فهرست مطالب

Journal Of Applied Fluid Mechanics
Volume:9 Issue: 1, Jan-Feb 2016

  • تاریخ انتشار: 1394/10/29
  • تعداد عناوین: 50
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  • Jaan Hui Pu, Yuefei Huang, Songdong Shao, K. Hussain Pages 1-10
    The Three Gorges Dam (TGD) constructed at the Yangtze River, China represents a revolutionary project to battle against the mage-scale flooding problems while improving the local economy at the same time. However, the large-scale fine-size sediment and pollutant material transport caused by the TGD operation are found to be inevitable and long-lasting. In this paper, a multi-fluid Incompressible Smoothed Particle Hydrodynamics (ISPH) model is used to simulate the multi-fluid flows similar to the fine sediment materials transport (in muddy flows) and water flow mixing process. The SPH method is a mesh-free particle modeling approach that can treat the free surfaces and multi-interfaces in a straightforward manner. The proposed model is based on the universal multi-fluid flow equations and a unified pressure equation is used to account for the interaction arising from the different fluid components. A Sub-Particle-Scale (SPS) turbulence model is included to address the turbulence effect generated during the flow process. The proposed model is used to investigate two cases of multi-fluid flows generated from the polluted flow intrusions into another fluid. The computations are found in good agreement with the practical situations. Sensitivity studies have also been carried out to evaluate the particle spatial resolution and turbulence modeling on the flow simulations. The proposed ISPH model could provide a promising tool to study the practical multi-fluid flows in the TGD operation environment.
    Keywords: Three gorges dam, Pollutant transport, Density difference, SPH, Multi, fluid, Fine sediment
  • Jacob Hirschhorn, Marisa Madsen, Antonio Mastroberardino, Javed Siddique Pages 11-17
    In this paper, we consider the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of powerlawfluidoveraflatplatewithslipboundaryconditions. Weuseasimilaritytransformation to convert the governing nonlinear partial differential equations into a system of ordinary differential equations and solve the resulting system numerically using MATLAB’s boundary value solver, bvp4c, and the shooting method. We present velocity and temperature profiles within the boundary layer and demonstrate the effect of changing the magnetic parameter, Prandtl number, and slip parameters.
    Keywords: Magnetohydrodynamic flow, Nonlinear boundary value problem, Slip flow, NonNewtonian fluid
  • M.R. Heidari, Ali Reza Pouramir Pages 19-26
    In this research, the effects of some liquid side injection from nozzle wall into exhaust gas of combustion chamber are studied. The side injection against main flow is as elliptical solid thing that change the symmetric of flow field on nozzle wall and causes some different pressure distribution on wall, and finally causes thrust vector deviation. Flows interaction causes some physical phenomena as bow shock wave in front of injection region. This paper explain the effects of this wave and variation velocity & pressure distribution at different cross sections of flow field and comparison results of air and other liquid fluid in thrust vector control system. The results are compared with experimental data and have well agreement with them. The results show that Freon is one of best injection liquid for this type of thrust vector control. Performance of Injection is optimum in relative position 35 to 40% nozzle divergence length.
    Keywords: Thrust vector control (TVC), Side jet, Liquid injection, Bow shock wave
  • Mostafa Rahimi, Mehdi Javadi Nodeh Pages 27-32
    An experimental investigation was conducted to study the potential use of the pressure reduction within the separated flow region followed by the wake at the leeward direction of a solid surface in natural ventilation of buildings. Air flow with mean velocity up to 7 m/s was directed onto a solid surface (circular plate and a semi-spherical surface) behind which the top end of a vertical vent pipe had been placed. Pressure reduction at the exit section of the pipe, which was well inside the separated flow region, induced an air flow within the pipe. This air flow rate from the stagnant surroundings into the wake region was measured under different geometrical configurations and for various wind velocities. The study revealed that the pressure reduction within the separated flow region would be applicable for natural ventilation of different spaces at least as an auxiliary system. The spaces include; sanitary places, crop protection stocks, industrial workshops and other spaces where no regular ventilation is required.
    Keywords: Natural ventilation, Separated flow region, Wind energy
  • Mohammad Reza Salimi, Mahdi Ramezanizadeh, Mohammad Taeibi, Rahni, Roozbeh Farhadi Azar Pages 33-42
    Flow hydrodynamic effects and film cooling effectiveness of placing a coolant port (upstream jet) just upstream of the main cooling jet were numerically investigated. The upstream jet was added such that the total cooling cross section (cross sections of the main and upstream jets) remains constant, in comparison to the case of ordinary cooling jet. The finite volume method and the unsteady SIMPLE algorithm on a multiblock non-uniform staggered grid arrangement were applied. The large eddy simulation (LES) approach with the one equation subgrid scale model was used. The jet to cross flow velocity ratio (for both of the main and the upstream jets) is 0.5 and the cross flow Reynolds number (based on the main jet parameters) is equal to 4700. The obtained results showed a significant improvement in the flow control capability and both centerline and span-wise averaged film cooling effectiveness applying the new cooling configuration. Effects of the upstream jet dimensions are also studied here. The obtained results showed that the span-wise width of the upstream jet has more essential influence on the cooling performance than that of its stream-wise width. Moreover, it is demonstrated that the film cooling performance could be enhanced even by applying an upstream jet which its temperature is as same as the cross-flow temperature, i.e. applying a hot upstream jet. Finally, it is shown that presence of the upstream jet decreases the stream-wise component of the velocity near the wall, which decreases the wall shear stress and the skin friction drag coefficient significantly.
    Keywords: Film cooling effectiveness, Upstream jet, Large eddy simulation, Effectiveness enhancement, Drag reduction
  • Kaladhar Kolla, Sandile Motsa, D. Srinivasacharaya Pages 43-50
    The radiation and thermal diffusion effects on mixed convection flow of couple stress fluid through a channel are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the Spectral Quasi-linearization Method (QLM). The results, which are discussed with the aid of the dimensionless parameters entering the problem, are seen to depend sensitively on the parameters.
