The effect of magnetohydrodynamic(MHD)plasma actuators on the control of hypersonic shock wave/turbulent boundary layer interactions is investigated here using Reynolds-averaged Navier-Stokes calculations with low mag...The effect of magnetohydrodynamic(MHD)plasma actuators on the control of hypersonic shock wave/turbulent boundary layer interactions is investigated here using Reynolds-averaged Navier-Stokes calculations with low magnetic Reynolds number approximation.A Mach 5 oblique shock/turbulent boundary layer interaction was adopted as the basic configuration in this numerical study in order to assess the effects of flow control using different combinations of magnetic field and plasma.Results show that just the thermal effect of plasma under experimental actuator parameters has no significant impact on the flow field and can therefore be neglected.On the basis of the relative position of control area and separation point,MHD control can be divided into four types and so effects and mechanisms might be different.Amongst these,D-type control leads to the largest reduction in separation length using magnetically-accelerated plasma inside an isobaric dead-air region.A novel parameter for predicting the shock wave/turbulent boundary layer interaction control based on Lorentz force acceleration is then proposed and the controllability of MHD plasma actuators under different MHD interaction parameters is studied.The results of this study will be insightful for the further design of MHD control in hypersonic vehicle inlets.展开更多
A three-dimensional （3-D） transient model has been developed to investigate plasma deformation driven by a magnetic field and its influence on arc stability in a circuit breaker. The 3-D distribution of electric cur...A three-dimensional （3-D） transient model has been developed to investigate plasma deformation driven by a magnetic field and its influence on arc stability in a circuit breaker. The 3-D distribution of electric current density is obtained from a current continuity equation along with the generalized Ohm＇s law; while the magnetic field induced by the current flowing through the arc column is calculated by the magnetic vector potential equation. When gas interacts with an arc column, fundamental factors, such as Ampere＇s law, Ohm＇s law, the turbulence model, transport equations of mass, momentum and energy of plasma flow, have to be coupled for aria- lyzing the phenomenon. The coupled interactions between arc and plasma flow are described in the fl＇amework of time-dependent magnetohydrodynamic （MHD） equations in conjunction with a K-~ turbulence model. Simulations have been focused on sausage and kink instabilities in plasma （these phenomena are related tO pinch effects and electromagnetic fields）. The 3-D sjm- ulation reveals the relation between plasma deformation and instability phenomena, which affect arc stability during circuit breaker operation. Plasma deformation is the consequence of coupled interactions between the electromagnetic force and plasma flow described in simulations.展开更多
The thin aluminum liners with an aspect ratio R/?r 1 have been imploded on the primary test stand(PTS) facility,where R is the outer radius of the liner and ?r is the thickness. The x-ray self-emission images present ...The thin aluminum liners with an aspect ratio R/?r 1 have been imploded on the primary test stand(PTS) facility,where R is the outer radius of the liner and ?r is the thickness. The x-ray self-emission images present azimuthally correlated perturbations in the liner implosions. The experiments show that at-10 ns before the stagnation, the wavelengths of perturbation are about 0.93 mm and 1.67 mm for the small-radius and large-radius liners, respectively. We have utilized the resistive magnetohydrodynamic code PLUTO to study the development of magneto-Rayleigh–Taylor(MRT) instabilities under experimental conditions. The calculated perturbation amplitudes are consistent with the experimental observations very well. We have found that both mode coupling and long implosion distance are responsible for the more developed instabilities in the large-radius liner implosions.展开更多
In a gas circuit breaker,metal vapor resulting from electrode erosion is injected into the arc plasma.The arc then burns in a mixture of SF;and electrode vapor,which has properties significantly different from those o...In a gas circuit breaker,metal vapor resulting from electrode erosion is injected into the arc plasma.The arc then burns in a mixture of SF;and electrode vapor,which has properties significantly different from those of pure SF;.Thermodynamic properties and transport coefficients of thermal plasmas formed in SF;-copper vapor mixtures change as a function of temperature and pressure.The property that is mostly affected by the presence of copper is electrical conductivity,which is important in magnetohydrodynamic（MHD） analysis.In this study,the transport coefficients of SF;in the presence of 10 percent copper are considered as the basis of MHD simulation.Comparisons are made between the results during arc formation for pure SF;and SF;-Cu mixture in a medium voltage（MV） circuit breaker.According to the transport coefficients influenced by the SF;-Cu mixture,the distribution of the electric potential, temperature,electromagnetic force density and current density of the arc column are presented and discussed.Also,the arc stability and pinch effect near current zero with 3-D simulation are investigated,which is advantageous to improving the efficiency of arc plasma simulation.展开更多
