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D D Ganji - One of the best experts on this subject based on the ideXlab platform.

  • magnetic field effect on naNoparticles migration and heat transfer of water alumina naNofluid in a channel
    Journal of Magnetism and Magnetic Materials, 2014
    Co-Authors: A Malvandi, D D Ganji
    Abstract:

    Abstract The present study is a theoretical investigation of the laminar flow and convective heat transfer of water/alumina naNofluid inside a parallel-plate channel in the presence of a uniform magnetic field. A modified two-component, four-equation, Nonhomogeneous equilibrium model was employed for the alumina/water naNofluid, which fully accounted for the effect of the naNoparticle volume fraction distribution. The No-Slip Condition of the fluid–solid interface is abandoned in favor of a Slip Condition which appropriately represents the Non-equilibrium region near the interface at micro/naNo channels. The results obtained indicated that naNoparticles move from the heated walls (naNoparticles depletion) toward the core region of the channel (naNoparticles accumulation) and construct a Non-uniform naNoparticles distribution. Moreover, in the presence of the magnetic field, the near wall velocity gradients increase, enhancing the Slip velocity and thus the heat transfer rate and pressure drop increase.

  • effects of naNoparticle migration on force convection of alumina water naNofluid in a cooled parallel plate channel
    Advanced Powder Technology, 2014
    Co-Authors: A Malvandi, D D Ganji
    Abstract:

    Abstract Force convective heat transfer of alumina/water naNofluid inside a cooled parallel-plate channel in the creeping flow regime and the presence of heat generation is investigated theoretically. A modified two-component four-equation Non-homogeneous equilibrium model is employed for the alumina/water naNofluid that fully accounts for the effects of naNoparticles volume fraction distribution. To impose the temperature gradients across the channel, the upper wall is subjected to a prescribed wall heat flux while the bottom wall is kept adiabatic. Moreover, due to the naNoparticle migration in the fluid, the No-Slip Condition of the fluid–solid interface at the walls is abandoned in favor of a Slip Condition that appropriately represents the Non-equilibrium region near the interface. The results indicated that naNoparticles move from the adiabatic wall (naNoparticles depletion) toward the cold wall (naNoparticles accumulation) and construct a Non-uniform naNoparticle distribution. Moreover, the aNomalous heat transfer rate occurs when the Brownian motion takes control of the naNoparticle migration (smaller naNoparticles).

  • Slip effects on unsteady stagnation point flow of a naNofluid over a stretching sheet
    Powder Technology, 2014
    Co-Authors: A Malvandi, F Hedayati, D D Ganji
    Abstract:

    Abstract Unsteady two-dimensional stagnation point flow of a naNofluid over a stretching sheet is investigated numerically. In contrast to the conventional No-Slip Condition at the surface, Navier's Slip Condition has been applied. The behavior of the naNofluid was investigated for three different naNoparticles in the water-base fluid, namely copper, alumina and titania. Employing the similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary ones and solved via Runge–Kutta–Fehlberg scheme. It was shown that a dual solution exists for negative values of the unsteadiness parameter A and, as it increases, the skin friction Cfr grows but the heat transfer rate Nur takes a decreasing trend. The results also indicated that, unlike the stretching parameter e, increasing in the values of the Slip parameter λ widen the ranges of the unsteadiness parameter A for which the solution exists. Furthermore, it was found that an increase in both e and λ intensifies the heat transfer rate.

Alois Würger - One of the best experts on this subject based on the ideXlab platform.

  • thermally driven marangoni surfers
    Journal of Fluid Mechanics, 2014
    Co-Authors: Alois Würger
    Abstract:

    We study autopropulsion of an interface particle that is driven by the Marangoni stress arising from a self-generated asymmetric temperature or concentration field. We calculate separately the long-range Marangoni flow $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\boldsymbol {v}}^{I}$ due to the stress discontinuity at the interface and the short-range velocity field ${\boldsymbol {v}}^{P}$ imposed by the No-Slip Condition on the particle surface. Both contributions are evaluated for a spherical floater with temperature moNopole and dipole moments. We find that the self-propulsion velocity is given by the amplitude of the ‘source doublet’ that belongs to the short-range contribution ${\boldsymbol {v}}^{P}$ . Hydrodynamic interactions, on the other hand, are determined by the long-range Marangoni flow ${\boldsymbol {v}}^{I}$ . Its dipolar part results in an asymmetric advection pattern of neighbouring particles, which in turn may perturb the kNown hexatic lattice or even favour disordered states.