    Keywords: Couple stress fluid, Mixed convection, Soret effect, Radiation effect, SQLM
  • X. Z. Zhu, T. S. Wang, G. Wang Pages 51-60
    The forward or backward stagger angles of the kneading disks have great effects on configures of the special center region along axial length in a novel tri-screw extruder. In this paper, the flow and mixing of a nonNewtonian polyethylene in kneading disks of a tri-screw extruder were simulated using three-dimensional finite element modeling based on mesh superposition technique. Three types of kneading disks, neutral stagger, staggered 30° forward and staggered 30° reverse were considered for the tri-screw extruder. The effects of stagger angles of kneading disks on the flow pattern in the tri-screw extruder were investigated. Moreover, at different stagger angles, the dispersive and distributive mixing efficiencies in the kneading disks of the tri-screw extruder and the twin-screw extruder were calculated and compared by means of mean shear rate, stretching rates, maximal stress magnitudes, mixing index, residence time distribution (RTD) and logarithm of area stretch. It is found that increasing the stagger angles decreases the axial velocities of polymer melt in the center region for the tri-screw extruder. The staggered 30° reverse is relatively reasonable for the tri-screw extruder and neutral stagger for the twin-screw extruder for the mixing efficiency. In comparison, the kneading disks in the tri-screw extruder have higher distributive and dispersive mixing efficiencies than those in the twin-screw extruder with the same stagger angles.
    Keywords: Kneading disks of tri, screw extruders, Stagger angles, Mixing efficiency, Residence time distribution, Finite element method
  • R. Muthucumaraswamy, Saravanan Balasubramani Pages 61-69
    MHD and thermal radiation effects on unsteady flow past an oscillating semi-infinite vertical plate with variable surface temperature and uniform mass flux have been studied. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable and fast converging implicit finite difference scheme. The effect of velocity, concentratiion and temperature profiles for different parameters like magnetic field, thermal radiation, Schmidt number, thermal Grashof number, mass Grashof number are studied. It is observed that the velocity decreases with increasing values of the magnetic field parameter or radiation parameter.
    Keywords: MHD, Radiation, Isothermal, Vertical plate, Finite, difference, Variable temperature, Mass flux
  • N. Rudraiah, Mallika K. S, Sujatha Nagaraja Pages 71-81
    Exact analysis of miscible dispersion of solute with interphase mass transfer in a poorly conducting couple stress fluid flowing through a rectangular channel bounded by porous layers is considered because of its application in many practical situations. The generalized dispersion model of Sankarasubramanian and Gill is used, which brings into focus the exchange coefficient, the convective coefficient and the dispersion coefficient. The exchange coefficient comes into picture due to the interphase mass transfer and independent of solvent fluid viscosity. It is observed that the convective coefficient increases with an increase in the porous parameter while it decreases with an increase in the couple stress parameter. The dispersion coefficient is plotted against wall reaction parameter for different values of porous parameter and couple stress parameter. It is noted that the dispersion coefficient decreases with an increase in the value of couple stress parameter but increases with porous parameter.
    Keywords: Poorly conducting fluid, Generalised dispersion, Interphase mass transfer, Couple stress fluid
  • Masoud Boroomand, Hamzeh Eshraghi, Abolghasem M. Tousi Pages 83-94
    This study, primarily reports the development of a 3D design procedure for axial flow tandem compressor stages and then the method is used to design a highly loaded tandem stage. In order to investigate the effects of such arrangement, another stage with conventional loading with single blade for both rotor and stator rows is designed with similar specification. In order to ease the comparison of results, chord lengths and hub/shroud geometries are selected with the same dimensions. At the next stage a three dimensional numerical model is developed to predict the characteristic performance of both tandem and conventional stages. The model is validated with the experimental results of NASA-67 stage and the level of the accuracy of the model is presented. Employing the model to simulate the performance of both stages at design and offdesign operating points show that, tandem stage can provide higher pressure ratio with acceptable efficiency. In another word, tandem stage is capable having the same pressure ratio at lower rotational speed. The safe operation domain and loss mechanism in tandem stage are also discussed in this report.
    Keywords: Compressor stage, Tandem stage, Highly loaded, Design point performance, Characteristic map
  • Loganathan Parasuram, Sivapoornapriya Chinnaiyan Pages 95-102
    An investigation is carried out to analyze the effects of heat and mass transfer over an impulsively started vertical plate in the presence of porous medium with chemical reaction. The unsteady, non-linear, coupled partial differential equations are solved by implicit finite difference scheme of Crank Nicolson type. The influence of various parameters like Prandtl number, Schmidt number, first order chemical reaction on the velocity, temperature and concentration are analyzed. The local skin friction, local Nusselt number, local Sherwood number, average skin friction, average Nusselt number and average Sherwood numbers are investigated. It is observed that the velocity and concentration boundary layer decreases with increasing chemical reaction. An increase in the Schmidt number reduces the concentration boundary layer thickness.
    Keywords: Heat transfer, Mass transfer, Porous medium, Chemical reaction, Finite difference
  • Gauri Seth, Rohit Sharma, Bidyasagar Kumbhakar Pages 103-117
    Investigation of unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, chemically reactive and optically thin radiating fluid past an exponentially accelerated moving vertical plate with arbitrary ramped temperature embedded in a fluid saturated porous medium is carried out. Exact solutions of momentum, energy and concentration equations are obtained in closed form by Laplace transform technique. The expressions for the shear stress, rate of heat transfer and rate of mass transfer at the plate for both ramped temperature and isothermal plates are derived. The numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is found that, for isothermal plate, the fluid temperature approaches steady state when 1.5 t . Consequently, the rate of heat transfer at isothermal plate approaches steady state when 1.5 t .
    Keywords: Natural convection, Magnetic field, Chemical reaction, Radiation, Arbitrary ramped temperature
  • Hadi Heidari, Mohammad Jafar Kermani, Mohsen Pirmohammadi Pages 119-130
    In this study natural convection heat transfer fluid flow and entropy generation in a porous inclined cavity in the presence of uniform magnetic field is studied numerically. For control of heat transfer and entropy generation, one or two partitions are attached to horizontal walls. The left wall of enclosure is heated with a sinusoidal function and right wall is cooled isothermally. Horizontal walls of the enclosure are adiabatic. The governing equations are numerically solved in the domain by the control volume approach based on the SIMPLE technique. The influence of Hartmann number, inclination angle, partition height, irreversibility distribution ratio, and partition location is investigated on the flow and heat transfer characteristics and the entropy generation. The obtained results indicated that the partition, magnetic field and rotation of enclosure can be used as control elements for heat transfer, fluid flow and entropy generation in porous medium.
