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Ioan Pop - One of the best experts on this subject based on the ideXlab platform.

  • magnetohydrodynamic Stagnation Point flow toward stretching shrinking permeable plate in porous medium filled with a nanofluid
    Proceedings of the Institution of Mechanical Engineers Part E: Journal of Process Mechanical Engineering, 2014
    Co-Authors: Sadegh Khalili, Reza Hosseini, Saeed Dinarvand, Majid Saber, Ioan Pop
    Abstract:

    In this article, the magnetohydrodynamic Stagnation Point flow and heat transfer of an incompressible viscous nanofluid over a shrinking/stretching permeable sheet is investigated theoretically and analytically. The ambient fluid velocity, stretching/shrinking velocity of sheet and the wall temperature are assumed to vary linearly with the distance from the Stagnation Point. The similarity solution is used to reduce the governing system of partial differential equations to a set of highly non-linear ordinary differential equations which are then solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in series form and graphical results are presented to investigate the influence of various pertinent parameters. Here, three different types of nanoparticles, namely copper Cu, alumina Al2O3 and titania TiO2 with water as the base fluid are considered. It is observed that, for all three nanoparticles, the magnitude of...

  • unsteady mixed convection flow of a nanofluid near orthogonal Stagnation Point on a vertical permeable surface
    Proceedings of the Institution of Mechanical Engineers Part E: Journal of Process Mechanical Engineering, 2014
    Co-Authors: Hossein Tamim, Saeed Dinarvand, Reza Hosseini, Sadegh Khalili, Ioan Pop
    Abstract:

    The unsteady mixed convection Stagnation-Point flow of a nanofluid toward a vertical surface is investigated numerically. The external velocity impinges normal to the vertical surface, the surface temperature, and the surface volume fraction of nanoparticles are assumed to vary linearly with the distance from the Stagnation Point. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing system of equations is first transformed into a dimensionless form, and then the resulting equations are solved numerically by using a fourth-order Runge–Kutta scheme coupled with a conventional shooting procedure. The features of the flow, heat, and mass transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The quantitative c...

  • magnetohydrodynamic Stagnation Point flow towards a stretching shrinking sheet with slip effects
    International Communications in Heat and Mass Transfer, 2013
    Co-Authors: Fazlina Aman, Anuar Mohd Ishak, Ioan Pop
    Abstract:

    Abstract The steady two-dimensional Stagnation-Point flow over a linearly stretching/shrinking sheet in a viscous and incompressible fluid in the presence of a magnetic field is studied. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. Results show that the skin friction coefficient decreases, but the heat transfer rate at the surface increases when the effect of slip at the boundary is taken into consideration. Dual solutions are found to exist for the shrinking sheet, while for the stretching sheet, the solution is unique.

  • Stagnation Point flow over a stretching shrinking sheet in a nanofluid
    Nanoscale Research Letters, 2011
    Co-Authors: Norfifah Bachok, Anuar Mohd Ishak, Ioan Pop
    Abstract:

    An analysis is carried out to study the steady two-dimensional Stagnation-Point flow of a nanofluid over a stretching/shrinking sheet in its own plane. The stretching/shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the Stagnation Point. The similarity equations are solved numerically for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid with Prandtl number Pr = 6.2. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction φ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.

  • Stagnation Point flow of a nanofluid towards a stretching sheet
    International Journal of Heat and Mass Transfer, 2011
    Co-Authors: M Mustafa, Ioan Pop, Tasawar Hayat, S Asghar, S Obaidat
    Abstract:

    Abstract This communication reports the flow of a nanofluid near a Stagnation-Point towards a stretching surface. The effects of Brownian motion and thermophoresis are further taken into account. The analytic solutions are developed by homotopy analysis method (HAM). Special emphasis has been given to the parameters of physical interest which include stretching ratio a / c , Prandtl number Pr , Lewis number Le , Brownian motion number Nb and thermophoresis number Nt . It is observed that reduced Nusselt number is an increasing function of ratio a / c . The comparison of the present results with the existing numerical solutions in a liming sense is also shown and this comparison is very good.

Tasawar Hayat - One of the best experts on this subject based on the ideXlab platform.

  • magnetohydrodynamic Stagnation Point flow of a jeffrey nanofluid with newtonian heating
    Journal of Aerospace Engineering, 2016
    Co-Authors: Tasawar Hayat, Maria Imtiaz, Ahmed Alsaedi
    Abstract:

    AbstractThe Stagnation Point flow of a Jeffrey nanofluid towards a stretching surface is addressed in the presence of Newtonian heating. The fluid is electrically conducting in the presence of an applied magnetic field. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. The governing nonlinear system is computed for convergent solutions. Results of velocity, temperature, and concentration fields are calculated in series forms. Effects of different parameters on velocity, temperature, and concentration profiles are shown and analyzed. The skin friction coefficient as well as Nusselt and Sherwood numbers are also computed and examined.