  • Thermally driven Marangoni surfers
    Journal of Fluid Mechanics, 2014
    Co-Authors: Alois Würger
    Abstract:

    We study auto-propulsion of a interface particle, which is driven by the Marangoni stress arising from a self-generated asymmetric temperature or concentration field. We calculate separately the long-range Marangoni flow v^{I} due to the stress discontinuity at the interface and the short-range velocity field v^{P} imposed by the No-Slip Condition on the particle surface; both contributions are evaluated for a spherical floater with temperature moNopole and dipole moments. We find that the self-propulsion velocity is given by the amplitude of the "source doublet" which belongs to short-range contribution v^{P}. Hydrodynamic interactions, on the other hand, are determined by the long-range Marangoni flow v^{I}; its dipolar part results in an asymmetric advection pattern of neighbor particles, which in turn may perturb the kNown hexatic lattice or even favor disordered states.

Franck Sueur - One of the best experts on this subject based on the ideXlab platform.

  • a kato type criterion for the zero viscosity limit of the incompressible navier stokes flows with vortex sheets data
    arXiv: Analysis of PDEs, 2017
    Co-Authors: Franck Sueur
    Abstract:

    There are a few examples of solutions to the incompressible Euler equations which are piecewise smooth with a discontinuity of the tangential velocity across a hypersurface evolving in time: the so-called vortex sheets. An important open problem is to determine whether or Not these solutions can be obtained as zero viscosity limits of the incompressible Navier-Stokes solutions in the energy space. In this paper we establish a couple of sufficient Conditions similar to the one obtained by Kato in [T.~Kato. Remarks on zero viscosity limit for Nonstationary Navier-Stokes flows with boundary. Seminar on Nonlinear partial differential equations, 85-98, Math. Sci. Res. Inst. Publ., 2, 1984] for the convergence of Leray solutions to the Navier-Stokes equations in a bounded domain with No-Slip Condition towards smooth solutions to the Euler equation.

  • a kato type theorem for the inviscid limit of the navier stokes equations with a moving rigid body
    Communications in Mathematical Physics, 2012
    Co-Authors: Franck Sueur
    Abstract:

    The issue of the inviscid limit for the incompressible Navier-Stokes equations when a No-Slip Condition is prescribed on the boundary is a famous open problem. A result by Kato (Math Sci Res Inst Publ 2:85–98, 1984) says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a No-Slip Condition at the interface, the issue of the inviscid limit is as least as difficult. However it is Not clear if the additional difficulties linked to the body’s dynamic make this issue more difficult or Not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type Condition implies the convergence of the fluid velocity and of the body velocity as well, which seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid.

  • a kato type theorem for the inviscid limit of the navier stokes equations with a moving rigid body
    arXiv: Analysis of PDEs, 2011
    Co-Authors: Franck Sueur
    Abstract:

    The issue of the inviscid limit for the incompressible Navier-Stokes equations when a No-Slip Condition is prescribed on the boundary is a famous open problem. A result by Tosio Kato says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a No-Slip Condition at the interface, the issue of the inviscid limit is as least as difficult. However it is Not clear if the additional difficulties linked to the body's dynamic make this issue more difficult or Not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type Condition implies the convergence of the fluid velocity and of the body velocity as well, what seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid.

A Malvandi - One of the best experts on this subject based on the ideXlab platform.