    Keywords: MHD, Free convection, Partition, Porous media
  • Muhammad Naveed, Zaheer Abbas, Muhammad Sajid Pages 131-138
    The two-dimensional boundary layer flow of an electrically conducting micropolar fluid and heat transfer subject to a transverse uniform magnetic field over a curved stretching sheet coiled in a circle of radius has been studied. The effect of thermal radiation is also considered using linearized Rosseland approximation. For mathematical formulation of the flow equations, curvilinear coordinates system is used. The governing partial differential equations describing the flow phenomena and heat transfer characteristics are reduced to ordinary differential equations by means of suitable transformations. The system of differential equations is solved numerically by shooting method using Runge-Kutta algorithm combined with the Newtons-Raphson technique. Some physical features of the flow and heat transfer in terms of fluid velocity, angular velocity, temperature profile, the skin-friction coefficient, couple wall stress and the local Nusselt number for several values of fluid parameters are analyzed, discussed and presented in graphs and tables. Comparison of the present results with the published data for the flat surface i.e. (→∞) is found in good agreement.
    Keywords: Micropolar fluid, MHD, Curved stretching surface, Thermal radiation, Numerical solution
  • Farid Fazlollahi, Ali Akbar Alemrajabi Pages 139-145
    Experimental investigation on heat transfer enhancement by applying electrohydrodynamics (EHD) in partially open multiple fined enclosures with different aperture position has been performed. The enclosure had five thermally and electrically insulated faces; while one face was copper finned plate with an aperture located on its opposite face. In the present study, different parameters including electric current, number of fins, aperture position, and corona polarity were investigated. It was concluded that heat transfer enhancement is proportional to the supplied current. Higher number of fins can lead to further heat transfer enhancement and as the location of aperture is shifted upward, the heat transfer coefficient is improved more significantly by EHD.
    Keywords: EHD, Convection, Fin, Corona, Aperture
  • Alireza Aghaei, Ghanbarali Sheikhzadeh, Hamidreza Ehteram, Maryam Hajiahmadi Pages 147-156
    In this paper, mixed convection fluid flow, heat transfer and entropy generation inside a triangular enclosure filled with CuO-water nanofluid with variable properties are investigated numerically. The inclined walls of enclosure are maintained at a constant temperature Tc. The moving bottom wall is kept at a constant temperature Th, which Th>Tc.The numerical simulation of mixed convection is carried out using a computer program (FORTRAN language) based on finite volume method and SIMPLER algorithm. This study is performed over a range of nanoparticle volume fractions(0-0.02-0.04) Richardson numbers(0.01, 0.1, 1, 10, 100), and angles of inclined walls(150, 300, 450, 600, 750) and a fixed Grashof number (Gr=104).In all investigated aspect ratios and Richardson numbers, average Nusselt number increased by enhancement of volume fraction till 0.02, but it is approximately constant by adding more nanoparticles till 0.04.It is also observed that in all aspect ratios and Richardson numbers, the variation of total entropy generation by enhancement of volume fraction is similar to Nusselt number.
    Keywords: Nanofluid, Entropy generation, Triangular enclosure, Mixed convection, Numerical solution, Brownian motion
  • Rajesh Vemula, O.Anwar Ba, Sridevi Chakrala Pages 157-167
    In the present study, the effects of chemical reaction on unsteady free convection flow of a viscous, electrically conducting, and incompressible fluid past a moving semi-infinite vertical cylinder with mass transfer and temperature oscillation is studied. The dimensionless governing partial differential equations are solved using an implicit finite-difference method of Crank–Nicolson type, which is stable and convergent. The transient velocity, transient temperature, and transient concentration profiles are studied for various parameters. The local as well as average skin-friction, Nusselt number, and Sherwood number are also analyzed and presented graphically. The results are compared with available computations in the literature, and are found to be in good agreement.
    Keywords: Free convection, MHD, Implicit finite, difference method, Heat, mass transfer, First order chemical reaction, Temperature oscillation
  • Ime J. Uwanta, M. M. Hamza Pages 169-176
    The problem of unsteady as well as steady hydromagnetic natural convection and mass transfer flow of viscous reactive, incompressible and electrically conducting fluid between two vertical walls in the presence of uniform magnetic field applied normal to the flow region is studied. Thermal diffusion, temperature dependent variable viscosity and thermal conductivity are assumed to exist within the channel. The governing partial differential equations are solved numerically using implicit finite difference scheme. Results of the computations for velocity, temperature, concentration, skin friction, rate of heat and mass transfer are presented graphically to study the hydrodynamic behavior of fluid in the channel.
    Keywords: Thermal diffusion, Variable thermal conductivity, Variable viscosity, Natural convection, Heat transfer, Mass transfer
  • Seyed Esmail Razavi, Mohammad Taghilou, Ahmad Rezaei Pages 177-183
    A novel multidimensional characteristics approach for inflow and outflow boundaries of compressible twodimensional flows is presented. The modified Riemann variables have been extracted from the Euler equations by considering the directions of waves reaching the inflow and outflow boundaries. By applying this model in a shortened computational domain, the boundaries can be located close to the nonlinear zone. The results of reduced and extended domains are in good agreement with each other. Using this model yields in a reduction of computational domain while keeping the solution accuracy and lowering the computation time.
    Keywords: Far field boundary conditions, Characteristics method, Euler equations, Compressible flows, Finite volume
  • Manoj Kumar Triveni, Rajsekhar Panua, Dipak Sen Pages 185-193
    The effect of different configurations of partial cold walls on laminar natural convection heat transfer for a right-angle triangular cavity heated from below has been studied numerically. The enclosure is filled with water and heat transfer surfaces such as hot and cold walls are maintained at constant temperature. The side and hypotenuse walls of the enclosure are detached from the middle and have been arranged in four different configurations, namely AB, BC, AD and CD for cooling purpose. The finite volume method is used to solve the dimensionless governing mass, momentum and energy equations. The problem has been solved to explore the effects of the pertinent parameters i.e. different configurations of cold walls and variation of Rayleigh number (105 ≤ Ra ≤ 107). Results are obtained from numerical simulation using commercial software package, FLUENT and presented in the form of streamlines and isotherms. The thermal performance of the enclosure has been expressed by local and average Nusselt numbers. From the analysis, it is observed that the temperature distribution and flow field are significantly affected by these parameters. The high heat transfer rate has been observed for the position AB while low for the position CD. Also, the heat transfer rate enhances as the Rayleigh number (Ra) increases.
