Showing papers on "Similarity solution published in 2015"

Unsteady boundary layer flow over a permeable curved stretching/shrinking surface

Abstract: The problem of unsteady viscous flow over a curved stretching/shrinking surface with mass suction is studied. A similarity transformation is used to reduce the system of partial differential equations to an ordinary differential equation. This equation is then solved numerically using the function bvp4c from Matlab for different values of the curvature, mass suction, unsteadiness and stretching/shrinking parameters. The physical quantities of interest, such as reduced skin friction, velocity and shear stress are obtained and discussed as functions of these parameters. Results show that for both cases of stretching and shrinking surfaces, multiple (dual, upper and lower branch) solutions exist for a certain range of curvature, mass suction, unsteadiness and stretching/shrinking parameters. This is an opposite situation than that of the plane stretching sheet. In order to establish which of these solutions are stable and which are not, a stability analysis has been performed. It is evident from the results that the pressure inside the boundary layer cannot be neglected for a curved stretching sheet, as distinct from a flat stretching sheet.

Flow of a generalised Newtonian fluid due to a rotating disk

Abstract: The boundary-layer flow due to a rotating disk is considered for a number of generalised Newtonian fluid models. In the limit of large Reynolds number the flow inside the three-dimensional boundary-layer is determined via a similarity solution. Results for power-law and Bingham plastic fluids agree with previous investigations. We present solutions for fluids that adhere to the Carreau viscosity model. It is well known that unlike the power-law and Bingham models the Carreau model is applicable for vanishingly small, and infinitely large shear rates, as such we suggest these results provide a more accurate description of non-Newtonian rotating disk flow.

Similarity solution to three dimensional boundary layer flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink

Abstract: Development of human society greatly depends upon solar energy. Heat, electricity and water from nature can be obtained through solar power. Sustainable energy generation at present is a critical issue in human society development. Solar energy is regarded one of the best sources of renewable energy. Hence the purpose of present study is to construct a model for radiative effects in three-dimensional of nanofluid. Flow of second grade fluid by an exponentially stretching surface is considered. Thermophoresis and Brownian motion effects are taken into account in presence of heat source/sink and chemical reaction. Results are derived for the dimensionless velocities, temperature and concentration. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration. Numerical computations are presented to examine the values of skin-friction coefficients, Nusselt and Sherwood numbers. It is observed that the values of skin-friction coefficients are more for larger values of second grade parameter. Moreover the radiative effects on the temperature and concentration are quite reverse.

Group Analysis of Free Convection Flow of a Magnetic Nanofluid with Chemical Reaction

Abstract: A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species) conservation are derived. Our (group) analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional to whilst the reaction rate is proportional to , where is the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

Unsteady Flow of Shear-Thinning Fluids in Porous Media with Pressure-Dependent Properties

Abstract: Inthispaper,amodelforinjectionofapower-lawshear-thinningfluidinamedium withpressure-dependentpropertiesisdevelopedinageneralizedgeometry(plane,radial,and spherical). Permeability and porosity are taken to be power functions of the pressure incre- ment with respect to the ambient value. The model mimics the injection of non-Newtonian fluids in fractured systems, in which fractures are already present and are enlarged and even- tually extended and opened by the fluid pressure, as typical of fracing technology. Empiric equations are combined with the fundamental mass balance equation. A reduced model is adopted, where the medium permeability resides mainly in the fractures; thefluid and porous medium compressibility coefficients are neglected with respect to the effects induced by pressure variations. At early and intermediate time, the flow interests only the fractures. In these conditions, the problem admits a self-similar solution, derived in closed form for an instantaneous injection (or drop-off) of the fluid, and obtained numerically for a generic monomial law of injection. At late times, the leak-off of the fluid towards the porous matrix is taken into accountvia a sink term in the mass balance equation. In this case, the original set of governing equations needs to be solved numerically; an approximate self-similar solution valid for a special combination of parameters is developed by rescaling time. An example of application in a radial geometry is provided without and with leak-off. The system behaviour isanalysedconsideringthespeedofthepressurefrontandthevariationofthepressurewithin

Large strain similarity solution for a spherical or circular opening excavated in elastic‐perfectly plastic media