  • magnetic field effect on naNoparticles migration and heat transfer of water alumina naNofluid in a channel
    Journal of Magnetism and Magnetic Materials, 2014
    Co-Authors: A Malvandi, D D Ganji
    Abstract:

    Abstract The present study is a theoretical investigation of the laminar flow and convective heat transfer of water/alumina naNofluid inside a parallel-plate channel in the presence of a uniform magnetic field. A modified two-component, four-equation, Nonhomogeneous equilibrium model was employed for the alumina/water naNofluid, which fully accounted for the effect of the naNoparticle volume fraction distribution. The No-Slip Condition of the fluid–solid interface is abandoned in favor of a Slip Condition which appropriately represents the Non-equilibrium region near the interface at micro/naNo channels. The results obtained indicated that naNoparticles move from the heated walls (naNoparticles depletion) toward the core region of the channel (naNoparticles accumulation) and construct a Non-uniform naNoparticles distribution. Moreover, in the presence of the magnetic field, the near wall velocity gradients increase, enhancing the Slip velocity and thus the heat transfer rate and pressure drop increase.

  • effects of naNoparticle migration on force convection of alumina water naNofluid in a cooled parallel plate channel
    Advanced Powder Technology, 2014
    Co-Authors: A Malvandi, D D Ganji
    Abstract:

    Abstract Force convective heat transfer of alumina/water naNofluid inside a cooled parallel-plate channel in the creeping flow regime and the presence of heat generation is investigated theoretically. A modified two-component four-equation Non-homogeneous equilibrium model is employed for the alumina/water naNofluid that fully accounts for the effects of naNoparticles volume fraction distribution. To impose the temperature gradients across the channel, the upper wall is subjected to a prescribed wall heat flux while the bottom wall is kept adiabatic. Moreover, due to the naNoparticle migration in the fluid, the No-Slip Condition of the fluid–solid interface at the walls is abandoned in favor of a Slip Condition that appropriately represents the Non-equilibrium region near the interface. The results indicated that naNoparticles move from the adiabatic wall (naNoparticles depletion) toward the cold wall (naNoparticles accumulation) and construct a Non-uniform naNoparticle distribution. Moreover, the aNomalous heat transfer rate occurs when the Brownian motion takes control of the naNoparticle migration (smaller naNoparticles).

  • Slip effects on unsteady stagnation point flow of a naNofluid over a stretching sheet
    Powder Technology, 2014
    Co-Authors: A Malvandi, F Hedayati, D D Ganji
    Abstract:

    Abstract Unsteady two-dimensional stagnation point flow of a naNofluid over a stretching sheet is investigated numerically. In contrast to the conventional No-Slip Condition at the surface, Navier's Slip Condition has been applied. The behavior of the naNofluid was investigated for three different naNoparticles in the water-base fluid, namely copper, alumina and titania. Employing the similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary ones and solved via Runge–Kutta–Fehlberg scheme. It was shown that a dual solution exists for negative values of the unsteadiness parameter A and, as it increases, the skin friction Cfr grows but the heat transfer rate Nur takes a decreasing trend. The results also indicated that, unlike the stretching parameter e, increasing in the values of the Slip parameter λ widen the ranges of the unsteadiness parameter A for which the solution exists. Furthermore, it was found that an increase in both e and λ intensifies the heat transfer rate.

A V Gorshkov - One of the best experts on this subject based on the ideXlab platform.

  • associated weber orr transform biot savart law and explicit form of the solution of 2d stokes system in exterior of the disc
    Journal of Mathematical Fluid Mechanics, 2019
    Co-Authors: A V Gorshkov
    Abstract:

    In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with No-Slip Condition on inner boundary and given velocity \(\mathbf {v}_\infty \) at infinity. It turned out it is the first application of the associated Weber–Orr transform to mathematical physics in comparison to classical Weber–Orr transform which is used in many researches. From No-Slip Condition for velocity field we will obtain Robin-type boundary Condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber–Orr transform. Also the explicit formula of Biot–Savart Law in polar coordinates will be given.

  • associated weber orr transform biot savart law and explicit solution of 2d stokes system in exterior of the disc
    arXiv: Analysis of PDEs, 2019
    Co-Authors: A V Gorshkov
    Abstract:

    In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with No-Slip Condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the associated Weber-Orr transform to mathematical physics in comparison to classical Weber-Orr transform which is used in many researches. From No-Slip Condition for velocity field we will obtain Robin-type boundary Condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber-Orr transform. Also the explicit formula of Biot-Savart Law in polar coordinates will be given.