    Keywords: Cold walls positions, Natural convection, Triangular enclosure, Rayleigh number
  • Zaheer Abbas, Tariq Javed, Nasir Ali, Muhammad Sajid Pages 195-203
    The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with diffusion of chemically reacting species on a porous plate is investigated. Due to a porous plate the suction is taken into an account. Using suitable transformations, the momentum and concentration equations are first transformed into nonlinear ordinary ones and then solved using a hybrid numerical method. This method combines the features of finite difference and shooting methods. The effects of various controlling parameters on the flow velocity, concentration profile, skin friction and rate of mass transfer on surface are analyzed graphically and in tabular form. Comparison of the present results with the previous reported results has been found in excellent agreement.
    Keywords: Third grade fluid, Chemical reaction, Stagnation point flow, Porous plate, Numerical solution
  • M.N. Kherief, Berrahil Farid, Kamel Talbi Pages 205-213
    Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined rectangular enclosure heated from one side and cooled from the adjacent side was considered. The governing equations were solved numerically for the stream function, vorticity and temperature using the finite-volume method for various Grashof and Hartman numbers and inclination angles and magnetic field directions. The results show that the orientation and the strength and direction of the magnetic field have significant effects on the flow and temperature fields. Counterclockwise inclination induces the formation of multiple eddies inside the enclosure significantly affecting the temperature field. Circulation inside the enclosure and therefore the convection become stronger as the Grashof number increases while the magnetic field suppresses the convective flow and the heat transfer rate.
    Keywords: Natural convection, Magnetic field, Inclined rectangular enclosure finite, volume, Lorentz force
  • Sabir Shehzad, T. Hayat, Ahmed Alsaedi Pages 215-223
    The magnetohydrodynamic (MHD) three-dimensional boundary layer flow of an incompressible Casson fluid in a porous medium is investigated. Heat transfer characteristics are analyzed in the presence of heat generation/absorption. Laws of conservation of mass, momentum and energy are utilized. Results are computed and analyzed for the velocities, temperature, skin-friction coefficients and local Nusselt number.
    Keywords: Three, dimensional flow, Casson fluid, Stretching surface, Heat generation, absorption
  • Loganathan Parasuram, Sivapoornapriya Chinnaiyan Pages 225-232
    An analysis is performed to investigate the ohmic heating and viscous dissipation effects on an unsteady natural convective flow over an impulsively started vertical plate in the presence of porous medium with radiation and chemical reaction. Numerical solutions for the governing boundary layer equations are presented by finite difference scheme of the Crank Nicolson type. The influence of various parameters on the velocity, the temperature, the concentration, the skin friction, the Nusselt number and the Sherwood number are discussed. It is observed that velocity and temperature increases with increasing values of permeability and increasing values of Eckert number, whereas it decreases with increasing values of magnetic parameter. An increase in ohmic heating and viscous heating increases the velocity boundary layer. An increase in ohmic heating decreases the temperature. An increase in magnetic field reduces the temperature profile. The velocity profile is highly influenced by the increasing values of permeability. It is observed that permeability has strong effect on velocity. An enhancement in ohmic heating increases the shear stress, decreases the rate of heat transfer and induces the rate of mass transfer.
    Keywords: Ohmic heating, Viscous dissipation, Chemical reaction, Porous medium, Finite difference
  • Samad Sattarzadeh, Alireza Jahangirian, Mir Yousef Hashemi Pages 233-241
    A dual-time implicit mesh-less method is presented for unsteady compressible flow calculations. Polynomial least-square (PLS) and Taylor series least-square (TLS) procedures are used to estimate the spatial derivatives at each node and their computational efficiencies are compared. Also, the effect of the neighbor stencil selection on the accuracy of the method is investigated. As a new approach, different neighboring stencils are used for the highly stretched point distribution inside the boundary layer region and the inviscid isotropic point distribution outside this area. The unsteady flows over stationary and moving objects at subsonic and transonic flow conditions are solved. Results indicate the computational efficiency of the method in comparison with the alternative approaches. The convergence histories of the flow solution show that the PLS method is computationally faster than TLS method. In addition, the eight point neighboring stencil inside the viscous region is more efficient than other choices.
    Keywords: Navier, Stokes equations, Unsteady compressible flow, Mesh less method, Moving boundary, Implicit method
  • Jie Zhang, Guangjun Gao, Xiaohui Xiong, Tanghong Liu, Feng Liu Pages 243-251
    To find the influence of different types of steel poles on measurements by wind speed sensors along highspeed railways, the three-dimensional Reynolds-averaged Navier-Stokes equations, combined with the k-ε turbulence model, were solved on an unstructured grid with a boundary layer using the finite volume method. The grid-independent validation was firstly conducted, and the accuracy of the present numerical simulation method was validated by experiments and simulations carried out by previous researchers. To ascertain angles of influence at different distances between the sensor and the virtual one, the flow field around a sensor was investigated with the method of altering the relative coordinates between the two sensors. After that, the flow fields and velocity distributions around steel poles were studied. It can be stated that behind the sensor, the closer the distance from the sensor center line, the larger the angle of influence. However, as the distance is varied from 0.3 to 1.0 m, the most adverse angles are not in excess of ±20°. In addition, the steel poles have a certain influence on the measurement results of sensors. A “two-sided petal acceleration region” with a “central pistil deceleration zone” comes into being. From the perspective of regions of influence in different wind directions, the influence region of the annulus pole is basically the same. For the square and H types, when the angle is 45°, the region of effect is the largest. For the same distance between the sensor and the pole, the space required between two sensors for the single H type is larger than that required by the annulus type. Thus, it is suggested that the distance between sensors and the pole should be 1.0 m with the anemometer located on the upstream side, and the distance between two anemometers should be 0.8 m.
    Keywords: High, speed railway, Grid, independence, Type of steel pole, Flow structure, Velocity distribution.