Magnetohydrodynamic （MHD） pressure drop in the Chinese Dual Functional Liquid Lithium-lead Test Blanket Module （DFLL-TBM） proposed for ITER is discussed in this paper. Electrical insulation between the coolant cha...Magnetohydrodynamic （MHD） pressure drop in the Chinese Dual Functional Liquid Lithium-lead Test Blanket Module （DFLL-TBM） proposed for ITER is discussed in this paper. Electrical insulation between the coolant channel surfaces and the liquid metal is required to reduce the MHD pressure drop to a manageable level. Insulation can be provided by a thin insulating coating, such as Al2O3, which can also serve as a tritium barrier layer, at the channel surfaces in contact with LiPb. The coating＇s effectiveness for reducing the MHD pressure drop is analysed through three-dimensional numerical simulation. A MHD-based commercial computational fluid dynamic （CFD） software FLUENT is used to simulate the LiPb flow. The effect on the MHD pressure drop due to cracks or faults in the coating layer is also considered. The insulating performance requirement for the coating material in DFLL-TBM design is proposed according to the analysis.展开更多
This paper generally compares the essential features between tokamaks and stellarators,based on previous review work individually made by authors on several specific topics,such as theories,bulk plasma transport and e...This paper generally compares the essential features between tokamaks and stellarators,based on previous review work individually made by authors on several specific topics,such as theories,bulk plasma transport and edge divertor physics,along with some recent results.It aims at summarizing the main results and conclusions with regard to the advantages and disadvantages in these two types of magnetic fusion devices.The comparison includes basic magnetic configurations,magnetohydrodynamic(MHD)instabilities,operational limits and disruptions,neoclassical and turbulent transport,confinement scaling and isotopic effects,plasma rotation,and edge and divertor physics.Finally,a concept of quasi-symmetric stellarators is briefly referred along with a comparison of future application for fusion reactors.展开更多
An analysis has been carried out to study the effects of radiation absorption and firstorder chemical reaction on unsteady mixed convective flow of a viscous incompressible electrically conducting fluid through a poro...An analysis has been carried out to study the effects of radiation absorption and firstorder chemical reaction on unsteady mixed convective flow of a viscous incompressible electrically conducting fluid through a porous medium of variable permeability between two long vertical non conducting wavy channels in the presence of heat generation.The unsteadiness in the flow is due to traveling thermal wave imposed on the walls.The governing equations are solved subject to the relevant boundary conditions with the assumption that the solution consists of a mean part and a perturbed part.The zeroth-order,the first order and the total solution of the problem are numerically evaluated and displayed graphically for pertinent parameters.This model finds applications in studying fixed-bed catalytic reactors and packed bed heat exchangers.展开更多
This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel.The nanoparticles of silver and alumina have...This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel.The nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal direction.Equations that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate variables.Homotopy analysis method is used for the solution of the resultant equations.In this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness factor.Temperature of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin film.Concentration distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.展开更多
The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a por...The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.展开更多
Magnetohydrodynamic (MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversi...Magnetohydrodynamic (MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversion in Tokamak fusion reactor. The physical model employed for simulations is refined from dual-coolant lead-lithium (DCLL) blanket. A magnetic-convection code based on a consistent and conservative scheme is developed with the help of finite volume method, and validated by some Benchmark analytical solutions. The flows inside duct with thermal insulating and electric conducting walls under exponential neutron volumetric heat source are simulated. Based on Boussinesq assumption, the influences of wall electrical conductivity and buoyancy on velocity fields, temperature distributions and Nusselt numbers are investigated. Results illustrates that the wall conductance ratio dominates the flow at low Grashof numbers and high wall conductance ratio, while buoyancy effect dominates the jet flow near side wall at a high Grashof number. In addition, the velocity along flow direction substantially impacts features of the Nusselt number and temperature distribution. Besides, the jet flow results in a higher Nusselt number and lower temperature.展开更多
This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which i...This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.展开更多
This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distr...This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.展开更多
Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip ...Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.展开更多
The chemical reaction effect on an unsteady magnetohydrodynamic （MHD） flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are ...The chemical reaction effect on an unsteady magnetohydrodynamic （MHD） flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations （ODEs） using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.展开更多
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. ...Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.展开更多
基金Project supported by the National Key R&D Program of China(Nos.2019YFA0405300 and 2019YFA0405203)the Chinese Scholarship Council(CSC)(No.201903170195)。
文摘The effect of magnetohydrodynamic(MHD)plasma actuators on the control of hypersonic shock wave/turbulent boundary layer interactions is investigated here using Reynolds-averaged Navier-Stokes calculations with low magnetic Reynolds number approximation.A Mach 5 oblique shock/turbulent boundary layer interaction was adopted as the basic configuration in this numerical study in order to assess the effects of flow control using different combinations of magnetic field and plasma.Results show that just the thermal effect of plasma under experimental actuator parameters has no significant impact on the flow field and can therefore be neglected.On the basis of the relative position of control area and separation point,MHD control can be divided into four types and so effects and mechanisms might be different.Amongst these,D-type control leads to the largest reduction in separation length using magnetically-accelerated plasma inside an isobaric dead-air region.A novel parameter for predicting the shock wave/turbulent boundary layer interaction control based on Lorentz force acceleration is then proposed and the controllability of MHD plasma actuators under different MHD interaction parameters is studied.The results of this study will be insightful for the further design of MHD control in hypersonic vehicle inlets.
文摘A three-dimensional （3-D） transient model has been developed to investigate plasma deformation driven by a magnetic field and its influence on arc stability in a circuit breaker. The 3-D distribution of electric current density is obtained from a current continuity equation along with the generalized Ohm＇s law; while the magnetic field induced by the current flowing through the arc column is calculated by the magnetic vector potential equation. When gas interacts with an arc column, fundamental factors, such as Ampere＇s law, Ohm＇s law, the turbulence model, transport equations of mass, momentum and energy of plasma flow, have to be coupled for aria- lyzing the phenomenon. The coupled interactions between arc and plasma flow are described in the fl＇amework of time-dependent magnetohydrodynamic （MHD） equations in conjunction with a K-~ turbulence model. Simulations have been focused on sausage and kink instabilities in plasma （these phenomena are related tO pinch effects and electromagnetic fields）. The 3-D sjm- ulation reveals the relation between plasma deformation and instability phenomena, which affect arc stability during circuit breaker operation. Plasma deformation is the consequence of coupled interactions between the electromagnetic force and plasma flow described in simulations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11605013,11775032,11805019,and 11705013)
文摘The thin aluminum liners with an aspect ratio R/?r 1 have been imploded on the primary test stand(PTS) facility,where R is the outer radius of the liner and ?r is the thickness. The x-ray self-emission images present azimuthally correlated perturbations in the liner implosions. The experiments show that at-10 ns before the stagnation, the wavelengths of perturbation are about 0.93 mm and 1.67 mm for the small-radius and large-radius liners, respectively. We have utilized the resistive magnetohydrodynamic code PLUTO to study the development of magneto-Rayleigh–Taylor(MRT) instabilities under experimental conditions. The calculated perturbation amplitudes are consistent with the experimental observations very well. We have found that both mode coupling and long implosion distance are responsible for the more developed instabilities in the large-radius liner implosions.
文摘In a gas circuit breaker,metal vapor resulting from electrode erosion is injected into the arc plasma.The arc then burns in a mixture of SF;and electrode vapor,which has properties significantly different from those of pure SF;.Thermodynamic properties and transport coefficients of thermal plasmas formed in SF;-copper vapor mixtures change as a function of temperature and pressure.The property that is mostly affected by the presence of copper is electrical conductivity,which is important in magnetohydrodynamic（MHD） analysis.In this study,the transport coefficients of SF;in the presence of 10 percent copper are considered as the basis of MHD simulation.Comparisons are made between the results during arc formation for pure SF;and SF;-Cu mixture in a medium voltage（MV） circuit breaker.According to the transport coefficients influenced by the SF;-Cu mixture,the distribution of the electric potential, temperature,electromagnetic force density and current density of the arc column are presented and discussed.Also,the arc stability and pinch effect near current zero with 3-D simulation are investigated,which is advantageous to improving the efficiency of arc plasma simulation.
