load, cyclic frequencies, aircraft grade bearing.

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Authors: Tapano Kumar Hotta, S P Venkateshan

Abstract:

Steady state experiments have been conducted for natural and mixed convection heat transfer, from five different sized protruding discrete heat sources, placed at the bottom position on a PCB and mounted on a vertical channel. The characteristic length ( Lh ) of heat sources vary from 0.005 to 0.011 m. The study has been done for different range of Reynolds number and modified Grashof number. From the experiment, the surface temperature distribution and the Nusselt number of discrete heat sources have been obtained and the effects of Reynold number and Richardson number on them have been discussed. The objective is to find the rate of heat dissipation from heat sources, by placing them at the bottom position on a PCB and to compare both modes of cooling of heat sources.

Keywords: Discrete heat source, mixed convection, natural convection, vertical channel

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Authors: Ashish Saini, A.K. Saxena

Abstract:

The genetic algorithm (GA) based solution techniques are found suitable for optimization because of their ability of simultaneous multidimensional search. Many GA-variants have been tried in the past to solve optimal power flow (OPF), one of the nonlinear problems of electric power system. The issues like convergence speed and accuracy of the optimal solution obtained after number of generations using GA techniques and handling system constraints in OPF are subjects of discussion. The results obtained for GA-Fuzzy OPF on various power systems have shown faster convergence and lesser generation costs as compared to other approaches. This paper presents an enhanced GA-Fuzzy OPF (EGAOPF) using penalty factors to handle line flow constraints and load bus voltage limits for both normal network and contingency case with congestion. In addition to crossover and mutation rate adaptation scheme that adapts crossover and mutation probabilities for each generation based on fitness values of previous generations, a block swap operator is also incorporated in proposed EGA-OPF. The line flow limits and load bus voltage magnitude limits are handled by incorporating line overflow and load voltage penalty factors respectively in each chromosome fitness function. The effects of different penalty factors settings are also analyzed under contingent state.

Keywords: Contingent operation state, Fuzzy rule base, Genetic Algorithms, Optimal Power Flow.

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Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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Authors: May Zin Lwin., Mya Mya Oo

Abstract:

In the first part of the research work, an electrolyzer (10.16 cm dia and 24.13 cm height) to produce hydrogen and oxygen was constructed for single slice O2/H2 fuel cell using cation exchange membrane. The electrolyzer performance was tested with 23% NaOH, 30% NaOH, 30% KOH and 35% KOH electrolyte solution with current input 4 amp and 2.84 V from the rectifier. Rates of volume of hydrogen produced were 0.159 cm3/sec, 0.155 cm3/sec, 0.169 cm3/sec and 0.163 cm3/sec respectively from 23% NaOH, 30% NaOH, 30% KOH and 35% KOH solution. Rates of volume of oxygen produced were 0.212 cm3/sec, 0.201 cm3/sec, 0.227 cm3/sec and 0.219 cm3/sec respectively from 23% NaOH, 30% NaOH, 30% KOH and 35% KOH solution (1.5 L). In spite of being tested the increased concentration of electrolyte solution, the gas rate does not change significantly. Therefore, inexpensive 23% NaOH electrolyte solution was chosen to use as the electrolyte in the electrolyzer. In the second part of the research work, graphite serpentine flow plates, fiberglass end plates, stainless steel screen electrodes, silicone rubbers were made to assemble the single slice O2/H2 polymer electrolyte membrane fuel cell (PEMFC).

Keywords: electrolyzer, electrolyte solution, fuel cell, rectifier

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Authors: Ali Reza Tahavvor, Saeed Hosseini, Nazli Jowkar, Behnam Amiri

Abstract:

Heat transfer of leaves is a crucial factor in optimal operation of metabolic functions in plants. In order to quantify this phenomenon in different leaves and investigate the influence of leaf shape on heat transfer, natural convection for pine, orange and olive leaves was simulated as representatives of different groups of leaf shapes. CFD techniques were used in this simulation with the purpose to calculate heat transfer of leaves in similar environmental conditions. The problem was simulated for steady state and threedimensional conditions. From obtained results, it was concluded that heat fluxes of all three different leaves are almost identical, however, total rate of heat transfer have highest and lowest values for orange leaves, and pine leaves, respectively.

Keywords: Computational fluid dynamic, heat flux, heat transfer, natural convection.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Arash Karimipour, M. Afrand, M. M. Bazofti

Abstract:

The periodic mixed convection of a water-copper nanofluid inside a rectangular cavity with aspect ratio of 3 is investigated numerically. The temperature of the bottom wall of the cavity is assumed greater than the temperature of the top lid which oscillates horizontally with the velocity defined as u = u0 sin (ω t). The effects of Richardson number, Ri, and volume fraction of nanoparticles on the flow and thermal behavior of the nanofluid are investigated. Velocity and temperature profiles, streamlines and isotherms are presented. It is observed that when Ri < 1, heat transfer rate is much greater than when Ri > 1. The higher value of Ri corresponds to a lower value of the amplitude of the oscillation of Num in the steady periodic state. Moreover, increasing the volume fraction of the nanoparticles increases the heat transfer rate.

