Search results for: Exciting Boundary Layer

Authors: Ibrahim Yakubu Seini, Oluwole Daniel Makinde

Abstract:

MHD chemically reacting viscous fluid flow towards a vertical surface with slip and convective boundary conditions has been conducted. The temperature and the chemical species concentration of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the vertical surface. The governing differential equations are modeled and transformed into systems of ordinary differential equations, which are then solved numerically by a shooting method. The effects of various parameters on the heat and mass transfer characteristics are discussed. Graphical results are presented for the velocity, temperature, and concentration profiles whilst the skin-friction coefficient and the rate of heat and mass transfers near the surface are presented in tables and discussed. The results revealed that increasing the strength of the magnetic field increases the skin-friction coefficient and the rate of heat and mass transfers toward the surface. The velocity profiles are increased towards the surface due to the presence of the Lorenz force, which attracts the fluid particles near the surface. The rate of chemical reaction is seen to decrease the concentration boundary layer near the surface due to the destructive chemical reaction occurring near the surface.

Keywords: Boundary layer, surface slip, MHD flow, chemical reaction, heat transfer, mass transfer.

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

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Authors: Ainon Syazana Ab. Hamid, Seripah Awang Kechil, Ahmad Sukri Abd. Aziz

Abstract:

The Marangoni convective instability in a horizontal fluid layer with the insoluble surfactant and nondeformable free surface is investigated. The surface tension at the free surface is linearly dependent on the temperature and concentration gradients. At the bottom surface, the temperature conditions of uniform temperature and uniform heat flux are considered. By linear stability theory, the exact analytical solutions for the steady Marangoni convection are derived and the marginal curves are plotted. The effects of surfactant or elasticity number, Lewis number and Biot number on the marginal Marangoni instability are assessed. The surfactant concentration gradients and the heat transfer mechanism at the free surface have stabilizing effects while the Lewis number destabilizes fluid system. The fluid system with uniform temperature condition at the bottom boundary is more stable than the fluid layer that is subjected to uniform heat flux at the bottom boundary.

Keywords: Analytical solutions, Marangoni Instability, Nondeformable free surface, Surfactant.

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Authors: Rabah Haoui

Abstract:

The aim of this work is to analyze a viscous flow around the axisymmetric blunt body taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier-Stokes equations is realized by using the finite volume method to determine the flow parameters and detached shock position. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, CFL coefficient and mesh size level are selected to ensure numerical convergence. The effect of the mesh size is significant on the shear stress and velocity profile. The best solution is obtained with using a very fine grid. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: Supersonic flow, viscous flow, finite volume, blunt body.

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Authors: Francois T. Pronk, Steven J. Hulshoff

Abstract:

A study of various turbulent inflow generation methods was performed to compare their relative effectiveness for LES computations of turbulent boundary layers. This study confirmed the quality of the turbulent information produced by the family of recycling and rescaling methods which take information from within the computational domain. Furthermore, more general inflow methods also proved applicable to such simulations, with a precursor-like inflow and a random inflow augmented with forcing planes showing promising results.

Keywords: Boundary layer, Flat plate, Inflow modeling, LES

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Authors: Indu Saini, Phool Singh, Vikas Malik

Abstract:

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Genetic Algorithm is used to calculate shooting angle. The initial value problems arisen during shooting are computed by Runge-Kutta Fehlberg method. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors.

Keywords: Boundary Layer Flow, Falkner–Skan equation, Genetic Algorithm, Shooting method.

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Authors: A. Abdalla, A. Kaltayev

Abstract:

This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.

Keywords: WENO scheme, non-reflection boundary conditions, NSCBC, supersonic flow.

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Authors: Aurélie Mabrouk, Vincent Lagneau, Caroline De Dieuleveult, Martin Bachet, Hélène Schneider, Christophe Coquelet

Abstract:

Resins are used in nuclear power plants for water ultrapurification. Two approaches are considered in this work: column experiments and simulations. A software called OPTIPUR was developed, tested and used. The approach simulates the onedimensional reactive transport in porous medium with convectivedispersive transport between particles and diffusive transport within the boundary layer around the particles. The transfer limitation in the boundary layer is characterized by the mass transfer coefficient (MTC). The influences on MTC were measured experimentally. The variation of the inlet concentration does not influence the MTC; on the contrary of the Darcy velocity which influences. This is consistent with results obtained using the correlation of Dwivedi&Upadhyay. With the MTC, knowing the number of exchange site and the relative affinity, OPTIPUR can simulate the column outlet concentration versus time. Then, the duration of use of resins can be predicted in conditions of a binary exchange.