  • thermally stratified Stagnation Point flow of casson fluid with slip conditions
    International Journal of Numerical Methods for Heat & Fluid Flow, 2015
    Co-Authors: Tasawar Hayat, Muhammad Farooq, Ahmed Alsaedi
    Abstract:

    Purpose – The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of Stagnation Point with slip effects. Design/methodology/approach – Homotopy analysis method is used to find the series solutions of the governing equations. Findings – Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field. Originality/value – The present analysis has not been existed in the literature yet.

  • newtonian heating in Stagnation Point flow of burgers fluid
    Applied Mathematics and Mechanics-english Edition, 2015
    Co-Authors: Muhammad Awais, Tasawar Hayat, Shafqat Ali, M S Alhuthali
    Abstract:

    The Newtonian heating effects in the Stagnation Point flow of a Burgers fluid are addressed in this paper. The boundary layer flow problems are stated in the spatial domain from zero to infinity. The solution expressions for the velocity and the temperature are obtained and examined for the influential variables. The tabulated values show comparison with the previous results. It is observed that the obtained results are in good agreement with the existing results in limiting sense.

  • unsteady Stagnation Point flow of second grade fluid with variable free stream
    alexandria engineering journal, 2014
    Co-Authors: Tasawar Hayat, S A Shehzad, Muhammad Qasim, Ahmed Alsaedi
    Abstract:

    Abstract This article discusses the Stagnation-Point flow of second grade fluid over an unsteady stretching surface in the presence of variable free stream. Flow analysis has been carried out with heat transfer analysis. The resulting partial differential equations have been converted into ordinary differential equations by employing the suitable transformations. Computations of dimensionless velocity and temperature fields have been performed by using homotopy analysis method (HAM). Graphs are plotted to examine the behaviors of arising physical parameters on the dimensionless velocity and temperature. Numerical values of skin-friction coefficient and local Nusselt number are computed and examined.

  • Thermally Stratified Stagnation Point Flow of an Oldroyd-B Fluid
    International Journal of Nonlinear Sciences and Numerical Simulation, 2014
    Co-Authors: Tasawar Hayat, Zakir Hussain, Muhammad Farooq, Ahmed Alsaedi, Mustafa Obaid
    Abstract:

    This paper is devoted to examine the thermally stratified mixed convection flow of an Oldroyd-B fluid. The Stagnation Point flow towards a stretching surface is discussed. The boundary layer flow and energy equations are employed. Resulting partial differential systems are converted into the ordinary differential systems. Convergent series solutions for velocity and temperature are developed and analyzed. Numerical values of Nusselt number is computed and examined. Comparison of present study is shown with the previous results. It is found that velocity decreases through the stratified effects.

Anuar Mohd Ishak - One of the best experts on this subject based on the ideXlab platform.

  • magnetohydrodynamic Stagnation Point flow towards a stretching shrinking sheet with slip effects
    International Communications in Heat and Mass Transfer, 2013
    Co-Authors: Fazlina Aman, Anuar Mohd Ishak, Ioan Pop
    Abstract:

    Abstract The steady two-dimensional Stagnation-Point flow over a linearly stretching/shrinking sheet in a viscous and incompressible fluid in the presence of a magnetic field is studied. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. Results show that the skin friction coefficient decreases, but the heat transfer rate at the surface increases when the effect of slip at the boundary is taken into consideration. Dual solutions are found to exist for the shrinking sheet, while for the stretching sheet, the solution is unique.

  • boundary layer Stagnation Point flow and heat transfer over an exponentially stretching shrinking sheet in a nanofluid
    International Journal of Heat and Mass Transfer, 2012
    Co-Authors: Norfifah Bachok, Anuar Mohd Ishak
    Abstract:

    Abstract An analysis is carried out to investigate the steady two-dimensional Stagnation-Point flow of a water based nanofluid over an exponentially stretching/shrinking sheet in its own plane. Using a similarity transformation, the governing mathematical equations are transformed into coupled, nonlinear ordinary differential equations which are then solved numerically for three types of nanoparticles, namely copper (Cu), alumina (Al2O3), and titania (TiO2) in the water based fluid with Prandtl number Pr = 6.2. The skin friction coefficient, the local Nusselt number and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction φ and the stretching/shrinking parameter λ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique. The range of the parameter λ where the similarity solution exists for the steady Stagnation-Point flow over an exponentially stretching/shrinking sheet is larger compared with the linear stretching/shrinking case.