  • Deyou Li, Ruzhi Gong, Hongjie Wang, Jian Zhang, Xianzhu Wei, L. F. Shu Pages 253-266
    The performance of a pump turbine in pump mode is of great importance to a pumped storage power plant. In order to obtain pump characteristics of a pump turbine, 3D steady simulations were carried out by solving Reynolds-averaged Navier-Stokes (RANS) equations using different two-equation turbulence models. Compared with the experimental data, SST k-ω turbulence model was chosen to simulate external characteristic curves under 32mm, 22mm and 18mm guide vanes openings. The results show a good agreement with the experimental data, especially near the best efficiency point. Finally, the detailed analysis was conducted within vaned distributor for these three guide vanes openings. The variation of flow field, pressure filed, energy characteristic and loss with the discharge and guide vanes opening were obtained through the analysis. This research could provide a basic understanding on pump characteristics of a pump turbine for designer.
    Keywords: Hydraulic machinery, Pump turbine, Numerical investigation, Vaned distributor, Pump mode
  • P. Sreenivasulu, T. Poornima, N. Bhaskar Reddy Pages 267-278
    An analysis of the thermal radiation effects on MHD boundary layer flow past a permeable exponential stretching surface in the presence of Joule heating and viscous dissipation is presented. Velocity and thermal slips are considered instead of no-slip conditions at the boundary. Stretching velocity and wall temperature are assumed to have specific exponential function forms. The governing system of partial differential equations is transformed into a system of ordinary differential equations using similarity transformations and then solved numerically using the Runge-Kutta fourth order method along with shooting technique. The effects of the various parameters on the velocity, shear stress, temperature and temperature gradient profiles are illustrated graphically and discussed in detail. The influence of the slip parameters causes significant fluctuations in velocity of the flow field. Viscous dissipation characterized by Eckert number enhances the temperature of the fluid, as the heat gets transferred from the sheet to the fluid.
    Keywords: MHD, Thermal radiation, Viscous dissipation, Boundary layer flow, Joule heating, Exponentially stretching surface
  • Ali Kazemipour, Mahyar Pourghasemi, Hossein Afshin, Bijan Farhanieh Pages 279-292
    Fire is a potential hazard in public transportation facilities such as subways or road tunnels due to its contribution to high number of deaths. To provide an insight into fire development behavior in tunnels which can serve as the basis for emergency ventilation design, model-scale railcar fire is explored numerically in this research. Fire growth and its spread are investigated by analyzing the HRR curve as the representative of fire behavior in different stages. Fire development has been predicted through a new approach using an Arrhenius-based pyrolysis model, established to predict the decomposition behavior of solid flammable materials exposed to heat flux. Using this approach, model-scale railcar fire curve is obtained and compared with experimental data. Reasonable agreement is achieved in two important stages of flashover and fully developed fire, confirming the accuracy of the presented approach. Moreover, effects of railcar material type, amount of available air, and surrounding are also discussed. Detailed illustrations of physical phenomena and flow structures have been provided and justified with experimental findings for better description of railcar fire behavior. The presented approach can be further used in other applications such as investigation of fire spread in a compartment, studying fire spread from a burning vehicle to another and reconstruction of fire incidents.
    Keywords: Heat release rate, Railcar fire, Pyrolysis, Fire safety, Cone calorimetry, Ventilation factor
  • J. Prasad, Hemalatha K Pages 293-302
    We analyzed in this paper the problem of mixed convection along a vertical plate in a non-Newtonian fluid saturated non-Darcy porous medium in the presence of melting and thermal dispersion-radiation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M), thermal dispersion (D), radiation (R), magnetic field (MH), viscosity index (n) and mixed convection (Ra/Pe) on fluid velocity and temperature are examined for aiding and opposing external flows.
    Keywords: Porous medium, non, Newtonian fluid, Melting, Thermal dispersion, Radiation, MHD
  • S. Moulai, Abdelkader Korichi, Guillaume Polidori Pages 303-310
    This paper investigates numerically the flow and heat transfer in air (Pr=0.71) by mixed convection past a heated square cylinder under aiding buoyancy effect in a confined channel. The numerical simulations are performed in the range of parameters 20≤Re≤45 and 1.61x103≤Gr≤6.33x103 for a fixed blockage ratio D/L of 0.1. The combination in the present study of these two Re and Gr parameters is reduced so that the Richarson number varies from 0,8 to 8, in order to neglect neither free convection (Ri<0.1) nor forced convection (Ri>10). The steady two-dimensional governing equations are solved by the finite volume formulation using the open source OpenFoam® code. The representative flow structure, isotherm patterns and local Nusselt number evolution are presented and discussed. The effect of both the Reynolds number and the buoyancy parameter on the fluid flow and the heat transfer are also analyzed. It is found that the wake region size strongly depends on both Reynolds and Grashof numbers and this region is shown to increase in size increasing the Reynolds number and/or decreasing the Grashof number. Moreover, increasing the Reynolds number leads to a heat transfer enhancement more pronounced on the front face of the obstacle, whereas increasing the Grashof number leads to a heat transfer enhancement more pronounced on the side faces.
    Keywords: Mixed convection, Vertical channel, Heated square cylinder
  • A. Malleswaran, Sivasankaran Sivanandam Pages 311-319
    A numerical investigation on mixed convection in a lid-driven square cavity has been performed in the presence of the uniform magnetic field. From the left-bottom corner of the cavity, three different lengths of heater are varied along bottom and left walls simultaneously. The finite volume method is employed to solve the governing equations. It is observed that the heater length in the x-direction is more effective than that of in the y-direction on the heat transfer and on the flow pattern. The magnetic field affects the average heat transfer rate more on vertical heaters than on the horizontal heaters.
    Keywords: Mixed convection, Magnetic field, Lid, driven cavity, Corner heating
  • Dr. S. Rawat, . Kapoor Saurabh, Prof R. Bhargava Pages 321-331
    This paper investigates the two dimensional flow, heat and mass transfer of chemically reacting Micropolar fluid over a non-linear stretching sheet with variable heat flux in a non-darcy porous medium. The rate of chemical reaction is assumed to be constant throughout the fluid i.e. homogenous. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equation, which is then solved using Finite element method. Numerical results regarding local Nussult No. are shown graphically with Magnetic number () for variation in heat transfer exponent (n). This study also analyzes the effect of velocity exponent m, heat transfer exponent n, material parameter K, Magnetic Number()Darcy NumberDax, Forchheimer Number Nfx, Prandtl number Pr, Schmidt Number Sc and Chemical reaction rate parameter x  on velocity, microrotation, temperature and concentration profiles. Velocity exponent m has a positive effect on the velocity, temperature and concentration profiles while microrotation decreases as m increases. Graphical results shows that the thermal boundary layer thickness decreases at and near the wall with the increase in heat flux exponent n. Also an increase in K leads to a decrease in skin friction parameter as well as the wall couple stress.