Keywords: ion exchange resin, mass transfer coefficient, modeling, OPTIPUR

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Authors: Vikas Kumar

Abstract:

The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. The results thus obtained are presented numerically and graphically in the paper.

Keywords: Axi-symmetric, ferrofluid, magnetic field, porous rotating disk.

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Authors: Masamitsu Chikaraishi, Mutsuto Kawahara

Abstract:

This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.

Keywords: Parameter identification, finite element method, average acceleration method, first order adjoint equation method, weighted gradient method, geological boundary, navier equation, optimal control theory.

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Authors: S. N. Hosseini, S. M. H. Karimian

Abstract:

A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.

Keywords: Immersed Boundary Method, conservation of mass and momentum laws, moving boundary, boundary condition.

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Authors: Md. Nasir Uddin, M. A. Alim, M. M. K. Chowdhury

Abstract:

The effect of mass transfer on MHD mixed convective flow along inclined porous plate with thermodiffusion have been analyzed on the basis of boundary layer approximations. The fluid is assumed to be incompressible and dense, and a uniform magnetic field is applied normal to the direction of the flow. A Similarity transformation is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. The behavior of velocity, temperature, concentration, local skin-friction, local Nusselt number and local Sherwood number for different values of parameters have been computed and the results are presented graphically, and analyzed thereafter. The validity of the numerical methodology and the results are questioned by comparing the findings obtained for some specific cases with those available in the literature, and a comparatively good agreement is reached.

Keywords: Mass transfer, inclined porous plate, MHD, mixed convection, thermodiffusion.

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Authors: Ziya Uddin

Abstract:

This paper deals with the theoretical and numerical investigation of magneto hydrodynamic boundary layer flow of a nanofluid past a wedge shaped wick in heat pipe used for the cooling of electronic components and different type of machines. To incorporate the effect of nanoparticle diameter, concentration of nanoparticles in the pure fluid, nanothermal layer formed around the nanoparticle and Brownian motion of nanoparticles etc., appropriate models are used for the effective thermal and physical properties of nanofluids. To model the rotation of nanoparticles inside the base fluid, microfluidics theory is used. In this investigation ethylene glycol (EG) based nanofluids, are taken into account. The non-linear equations governing the flow and heat transfer are solved by using a very effective particle swarm optimization technique along with Runge-Kutta method. The values of heat transfer coefficient are found for different parameters involved in the formulation viz. nanoparticle concentration, nanoparticle size, magnetic field and wedge angle etc. It is found that, the wedge angle, presence of magnetic field, nanoparticle size and nanoparticle concentration etc. have prominent effects on fluid flow and heat transfer characteristics for the considered configuration.

Keywords: Heat transfer, Heat pipe, numerical modeling, nanofluid applications, particle swarm optimization, wedge shaped wick.

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Authors: A. Mahdy

Abstract:

In this paper, a non-similraity analysis has been presented to exhibit the two-dimensional boundary layer flow of magnetohydrodynamic (MHD) natural convection of tangent hyperbolic nanofluid nearby a vertical permeable cone in the presence of variable wall temperature impact. The mutated boundary layer nonlinear governing equations are solved numerically by the an efficient implicit finite difference procedure. For both nanofluid effective viscosity and nanofluid thermal conductivity, a number of experimental relations have been recognized. For characterizing the nanofluid, the compatible nanoparticle volume fraction model has been used. Nusselt number and skin friction coefficient are calculated for some values of Weissenberg number W, surface temperature exponent n, magnetic field parameter Mg, power law index m and Prandtl number Pr as functions of suction parameter. The rate of heat transfer from a vertical permeable cone in a regular fluid is less than that in nanofluids. A best convection has been presented by Copper nanoparticle among all the used nanoparticles.

Keywords: Tangent hyperbolic nanofluid, finite difference, non-similarity, isothermal cone.