  • Stagnation Point flow over a stretching shrinking sheet in a nanofluid
    Nanoscale Research Letters, 2011
    Co-Authors: Norfifah Bachok, Anuar Mohd Ishak, Ioan Pop
    Abstract:

    An analysis is carried out to study the steady two-dimensional Stagnation-Point flow of a nanofluid over a stretching/shrinking sheet in its own plane. The stretching/shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the Stagnation Point. The similarity equations are solved numerically for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid with Prandtl number Pr = 6.2. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction φ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.

  • mhd Stagnation Point flow towards a shrinking sheet
    International Journal of Numerical Methods for Heat & Fluid Flow, 2011
    Co-Authors: Yian Yian Lok, Anuar Mohd Ishak, Ioan Pop
    Abstract:

    Purpose – The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the Stagnation Point are studied.Design/methodology/approach – A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.Findings – The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.Practical implications – The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and fi...

  • mhd mixed convection flow near the Stagnation Point on a vertical permeable surface
    Physica A-statistical Mechanics and Its Applications, 2010
    Co-Authors: Anuar Mohd Ishak, Roslinda Mohd. Nazar, Norfifah Bachok, Ioan Pop
    Abstract:

    The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the Stagnation-Point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the Stagnation-Point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.

Roslinda Mohd. Nazar - One of the best experts on this subject based on the ideXlab platform.

  • mhd mixed convection flow near the Stagnation Point on a vertical permeable surface
    Physica A-statistical Mechanics and Its Applications, 2010
    Co-Authors: Anuar Mohd Ishak, Roslinda Mohd. Nazar, Norfifah Bachok, Ioan Pop
    Abstract:

    The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the Stagnation-Point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the Stagnation-Point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.

  • mhd Stagnation Point flow towards a stretching sheet
    Physica A-statistical Mechanics and Its Applications, 2009
    Co-Authors: Anuar Mohd Ishak, Roslinda Mohd. Nazar, Khamisah Jafar, Ioan Pop
    Abstract:

    The steady two-dimensional MHD Stagnation Point flow towards a stretching sheet with variable surface temperature is investigated. The governing system of partial differential equations are transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. e>1, and the opposite is observed when e<1.

  • forced convection boundary layer flow at a forward Stagnation Point with newtonian heating
    Chemical Engineering Communications, 2009
    Co-Authors: Mohd Zuki Salleh, Roslinda Mohd. Nazar, Ioan Pop
    Abstract:

    The steady forced convection boundary layer flow near the forward Stagnation Point of an infinite plane wall generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is investigated in this study. The governing partial differential equations are first transformed into a system of ordinary differential equations before they are solved numerically by a finite-difference scheme, namely the Keller box method. Numerical solutions are obtained for a large range of values of the Prandtl number.

  • magnetohydrodynamic mhd flow of a micropolar fluid towards a Stagnation Point on a vertical surface
    Computers & Mathematics With Applications, 2008
    Co-Authors: Anuar Mohd Ishak, Roslinda Mohd. Nazar, Ioan Pop
    Abstract:

    The steady MHD mixed convection Stagnation Point flow towards a vertical surface immersed in an incompressible micropolar fluid is investigated. The external velocity impinges normal to the wall and the wall temperature is assumed to vary linearly with the distance from the Stagnation Point. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides that usually reported in the literature for the opposing flow.

  • mixed convection on the Stagnation Point flow toward a vertical continuously stretching sheet
    Journal of Heat Transfer-transactions of The Asme, 2007
    Co-Authors: Anuar Mohd Ishak, Roslinda Mohd. Nazar, Ioan Pop
    Abstract:

    The Stagnation Point flow toward a stretching vertical sheet is investigated in this study. The temperature and velocity of the sheet as well as the velocity of the external flow are assumed to vary in a power law with the distance from the Stagnation Point. The governing system of equations is first transformed into a dimensionless form, and then the resulting equations are solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that, for opposing flow, dual solutions exist in the neighborhood of the separation region, whereas for assisting flow the solution is unique.

R. Nazar - One of the best experts on this subject based on the ideXlab platform.

  • Mixed convection Stagnation Point flow of a micropolar fluid towards a stretching sheet
    Meccanica, 2007
    Co-Authors: A. Ishak, R. Nazar
    Abstract:

    The mixed convection two-dimensional boundary layer flow of a micropolar fluid near the Stagnation Point on a stretching vertical sheet is investigated. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the Stagnation Point. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a finite-difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed. Both assisting and opposing flows are considered. Results are presented in terms of the skin friction coefficient and the local Nusselt number with selections of velocity, microrotation and temperature profiles. Dual solutions are found to exist for the opposing flow.

  • Mixed convection boundary layers in the Stagnation-Point flow toward a stretching vertical sheet
    Meccanica, 2006
    Co-Authors: A. Ishak, R. Nazar
    Abstract:

    An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional Stagnation-Point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the Stagnation-Point. Two equal and opposite forces are impulsively applied along the x -axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.