基金Anhui Provincial Natural Science Foundation of China(No.070413085)Anhui Education Department Natural Science Foundation of China(No.2006KJ264)
文摘Magnetohydrodynamic （MHD） pressure drop in the Chinese Dual Functional Liquid Lithium-lead Test Blanket Module （DFLL-TBM） proposed for ITER is discussed in this paper. Electrical insulation between the coolant channel surfaces and the liquid metal is required to reduce the MHD pressure drop to a manageable level. Insulation can be provided by a thin insulating coating, such as Al2O3, which can also serve as a tritium barrier layer, at the channel surfaces in contact with LiPb. The coating＇s effectiveness for reducing the MHD pressure drop is analysed through three-dimensional numerical simulation. A MHD-based commercial computational fluid dynamic （CFD） software FLUENT is used to simulate the LiPb flow. The effect on the MHD pressure drop due to cracks or faults in the coating layer is also considered. The insulating performance requirement for the coating material in DFLL-TBM design is proposed according to the analysis.
文摘This paper generally compares the essential features between tokamaks and stellarators,based on previous review work individually made by authors on several specific topics,such as theories,bulk plasma transport and edge divertor physics,along with some recent results.It aims at summarizing the main results and conclusions with regard to the advantages and disadvantages in these two types of magnetic fusion devices.The comparison includes basic magnetic configurations,magnetohydrodynamic(MHD)instabilities,operational limits and disruptions,neoclassical and turbulent transport,confinement scaling and isotopic effects,plasma rotation,and edge and divertor physics.Finally,a concept of quasi-symmetric stellarators is briefly referred along with a comparison of future application for fusion reactors.
文摘An analysis has been carried out to study the effects of radiation absorption and firstorder chemical reaction on unsteady mixed convective flow of a viscous incompressible electrically conducting fluid through a porous medium of variable permeability between two long vertical non conducting wavy channels in the presence of heat generation.The unsteadiness in the flow is due to traveling thermal wave imposed on the walls.The governing equations are solved subject to the relevant boundary conditions with the assumption that the solution consists of a mean part and a perturbed part.The zeroth-order,the first order and the total solution of the problem are numerically evaluated and displayed graphically for pertinent parameters.This model finds applications in studying fixed-bed catalytic reactors and packed bed heat exchangers.
文摘This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel.The nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal direction.Equations that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate variables.Homotopy analysis method is used for the solution of the resultant equations.In this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness factor.Temperature of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin film.Concentration distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.
文摘The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.
基金the support from the National Key Research and Development Program of China(2017YFE0301300)the National Natural Science Foundation of China(51776194 and 51376175)
文摘Magnetohydrodynamic (MHD) mixed convection under strong magnetic field and volumetric heat source for buoyancy-assisted flows are studied numerically in this paper. Blanket is one of key components for energy conversion in Tokamak fusion reactor. The physical model employed for simulations is refined from dual-coolant lead-lithium (DCLL) blanket. A magnetic-convection code based on a consistent and conservative scheme is developed with the help of finite volume method, and validated by some Benchmark analytical solutions. The flows inside duct with thermal insulating and electric conducting walls under exponential neutron volumetric heat source are simulated. Based on Boussinesq assumption, the influences of wall electrical conductivity and buoyancy on velocity fields, temperature distributions and Nusselt numbers are investigated. Results illustrates that the wall conductance ratio dominates the flow at low Grashof numbers and high wall conductance ratio, while buoyancy effect dominates the jet flow near side wall at a high Grashof number. In addition, the velocity along flow direction substantially impacts features of the Nusselt number and temperature distribution. Besides, the jet flow results in a higher Nusselt number and lower temperature.
文摘This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.
文摘This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.
基金Project supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-12-108A)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.
文摘The chemical reaction effect on an unsteady magnetohydrodynamic （MHD） flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations （ODEs） using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.
文摘Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.