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Authors: Omar.S. Qaftan, T. T. Sabbagh

Abstract:

This paper studies the free-field response by adopting a flexible membrane container as soil boundary for experimental shaking table tests. The influence of the soil container boundary on the soil behaviour and the dynamic soil properties under seismic effect were examined. A flexible container with 1/50 scale factor was adopted in the experimental tests, including construction, instrumentation, and determination of the results of dynamic tests on a shaking table. Horizontal face displacements and accelerations were analysed to determine the influence of the container boundary on the performance of the soil. The outputs results show that the flexible boundary container allows more displacement and larger accelerations. The soil in a rigid wall container cannot deform as similar as the soil in the real field does. Therefore, the response of flexible container tested is believed to be more reliable for soil boundary than that in the rigid container.

Keywords: Soil, boundary, seismic, earthquake, ground motion.

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Authors: Pan Cheng, Jin Huang, Guang Zeng

Abstract:

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

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Authors: M.kayhani, M.Nourouzi, A. Amiri Delooei

Abstract:

This study presents an exact general solution for steady-state conductive heat transfer in cylindrical composite laminates. Appropriate Fourier transformation has been obtained using Sturm-Liouville theorem. Series coefficients are achieved by solving a set of equations that related to thermal boundary conditions at inner and outer of the cylinder, also related to temperature continuity and heat flux continuity between each layer. The solution of this set of equations are obtained using Thomas algorithm. In this paper, the effect of fibers- angle on temperature distribution of composite laminate is investigated under general boundary conditions. Here, we show that the temperature distribution for any composite laminates is between temperature distribution for laminates with θ = 0° and θ = 90° .

Keywords: exact solution, composite laminate, heat conduction, cylinder, Fourier transformation.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: Inwon Lee, Victor M. Kulik, Andrey V. Boiko, Ho Hwan Chun

Abstract:

A specially designed flat plate was mounted vertically over the axial line in the wind tunnel of the Aerospace Department of the Pusan National University. The plate is 2 m long, 0.8 m high and 8 cm thick. The measurements were performed in velocity range from 15 to 60 m/s. A sand paper turbulizer was placed close to the plate nose to provide fully developed turbulent boundary layer over the most part of the plate. Strain balances were mounted in the trailing part of the plate to measure the skin friction drag over removable insertions of 0.55×0.25m2 size. A set of the insertions was designed and manufactured: 3mm thick polished metal surface and three compliant surfaces. The compliant surfaces were manufactured of a silicone rubber Silastic® S2 (Dow Corning company). To modify the viscoelastic properties of the rubber, its composition was varied: 90% of the rubber + 10% catalyst (standard), 92.5% + 7.5% (weak), 85% + 15% (strong). Modulus of elasticity and the loss tangent were measured accurately for these materials in the frequency range from 40 Hz to 3 KHz using the unique proposed technique.

Keywords: boundary layer, compliant coating, drag reduction, hot wire, wind tunnel.

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Authors: Rama Bhargava, Mania Goyal

Abstract:

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

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

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Ami Nomura, Ken Imanishi, Yukinori Taniguchi, Etsuko Ueda, Tadahiro Wada, Shinichi Enoki

Abstract:

Recently, there have been a lot of earthquakes in Japan. It is necessary to promote seismic isolation devices for buildings. The devices have been hardly diffused in attached houses, because the devices are very expensive. We should develop a low-cost seismic isolation device for detached houses. We suggested a new seismic isolation device which uses a two-layer circular tube as a unit. If hysteresis is produced in the two-layer circular tube under lateral compression load, we think that the two-layer circular tube can have energy absorbing capacity. It is necessary to contact the outer layer and the inner layer to produce hysteresis. We have previously reported how the inner layer comes in contact with the outer layer from a perspective of analysis used mechanics of materials. We have clarified that the inner layer comes in contact with the outer layer under a lateral compression load. In this paper, we explored contact area between the outer layer and the inner layer under a lateral compression load by using FEA. We think that changing the inner layer’s thickness is effective in increase the contact area. In order to change the inner layer’s thickness, we changed the shape of the inner layer. As a result, the contact area changes depending on the inner layer’s thickness. Additionally, we experimented to check whether hysteresis occurs in fact. As a consequence, we can reveal hysteresis in the two-layer circular tube under the condition.

Keywords: Contact area, energy absorbing capacity, hysteresis, seismic isolation device.