Keywords: Nanofluid, Top lid oscillation, Mixed convection, Volume fraction

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Authors: R. Aminzadeh, M. Abarzani, J. Sargolzaei

Abstract:

In this study, the kinetics of osmotic dehydration of melons (Tille variety) in a ternary system followed by air-drying for preserving melons in the summer to be used in the winter were investigated. The effect of different osmotic solution concentrations 30, 40 and 50% (w/w) of sucrose with 10% NaCl salt and fruit to solution ratios 1:4, 1:5 and 1:6 on the mass transfer kinetics during osmotic dehydration of melon in ternary solution namely sucrosesalt- water followed by air-drying were studied. The diffusivity of water during air-drying was enhanced after the fruit samples were immersed in the osmotic solution after 60 min. Samples non-treated and pre-treated during one hour in osmotic solutions with 60% (w/w) of sucrose with 10% NaCl salt and fruit to solution ratio of 1:4 were dried in a hot air-dryer at 60oC (2 m/s) until equilibrium was achieved.

Keywords: Air drying, Effective diffusion coefficient, Mass transfer kinetic, Melon, Osmotic dehydration.

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Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi

Abstract:

The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.

Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.

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Authors: Aritras Roy, Rinku Mukherjee

Abstract:

The current study couples a quasi-steady Vortex Lattice Method and a camber correcting technique, ‘Decambering’ for unsteady post-stall flow prediction. The wake is force-free and discrete such that the wake lattices move with the free-stream once shed from the wing. It is observed that the time-averaged unsteady coefficient of lift sees a relative drop at post-stall angles of attack in comparison to its steady counterpart for some angles of attack. Multiple solutions occur at post-stall and three different algorithms to choose solutions in these regimes show both unsteadiness and non-convergence of the iterations. The distribution of coefficient of lift on the wing span also shows sawtooth. Distribution of vorticity changes both along span and in the direction of the free-stream as the wake develops over time with distinct roll-up, which increases with time.

Keywords: Post-stall, unsteady, wing, aerodynamics.

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Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

Abstract:

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: State of charge estimation, battery modeling, one-state hysteresis, filtering and estimation.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Z. Pavlík, J. Fořt, J. Žumár, M. Pavlíková, R. Černý

Abstract:

The cup method is applied for the measurement of water vapor transport properties of porous materials worldwide. However, in practical applications the experimental results are often used without taking into account some secondary effects which can play an important role under specific conditions. In this paper, the effect of temperature on water vapor transport properties of cellular concrete is studied, together with the influence of sample thickness. At first, the bulk density, matrix density, total open porosity and sorption and desorption isotherms are measured for material characterization purposes. Then, the steady state cup method is used for determination of water vapor transport properties, whereas the measurements are performed at several temperatures and for three different sample thicknesses.

Keywords: Water vapor transport, cellular concrete, cup method, temperature, sample thickness.

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Authors: Daniel Kade, Oğuzhan Özcan, Rikard Lindell

Abstract:

Motion capturing technology has been used for quite a while and several research has been done within this area. Nevertheless, we discovered open issues within current motion capturing environments. In this paper we provide a state-of-the-art overview of the addressed research areas and show issues with current motion capturing environments. Observations, interviews and questionnaires have been used to reveal the challenges actors are currently facing in a motion capturing environment. Furthermore, the idea to create a more immersive motion capturing environment to improve the acting performances and motion capturing outcomes as a potential solution is introduced. It is hereby the goal to explain the found open issues and the developed ideas which shall serve for further research as a basis. Moreover, a methodology to address the interaction and systems design issues is proposed. A future outcome could be that motion capture actors are able to perform more naturally, especially if using a non-body-worn solution.

Keywords: Immersive acting environment, Interaction in a mediated environment, Motion capturing, MoCap.

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Authors: Young Sik Kim, Tae Kwon Ha

Abstract:

Effect of Zn addition on the microstructure and mechanical properties of Mg-Zn alloys with Zn contents from 6 to 10 weight percent was investigated in this study. Through calculation of phase equilibria of Mg-Zn alloys, carried out by using FactSage® and FTLite database, solution treatment temperature was decided as temperatures from 300 to 400oC, where supersaturated solid solution can be obtained. Solid solution treatment of Mg-Zn alloys was successfully conducted at 380oC and supersaturated microstructure with all beta phase resolved into matrix was obtained. After solution treatment, hot rolling was successfully conducted by reduction of 60%. Compression and tension tests were carried out at room temperature on the samples as-cast, solution treated, hot-rolled and recrystallized after rolling. After solid solution treatment, each alloy was annealed at temperatures of 180 and 200oC for time intervals from 1 min to 48 hrs and hardness of each condition was measured by micro-Vickers method. Peak aging conditions were deduced as at the temperature of 200oC for 10 hrs. By addition of Zn by 10 weight percent, hardness and strength were enhanced.

Keywords: Mg-Zn alloy, Heat treatment, Microstructure, Mechanical properties, Hardness.

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: Convection flow, internal heat generation, similarity, spectral method, numerical analysis, Williamson nanofluid.

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