    Keywords: Micropolar fluid, MHD, Stretching Sheet, Chemical reaction rate parameter
  • Sabah Hamidi, M.J. Kermani Pages 333-341
    In this research a numerical study of water production from compressible moist-air flow by condensing of the vapor component of the atmospheric air through a converging-diverging nozzle is performed. The atmospheric air can be sucked by a vacuum compressor. The geographical conditions represent a hot and humid region, for example Bandar Abbas, Iran, with coordinates, 270 11’ N and 560 16’ E and summer climate conditions of about 40℃and relative humidity above 80%. Parametric studies are performed for the atmospheric-air temperature between, 40℃ to 50℃, and relative humidity between49.6% to 100.%. For these ranges of operating conditions and a nozzle with the area ratio of 1.17, the liquid mass flow rates falls in the range 0.272 to 0.376 kg/s. The results show that, the energy consumed by the compressor for production 1 kg of water will be 1.279 kWh. The price of 1 kWh is 372 Rials, therefore the price for the production of 1 kg liquid water will be 475.8 Rials, therefore, the scheme is economically suitable.
    Keywords: Water Production, Condensation of Moist, Air, Equilibrium thermodynamic, Roe's scheme
  • Bapuji Pullepu, Sambath P., Selva Rani M., A.J. Chamkha, K.K. Viswanathan Pages 343-356
    The purpose of this paper is to present a mathematical model for the combined effects of chemical reaction and heat generation/absorption on unsteady laminar free convective flow with heat and mass transfer over an incompressible viscous fluid past a vertical permeable cone with uniform wall temperature and concentration (UWT/UWC).The dimensionless governing boundary layer equations of the flow that are transient, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicholson type. The velocity, temperature, and concentration profiles have been studied for various parameters viz., chemical reaction parameter, the heat generation and absorption parameter, Schmidt number Sc, Prandtl number Pr, buoyancy ratio parameter N. The local as well as average skin friction, Nusselt number, Sherwood number, are discussed and analyzed graphically. The present results are compared with available results in open literature and are found to be in excellent agreement.
    Keywords: Chemical reaction, Finite difference method, Free convection, Heat generation, absorption, Nonuniform surface temperature, Non, uniform surface concentration, Unsteady, Vertical cone
  • Pankaj Gohil, Rajeshwer Saini Pages 357-365
    Cavitation is undesirable phenomena and more prone in reaction turbines. It is one of the challenges in any hydro power plant which cause vibration, degradation of performance and the damage to the hydraulic turbine components. Under the present study, an attempt has been made to carry out a numerical analysis to investigate the cavitation effect in a Francis turbine. Three dimensional numerical study approach of unsteady and SST turbulence model are considered for the numerical analysis under multiphase flow such as cavitating flow. The performance parameters and cavitating flow under different operating conditions have been predicted using commercial CFX code. Three different operating conditions under cavitation and without cavitation with part load and overload conditions of the turbine for a plant sigma factor are investigated. The results are presented in the form of efficiency, pressure fluctuation, vortex rope and vapor volume fraction. It has been observed that variation in efficiency and vapor volume fraction is found to be nominal between cavitation and without cavitation conditionsat rated discharge and rated head. Turbine efficiency loss and vapor bubbles formation towards suction side of the runner blade are found to be maximum under overload condition. However, the pressure pulsation has been found maximum under part load condition in the draft tube. The simulation results are found to be in good agreement with model test results for efficiency. The locations of cavitating zone observed wellwith the result of previous studies.
    Keywords: Cavitation, Francis Turbine, Efficiency, CFX
  • Arman Hamedi, Mehdi Shamshiri, Mahmud Charmiyan, . Ebrahim Shirani Pages 367-378
    Electroosmosis is the predominant mechanism for flow generation in lab-on-chip devices. Since most biofluids encountered in these devices reveal non-Newtonian behavior, a special understanding of the fundamental physics of the relevant transport phenomena seems vital for an accurate design of such miniaturized devices. In this study, a numerical analysis is presented to explore transport characteristics of typical non-Newtonian biofluids through annular microchannels under combined action of pressure and electrokinetic forces. The flow is considered steady and hydrodynamically fully developed. A finite difference method is used to solve the Poisson-Boltzmann and Cauchy momentum equations, while the classical boundary condition of no velocity-slip for the flow field is applied. The Poisson-Boltzmann equation is solved in the exact form without using the Debye-Hückel approximation. After numerically solving the governing equations, role of the key parameters in hydrodynamic behavior of the flow is analyzed and discussed.
    Keywords: Annular microchannel, Non, Newtonian Biofluid flow, Electrokinetic, rheological behaviors, Numerical investigation
  • R. M. Kasmani, Sivasankaran Sivanandam, M. Bhuvaneswari, Z. Siri Pages 379-388
    The aim of the present study is to examine the convective heat transfer of nanofluid past a wedge subject to first-order chemical reaction, heat generation/absorption and suction effects. The influence of wedge angle parameter, thermophoresis, Dufour and Soret type diffusivity are included. The local similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Shooting method integrated with fourth-order Runge-Kutta method is used to solve the ordinary differential equations. The skin friction, heat and mass transfer rates as well as the effects of various parameters on velocity, temperature and solutal concentration profiles are analyzed. The results indicate that when the chemical reaction parameter increases, the heat transfer coefficient increases while the mass transfer coefficient decreases. The effect of chemical reaction parameter is very important in solutal concentration field compared to velocity and temperature profiles since it decreases the solutal concentration of the nanoparticle.