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Authors: S. Zhuiykov, Zh. Hai, H. Xu, C. Xue

Abstract:

Unique and distinctive properties could be obtained on such two-dimensional (2D) semiconductor as tungsten trioxide (WO₃) when the reduction from multi-layer to one fundamental layer thickness takes place. This transition without damaging single-layer on a large spatial resolution remained elusive until the atomic layer deposition (ALD) technique was utilized. Here we report the ALD-enabled atomic-layer-precision development of a single layer WO₃ with thickness of 0.77±0.07 nm on a large spatial resolution by using (^tBuN)₂W(NMe₂)₂ as tungsten precursor and H₂O as oxygen precursor, without affecting the underlying SiO₂/Si substrate. Versatility of ALD is in tuning recipe in order to achieve the complete WO₃ with desired number of WO₃ layers including monolayer. Governed by self-limiting surface reactions, the ALD-enabled approach is versatile, scalable and applicable for a broader range of 2D semiconductors and various device applications.

Keywords: Atomic layer deposition, tungsten oxide, WO3, two-dimensional semiconductors, single fundamental layer.

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Authors: Mehdi Shamshiri, Mahmud Ashrafizaadeh

Abstract:

The significant effects of the interactions between the system boundaries and the near wall molecules in miniaturized gaseous devices lead to the formation of the Knudsen layer in which the Navier-Stokes-Fourier (NSF) equations fail to predict the correct associated phenomena. In this paper, the well-known lattice Boltzmann method (LBM) is employed to simulate the fluid flow and heat transfer processes in rarefied gaseous micro media. Persuaded by the problematic deficiency of the LBM in capturing the Knudsen layer phenomena, present study tends to concentrate on the effective molecular mean free path concept the main essence of which is to compensate the incapability of this mesoscopic method in dealing with the momentum and energy transport within the above mentioned kinetic boundary layer. The results show qualitative and quantitative accuracy comparable to the solutions of the linearized Boltzmann equation or the DSMC data for the Knudsen numbers of O (1) .

Keywords: Fluid flow and Heat transfer, Knudsen layer, Lattice Boltzmann method (LBM), Micro-scale numerical simulation, Transition regime.

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Authors: Bandaris Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.

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Authors: E. Livya, G. Anitha, P. Valli

Abstract:

The main objective of aircraft aerodynamics is to enhance the aerodynamic characteristics and maneuverability of the aircraft. This enhancement includes the reduction in drag and stall phenomenon. The airfoil which contains dimples will have comparatively less drag than the plain airfoil. Introducing dimples on the aircraft wing will create turbulence by creating vortices which delays the boundary layer separation resulting in decrease of pressure drag and also increase in the angle of stall. In addition, wake reduction leads to reduction in acoustic emission. The overall objective of this paper is to improve the aircraft maneuverability by delaying the flow separation point at stall and thereby reducing the drag by applying the dimple effect over the aircraft wing. This project includes both computational and experimental analysis of dimple effect on aircraft wing, using NACA 0018 airfoil. Dimple shapes of Semi-sphere, hexagon, cylinder, square are selected for the analysis; airfoil is tested under the inlet velocity of 30m/s and 60m/s at different angle of attack (5˚, 10˚, 15˚, 20˚, and 25˚). This analysis favors the dimple effect by increasing L/D ratio and thereby providing the maximum aerodynamic efficiency, which provides the enhanced performance for the aircraft.

Keywords: Airfoil, Boundary layer, Dimple effect, Flow separation, Stall reduction.

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Authors: M. Ghalambaz, A.R. Noghrehabadi, M.A. Behrang, E. Assareh, A. Ghanbarzadeh, N.Hedayat

Abstract:

This study presents a hybrid neural network and Gravitational Search Algorithm (HNGSA) method to solve well known Wessinger's equation. To aim this purpose, gravitational search algorithm (GSA) technique is applied to train a multi-layer perceptron neural network, which is used as approximation solution of the Wessinger's equation. A trial solution of the differential equation is written as sum of two parts. The first part satisfies the initial/ boundary conditions and does not contain any adjustable parameters and the second part which is constructed so as not to affect the initial/boundary conditions. The second part involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. In order to demonstrate the presented method, the obtained results of the proposed method are compared with some known numerical methods. The given results show that presented method can introduce a closer form to the analytic solution than other numerical methods. Present method can be easily extended to solve a wide range of problems.

Keywords: Neural Networks, Gravitational Search Algorithm (GSR), Wessinger's Equation.

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

Abstract:

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

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

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Authors: U. C. Amadi, N. A. Udoh

Abstract:

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.

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Authors: Anna Bykalyuk, Frédéric Kuznik, Kévyn Johannes

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In this paper the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).

Keywords: CFD modeling, natural convection, thermal conductive plate, time-depending boundary conditions.

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