Abstract: Summary This paper deals with the unloading problem of a spherical or circular opening excavated in elastic-perfectly plastic media with a nonassociated Mohr–Coulomb yield criterion. A large strain similarity solution, using incremental velocity approach, is presented by replacing partial differential equations from stress equilibrium, constitutive law, consistency condition, and displacement equation with first-order ordinary differential equations. The classical Runge–Kutta method is used to solve the first-order ordinary differential equations. Comparisons among small and large strain solutions are made using some data sets of soil and rock. The results show that the displacements by large strain similarity solution are smaller than those by exact small strain solution and somewhat larger than those by large strain solution using total strain approach. Copyright © 2014 John Wiley & Sons, Ltd.

Evaluation of the heat transfer rate increases in retention pools nuclear waste

Abstract: In this paper, we have tried to find a solution for quick transfer of nuclear wastes from pools of cool water to dry stores to reduce the environmental concerns and financial cost of burying atomic waste. Therefore, the rate of heat transfer from atomic waste materials to the outer surface of the container should be increased. This can be achieved by covering the bottom of the pool space with conical fins (vertically) embedded in porous medium and allowing natural convection flow of Newtonian nanofluid upon it. In this research, we studied the rate of heat transfer by using such special space. In this study, Heat transfer boundary layer flow in Nano-fluidics shifting from a vertical cone in porous medium, two-dimensional, steady, incompressible and low speed flow have been considered and attempts have been made to obtain analytical solutions for it. The obtained nonlinear ordinary differential equation has been solved through homotopy analysis method (HAM), considering boundary conditions and Nusselt number. Also, Nusselt number, which is an important parameter in heat transfer, is calculated using the obtained analytical solution by HAM. A comparison of the obtained analytical solution with the numerical results represented a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.

Unsteady turbulent buoyant plumes

Abstract: We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed integral model. Therefore, our model does not exhibit the mathematical pathologies that appear in previously proposed unsteady integral models of turbulent plumes. A stability threshold for the value of the shape factor is identified, resulting in a range of its values where the amplitude of small perturbations to the steady solutions decay with distance from the source. The hyperbolic character of the system allows the formation of discontinuities in the fields describing the plume properties during the unsteady evolution. We compute numerical solutions to illustrate the transient development following an abrupt change in the source conditions. The adjustment to the new source conditions occurs through the propagation of a pulse of fluid through the plume. The dynamics of this pulse are described by a similarity solution and, by constructing this new similarity solution, we identify three regimes in which the evolution of the transient pulse following adjustment of the source qualitatively differ.

Similarity solution to fractional nonlinear space-time diffusion-wave equation

Abstract: In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.

Systematic errors of skin-friction measurements by oil-film interferometry

Abstract: In recent years, the independent measurement of wall shear stress with oil-film or oil-drop interferometry has become a cornerstone of turbulent-boundary-layer research as many arguments depend critically on a precise knowledge of the skin friction tau(w)*. To our knowledge, all practitioners of oil-drop interferometry have so far used the leading-order similarity solution for asymptotically thin, wedge-shaped, two-dimensional oil films established by Tanner & Blows (J. Phys. E: Sci. Instrum., vol. 9, 1976, pp. 194202) to relate the evolution of drop thickness to tau(w)*. It is generally believed that this procedure, if carefully implemented, yields the true time-averaged tau(w)* within +/- 1% or possibly better, but the systematic errors due to the finite thickness of the oil film have never been determined. They are analysed here for oil films with a thickness of the order of a viscous unit in a zero-pressure-gradient turbulent boundary layer. Neglecting spanwise surface curvature and surface tension effects, corrections due to the secondary air boundary layer above the oil film are derived with a linearised triple-layer approach that accounts for the turbulent shear-stress perturbation by means of modified van-Driest-type closure models. In addition, the correction due to processing oil drops with a slight streamwise surface curvature as if they were exact wedges is quantified. Both corrections are evaluated for oil-drop interferograms acquired in a zero-pressure-gradient turbulent boundary layer at a Reynolds number of around 3500, based on displacement thickness, and are shown to produce a reduction of the friction velocity relative to the basic Tanner and Blows theory of between -0.1% and -1.5 %, depending on the mixing-length model. Despite the uncertainty about the true correction, the analysis allows the formulation of some guidelines on where and when to analyse interference fringes in order to minimise the error on the measured wall shear stress.