    Keywords: Heat transfer, Nanofluid, Chemical reaction, Thermophoresis
  • Fahad Abbasi, T. Hayat, Ahmed Alsaedi Pages 389-396
    This article addresses the peristaltic transport of Eyring-Prandtl fluid in an inclined asymmetric channel. Heat and mass transfer phenomena along with Soret and Dufour effects is analyzed. Effects of inclined magnetic field and Joule heating are also discussed. Long wavelength approximation is adopted. Numerical computations for flow quantities of interest are analyzed. It is found that the parabolic velocity profile tends to shift from center of the channel towards the channel walls in the case of opposing flow. Velocity and temperature decrease whereas concentration increases by increasing the non-Newtonian parameter. Further the dependence of magnetic field on the angle is quite significant.
    Keywords: Peristaltic transport, Inclined magnetic field, Soret, Dufour effects, Joule heating
  • Saeed Kavousfar, Esmaeil Esmaeilzadeh, Hossein Mahdavy Moghaddam, Sohrab Gholamhosein Pouryoussefi, Masoud Mirzaei Pages 397-406
    In this paper, the air flow around a blunt flat plate with a rounded leading edge has been experimentally examined with and without the presence of a plasma actuator. Tests have been conducted with Reynolds numbers ranging from 104 to 105. Significant phenomena in this flow field is the flow separation at the leading edge of the body, which called separation bubble. There are two considerably dimensionless parameters in this experiment. One of them is the leading edge radius ratio to body thickness and other one is the ratio of maximum velocity induced by plasma actuator to free stream velocity. Geometries with the values of R/D=0, 1/16, 2/16, 4/16 were tested. For each geometry, the effectiveness of plasma actuator on the separation bubble is studied in different values of velocity ratio. The results show that, the effect of plasma actuator for the geometry with sharp edge (R/D=0), is negligible, while in geometry with rounded edge, the plasma actuator has significant effect on the separation bubble domain. This effectiveness is enhanced, by increasing of leading edge radius and velocity ratio, so that in rounded edge geometry (R/D=4/16) length of separation bubble is reduced about 75%.
    Keywords: Active flow control, Bluff body, Plasma actuator, Pressure distribution, Reattachment point
  • M. Battira, Rachid BessaÏh Pages 407-418
    This work aims to study numerically the steady natural convection in a vertical cylinder filled with an Al2O3 nanofluid under two different external magnetic fields (Br, Bz) either in the radial or axial directions. The cylinder having an aspect ratio H/R0=1 is bounded by the top and the bottom disks at temperatures Tc and Th, and by an adiabatic side wall. The equations of continuity, Navier-Stokes and energy are non-dimensionalized and then discretized by the finite volume method. A computer program based on the SIMPLER algorithm is developed and compared with the numerical results found in the literature. The effects of nano-size solid volume fraction ranging from 0 to 0.1 and application of the magnetic field in either directions axial and radial for various values of Hartmann numbers on flow and thermal fields, and on local and average Nusselt numbers are presented and discussed for two values of Rayleigh numbers (Ra=103 and 104). The behaviors of average Nusselt number, streamlines, temperature contours, and the both components of velocity are illustrated. The results indicate that for small values of the Hartmann number, where the flow remains due to the convection, the average Nusselt number decreases when increasing the solid volume fraction and this decrease is more important if the magnetic field is applied in the axial direction and by increasing the Hartmann numbers. The increasing in the solid volume fraction increases the performance of heat transfer in the nanofluid.
    Keywords: Natural convection, Nanofluid, Magnetic field
  • Taoufik Naffouti, Jamil Zinoubi, Che Sidik Nor Azwadi, Rejeb Ben Maad Pages 419-430
    The aim of this paper is to analyze the laminar free convective flow generated by two identical hot blocks in two-dimensional enclosure cooled by the sides in order to optimize the heat transfer. The top wall and the flat surfaces on bottom wall are adiabatic except for the active sources located symmetrically. Each source of a rectangular form is heated at a uniform temperature while the Prandtl number is fixed at 0.71. Thermal Lattice Boltzmann model of D2Q4-D2Q9 is applied to solve the thermal flow problem. Numerical simulations have been conducted to reveal the effects of various parameters; Rayleigh number 103 ≤ Ra ≤ 106, spacing between blocks 0.1 ≤ D ≤ 0.6, block height 0.05 ≤ H ≤ 0.4 and aspect ratio of the enclosure 1 ≤ A ≤ 4 on fluid flow and heat transfer. The computational results by Lattice Boltzmann method have been found to be in good agreement with previous works. The results are presented in the form of isotherms and streamlines plots as well as the variation of the average Nusselt number along horizontal and vertical hot walls. It is found that increasing Rayleigh number and distance between active blocks enhance the heat transfer. The simulations show that the block height and aspect ratio are the most important parameters affecting dynamic and thermal fields and consequently the heat transfer efficiency in the enclosure.
    Keywords: Free convection, 2, D enclosure, Active blocks, Lattice Boltzmann method, Optimum heat
  • Fan Jiang, Yun Long, Yijun Wang, Zhenzhang Liu, Conggui Chen Pages 431-441
    The volume of fluid (VOF) model together with the continuum surface stress (CSS) model is proposed to simulate the core annular of non-Newtonian oil and water flow through the rectangle return bends (∏-bends). A comprehensive investigation is conducted to generate the profiles of volume fraction, pressure and velocity. The influences of oil properties, flow direction, and bend geometric parameters on hydrodynamic of nonNewtonian oil and water core annular flow in ∏-bends are discussed. Through computational simulations the proper bend geometric parameters were identified, these results are useful for designing and optimizing the pipefitting system.
    Keywords: core annular flow, Non, Newtonian, Two, phase flow, Rectangle return bends, VOF, CSS
  • Dang Tienphuc, Gu Zhengqi, Chen Zhen Pages 443-450
    The steady Reynolds-Averaged Navier-Stokes (RANS) method with the Realizable kturbulence model was used to analyze the flow field around a race car (generic Formula One). This study was conducted using the ANSYS software package. The numerical simulations were conducted at a Reynolds number based on the race car model (14.9×106). The time-averaged velocity field, flow topology, velocity magnitude, static pressure magnitude and vortex regions of the flow fields are presented in this paper. The measurements were performed on the vertical and cross-sectional planes. The results are presented graphically, showing the main characteristics of the flow field around the whole race car, whereas most previous studies only mention the flow field around individual components of race cars. The Realizable kturbulence model results showed consistency with the valuable validation data, which helps to elucidate the flow field around a model generic Formula one race car.