A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids

Abstract: A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluid in which the stress, an arbitrary function of rates of strain, is studied. It is shown that under any group of transformation, for an arbitrary stress function, not all non-Newtonian fluids possess a similarity solution for the flow past a wedge inclined at arbitrary angle except Ostwald-de-Waele power-law fluid. Further it is observed, for non-Newtonian fluids of any model only 90 ° of wedge flow leads to similarity solutions. Our results contain a correction to some flaws in Pakdemirli׳s [14] (1994) paper on similarity analysis of boundary layer equations of a class of non-Newtonian fluids.

Radiation, Heat Generation and Viscous Dissipation Effects on MHD Boundary Layer Flow for the Blasius and Sakiadis Flows with a Convective Surface Boundary Condition

Abstract: This study is devoted to investigate the radiation, heat generation viscous dissipation and magnetohydrodynamic effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique alongside with the forth order of Runge-Kutta method and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Magnetic field parameter M, Grashof number Gr, Prandtl number Pr, radiation parameter NR, Heat generation parameter Q, Convective parameter

Finite Reynolds number properties of a turbulent channel flow similarity solution

Abstract: Finite Reynolds number behaviors of the asymptotically logarithmic mean velocity profile in fully developed turbulent channel flow are investigated. The scaling patch method of Fife et al. [“Multiscaling in the presence of indeterminacy: Wall-induced turbulence,” Multiscale Model. Simul. 4, 936 (2005)] is used to reveal invariance properties admitted by the appropriately simplified form of the mean momentum equation. These properties underlie the existence of a similarity solution to this equation over an interior inertial domain. The classical logarithmic mean velocity profile equation emerges from this similarity solution as the Reynolds number becomes large. Originally demonstrated via numerical integration, it is now shown that the solution to the governing nonlinear equation can be found by straight-forward analytical integration. The resulting solution contains both linear and logarithmic terms, but with the coefficient on the linear term decaying to zero as the Reynolds number tends to infinity. In this way, the universality of the classical logarithmic law comports with the existence of an invariant form of the mean momentum equation and is accordingly described by the present similarity solution. Existing numerical simulation data are used to elucidate Reynolds number dependent properties of the finite Reynolds number form of the similarity solution. Correspondences between these properties and those indicated by finite Reynolds number corrections to the classical overlap layer formulation for the mean velocity profile are described and discussed.

Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

Abstract: The free convective flow of an incompressible micropolar fluid along permeable vertical plate under the convective boundary condition is investigated. The Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method. A quantitative comparison of the numerical results is made with previously published results for special cases and the results are found to be in good agreement. The results of the physical parameters on the developments of flow, temperature, concentration, skinfriction, wall couple stress, heat transfer, and mass transfer characteristics along vertical plate are given and the salient features are discussed.

Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

Abstract: A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n . The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b ≥0. The cases k ⋛ 1 are associated with wide, triangular and narrow cross sections. For b >0, the cases k ≷ 1 describe widening channels and squeezing fractures; b =0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like t α , scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume ( α ), the fluid rheological behaviour ( n ), and the transversal ( k ) and longitudinal ( b ) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.

Equilibrium similarity solution of the turbulent transport equation along the centreline of a round jet

Abstract: A novel similarity-based form is derived of the transport equation for the second-order velocity structure function of along the centreline of a round turbulent jet using an equilibrium similarity analysis. This self-similar equation has the advantage of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. It is suggested that the normalised third-order structure function can be uniquely determined when the normalised second-order structure function, the power-law exponent of and the decay rate constants of and are available. In addition, the current analysis demonstrates that the assumption of similarity, combined with an inverse relation between the mean velocity and the streamwise distance from the virtual origin (i.e. ), is sufficient to predict a power-law decay for the turbulence kinetic energy ( ), rather than requiring a power-law decay ( ) as an additional ad hoc assumption. On the basis of the current analysis, it is suggested that the mean kinetic energy dissipation rate, , varies as . These theoretical results are tested against new experimental data obtained along the centreline of a round turbulent jet as well as previously published data on round jets for over the range . For the present experiments, exhibits power-law behaviour with . The validity of this solution is confirmed using other experimental data where follows a power law with . The present similarity form of the transport equation for is also shown to be closely satisfied by the experimental data.

Filling box flows in porous media

Abstract: We report upon a theoretical and experimental investigation of a porous medium ‘filling box’ flow by specifically examining the details of the laminar descending plume and its outflow in a control volume having an impermeable bottom boundary and sidewalls. The plume outflow initially comprises a pair of oppositely directed gravity currents. The gravity currents propagate horizontally until they reach the lateral sidewalls at . The flow then becomes of filling box type, with a vertically ascending ‘first front’ separating discharged plume fluid below from ambient fluid above. The flow details are described analytically by first deriving a new similarity solution for Darcy plumes with , where is the Peclet number. From the similarity solution so obtained, we then derive expressions for the plume volume flux and mean reduced gravity as functions of the vertical distance from the source. Regarding the plume outflow, a similarity solution adopted from Huppert & Woods (J. Fluid Mech., vol. 292, 1995, pp. 55–69) describes the height and front speed of the gravity currents, whereas a semi-implicit finite difference scheme is used to predict the first front elevation versus time and horizontal distance. As with high-Reynolds-number filling box flows, that studied here is an example of a coupled problem: the gravity current source conditions are prescribed by the plume volume flux and mean reduced gravity. Conversely, discharged plume fluid may be re-entrained into the plume, be it soon or long after reaching the bottom impermeable boundary. To corroborate our model predictions, analogue laboratory experiments are performed with fresh water and salt water as the working fluids. Our experiments consider as independent variables the porous medium bead diameter and the plume source volume flux and reduced gravity. Predictions for the gravity current front position and height compare favourably against analogue measured data. Good agreement is likewise noted when considering either the mean elevation or the profile of the first front. Results from this study may be adopted in modelling geological plumes. For example, our equations can be used to predict the time required for discharged plume fluid to return to the point of injection in the case of aquifers closed on the sides and below by impermeable boundaries.

A numerical study of similarity solution for mixed-convection copper-water nanofluid boundary layer flow over a horizontal plate

Abstract: دییامن هدافتسا لیذ ترابع زا هلاقم نیا هب عاجرا يارب : Please cite this article using: M. Ziaei-Rad, A. Kasaeipoor, A Numerical study of similarity solution for mixed-convection copper-water nanofluid boundary layer flow over a horizontal plate, Modares Mechanical Engineering, Vol. 14, No. 14, pp. 190-198, 2015 (In Persian) بآ لایسونان يارب یبیکرت ییاجباج يزرم هیلا نایرج یهباشت لح يددع هعلاطم سم زا

Local Non-similarity Solution for MHD Mixed Convection Flow of aNanofluid Past a Permeable Vertical Plate in the Presence of ThermalRadiation Effects

Abstract: Combined heat and mass transfer on mixed convection non-similar flow of electrically conducting nanofluid along a permeable vertical plate in the presence of thermal radiation is investigated. The governing partial differential equations of the problem are transformed into a system of non linear ordinary differential equations by applying the Sparrow–Quack–Boerner local non-similarity method (LNM). Furthermore, the obtained equations are solved numerically by employing the Fourth or fifth order Runge Kutta Fehlberg method with conjunction to shooting technique. The profiles of flow and heat transfer are verified by using five types of nanofluids of which metallic or nonmetallic nanoparticles, namely Copper (Cu), Alumina (Al2O3), Copper oxide (CuO), silver (Ag) and Titanium (TiO2) with a water-based fluid. Rosseland approximation model on black body is used to represent the radiative heat transfer. Effects of thermal radiation, buoyancy force parameters and volume fraction of nanofluid on the velocity and temperature profiles in the presence of suction/injection are depicted graphically. Comparisons with previously published works are performed, and excellent agreement between the results is obtained. The conclusion is that the flow fields is affected by these parameters.