    Keywords: Numerical simulation, Vehicle aerodynamics, RANS equations, Race car, Flow field
  • Ali Shokrgozar Abbasi, Asghar Baradaran Rahimi, Hamidreza Mozayeni Pages 451-461
    General formulation and solution of Navier-Stokes and energy equations are sought in the study of threedimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration towards the main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z- direction, with strain rate a impinges on this flat plate and produces an unsteady three-dimensional axisymmetric flow in which the plate moves along z direction with variable velocity and acceleration in general. A reduction of Navier-Stokes and energy equations is obtained by use of appropriate similarity transformations, for the first time. The obtained ordinary differential equations are solved by using finite-difference numerical techniques. Velocity and pressure profiles along with temperature profiles are presented for different examples of the plate velocity functions and selected Prandtl numbers. According to the results obtained, the velocity and thermal boundary layers feel the effect of variations of the plate velocity more than the plate acceleration. It means that the minimum boundary layer thickness happens at the maximum value of the plate velocity and acceleration effect plays a secondary role.
    Keywords: Stagnation, point flow, heat transfer, Unsteady flow, Viscous fluid, Accelerated plate, Similarity solution, Three, dimensional axisymmetric
  • Deepa Sinha, Preeti Jain, P.G. Siddheshwar, N. S. Tomer Pages 463-474
    Steady, transverse boundary layer flow and heat transfer caused by an exponentially stretching cylinder of constant radius immersed in an uniform flow of an incompressible, viscous nanoliquid are considered in thepresentstudy. Thepaperdiscussesasystematicprocedureofobtainingalocalsimilaritytransformation that reduces the governing partial differential equations into ordinary differential equations. Power series solution is then obtained for velocity, temperature and nanoparticle concentration distributions using the uni-variate differential transform method. Help is sought from Domb-Sykes plots in making a decision on the minimum number of terms required in the power series expansion to ensure convergence. Radius of convergence is quite naturally suggested by these plots. Pad´ e approximants are then appropriately decided upontoincreasetheradiusofconvergence. Thealgorithmusedsucceedsincapturingboundaryeffects,free stream flow effects and nanoparticle effects on flow and heat transfer. An important finding of the paper is thepredictionofacceleratedcoolingofthestretchingcylinderduetothenanoparticlesinthecoolingliquid. Inhavingadesirablepropertyfortheextrudingcylindernanoliquidcoolantseemsanattractiveproposition.
    Keywords: Nanoliquid, Stretching cylinder, Free stream, Domb, Sykes, Buongiorno
  • Nidhi Pandya, Ashish Shukla Pages 475-785
    This paper investigates study of MHD(Magnetohydrodynamics) flow of viscous incompressible fluid past an inclined porous plate embedded in porous medium with the effects of Thermophoresis, Dufour, Hall, radiation,viscousdissipation,chemicalreactionandheatgenerationorabsorption. Nondimensionalpartial differential equations of governing equations of flow are solved numerically by applying Crank-Nicolson finitedifferencemethodfordifferentvaluesofparameters. Velocity,temperature,concentrationprofilesare discussed through graphs for different values of parameters and skin friction coefficients, Nusselt number and Sherwood number are discussed through tables.
    Keywords: MHD, Dufoureffect, Thermophoresiseffect, Halleffect, radiationeffect, HeatandMasstransfer, chemical reaction, Crank, Nicolson method
  • Joseph Houben, Erwin Brunnmair, Christian Weiss, Stefan Pirker Pages 487-499
    A problem of cyclone separators is the low grade efficiency of small particles. Therefore, a high efficiency cyclone separator has been developed and successfully tested in former work. In this cyclone separator, a vortex stabilizer is used to suppress the vortex core precession. In this article, the pressure and flow field in this cyclone separator are calculated by means of computational fluid dynamics using the commercial software Ansys Fluent 13. The position of the vortex core is tracked in these simulations by searching the position of minimal dynamic pressure and the centre of moment of the horizontal velocity components as function of the axial coordinate. The results are compared with experimental data. It is demonstrated that when using a stabilizer, the vortex is kept in position. Furthermore the maximum of the tangential velocity is found to be larger, which is known to have a positive effect on the separation of small particles in the inner solid body rotation vortex.
    Keywords: Computational Fluid Dynamics, preceeding vortex core, cyclone separator, pressure drop
  • Dr. Srinivas Jangili, Ramana Murthy Josyula Pages 501-507
    The paper deals with the flow of two immiscible couple stress fluids between two homogeneous permeable beds. The flow is considered in two zones: zone I and II contain free flow of two immiscible couple stress fluids between two permeable porous beds at the bottom and top. The flow in the free channel bounded by two permeable beds is assumed to be governed by Stokes’s couple stress fluid flow equations and that in the permeable beds by Darcy’s law. The continuity of velocity, vorticity, shear stress and couple stress are imposed at the fluid-fluid interface and Beavers-Joseph (BJ) slip boundary conditions are employed at the fluid-porous interface. The equations are solved analytically and the expressions for velocity, skin friction and volumetric flow rate are obtained. The effects of the physical governing parameters on velocity are investigated.
    Keywords: Immiscible uids, Couple stress uid, Permeable beds, Darcy's law, Beavers, Joseph (BJ) slip boundary condition
  • Mohammed Abdulhameed, Ishak Hashim, Habibis Saleh, Rozaini Roslan Pages 509-517
    The problem of transient flow of incompressible third grade fluid on the two-dimensional magnetohydrodynamic (MHD) flow in a porous space is analyzed. The flow is generated due to the motion of the plate in its plane with a periodic velocity. Under the flow assumptions, the governing nonlinear partial differential equation is transformed into steady-state and transient nonlinear equations. The reduced equation for the transient flow is solved analytically using symmetry approach while the nonlinear steady-state equation is solvedusingamodifiedversionofHe’shomotopyperturbationmethod. Theeffectofseveraloperatingparameters on the flowhydromagnetic isdiscussed. The results indicated that for the considered case,t =1.5 is the moment after which the time-dependent transient motion of the fluid can be approximated with the steady-state motion, described by the steady-state solution. It is clear that, after this value of time t the time-dependent transient solution can be neglected.
    Keywords: Periodic wall, Transient ow, Third, grade uid, Analytical solutions, Magnetohydrodynamic, Porous space