Flow and Heat Transfer of a Nanofluid over an Exponentially Shrinking Sheet

Abstract: A mathematical model of the steady boundary layer flow and heat transfer of nanofluid due to an exponentially shrinking sheet is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into ordinary differential equation by similarity transformations. The transformed equations are solved numerically by using shooting method. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion Br and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Similarity and singularity in adhesive elastohydrodynamic touchdown

Abstract: We consider the touchdown of an elastic sheet as it adheres to a wall, which has a dynamics that is limited by the viscous resistance provided by the squeeze flow of the intervening liquid trapped between the two solid surfaces. The dynamics of the sheet is described mathematically by elastohydrodynamic lubrication theory, coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion and the viscous thin film flow. We use a combination of numerical simulations of the governing partial differential equation and a scaling analysis to describe the self-similar solution of the touchdown of the sheet as it approaches the wall. An analysis of the equation satisfied by the similarity variables in the vicinity of the touchdown event shows that an entire sequence of solutions are allowed. However, a comparison of these shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics and adhesion.

An examination of the high-order statistics of developing jets, lazy and forced plumes at various axial distances from their source

Abstract: In this study, direct numerical simulations of a turbulent free jet (Re = 2000), a lazy plume (), and a forced plume (Re = 1684, Ri = 0.025) are compared. The evolution of the various fluxes and the so-called source parameter, Γ, are examined as a function of distance from the source. The first-, second-, and third-order statistics of the flows are calculated and discussed. The radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances, one axial distance before the flows have adjusted to their similarity solution, and the other beyond the similarity adjustment length scale. Vortical structures are visualised and discussed along with entrainment. The source term Γ was not found to monotonically decrease with axial distance from the source as predicted by past researchers. While the mean flow and turbulent velocity statistics of the simulated lazy and forced plumes took on similar behaviour far f...

Hydromagnetic Boundary Layer Flow and Heat Transfer Characteristics of a Nanofluid over an Inclined Stretching Surface in the Presence of a Convective Surface: A Comprehensive Study

Abstract: In this paper we investigate numerically the hydromagnetic boundary layer flow and heat transfer characteristics of a nanofluid using three types of nanoparticles (copper, aluminium oxide and titanium dioxide) having various shapes (spherical, cylindrical, arbitrary, etc) by considering three kinds of base fluids (water, ethylene glycol and engine oil) over a nonlinear inclined stretching surface, taking into account the effect of convective surface condition. Using similarity transformations, the governing nonlinear partial differential equations of the physical model are transformed into non-dimensional ordinary differential equations which are solved for local similar solutions using the very robust computer algebra software, Maple 13. The numerical simulation is carried out to investigate the role of the pertinent parameters on the flow and temperature fields as well as on the rate of heat transfer and on the rate of shear stress. The results show that the addition of nanoparticles to the base fluid may not always increase the rate of heat transfer. It depends significantly on the surface convection, type of base fluid and nanoparticles. The finding of this study will open a gate for better understanding of nanofluid characteristics.

Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet

Abstract: This work deals with the boundary layer flow and heat transfer of an electrically conducting viscous fluid over a stretching sheet. Lie-group method is applied for determining the symmetry reductions for the governing equations by reducing the number of independent variables in the given system of partial differential equations by one, leading to a system of non-linear ordinary differential equation. The resulting system is then solved numerically using shooting method coupled with Runge-Kutta scheme. Effects of various values of physical parameters on the horizontal and vertical velocities, temperature profiles, wall heat transfer and the wall shear stress (skin friction), have been studied and the results are plotted. Furthermore, a comparison between the present results with existing numerical and homotopy methods has been reported and we found that they are in a good agreement.

Slip Effects on MHD Stagnation Point-flow and Heat Transfer over a Porous Rotating Disk

Abstract: The main concern of present study is to investigate the MHD stagnation flow past a porous rotating disk in the presence of the velocity slip condition. The boundary-layer governing partial differential equations (PDEs) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum and energy equations using similarity solution. The velocity profiles in radial, tangential and axial directions and temperature distribution are obtained via a semi analytical/numerical method, called Homotopy Analysis Method (HAM). An excellent agreement is observed between some of the obtained results of the current study and those of previously published studies. The influences of physical flow parameters such as magnetic interaction