Showing papers on "Fluid dynamics published in 2016"

Computational Methods For Fluid Dynamics

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Evidence for hydrodynamic electron flow in PdCoO2

Abstract: Electron transport is conventionally determined by the momentum-relaxing scattering of electrons by the host solid and its excitations. Hydrodynamic fluid flow through channels, in contrast, is determined partly by the viscosity of the fluid, which is governed by momentum-conserving internal collisions. A long-standing question in the physics of solids has been whether the viscosity of the electron fluid plays an observable role in determining the resistance. We report experimental evidence that the resistance of restricted channels of the ultrapure two-dimensional metal palladium cobaltate (PdCoO2) has a large viscous contribution. Comparison with theory allows an estimate of the electronic viscosity in the range between 6 × 10–3 kg m–1 s–1 and 3 × 10–4 kg m–1 s–1, versus 1 × 10–3 kg m–1 s–1 for water at room temperature.

The Mathematics of Reservoir Simulation

Abstract: Problems arising in the modeling of processes for hydrocarbon recovery Finite element and finite difference methods for continuous flows in porous media A front tracking reservoir simulator Five-spot validation studies and the water coning problem Statistical fluid dynamics: The influence of geometry on surface instabilities Some numerical methods for discontinuous flows in porous media.

Evidence for Hydrodynamic Electron Flow in PdCoO2.

Abstract: Electron transport is conventionally determined by the momentum-relaxing scattering of electrons by the host solid and its excitations. Hydrodynamic fluid flow through channels, in contrast, is determined partly by the viscosity of the fluid, which is governed by momentum-conserving internal collisions. A long-standing question in the physics of solids has been whether the viscosity of the electron fluid plays an observable role in determining the resistance. We report experimental evidence that the resistance of restricted channels of the ultrapure two-dimensional metal palladium cobaltate (PdCoO2) has a large viscous contribution. Comparison with theory allows an estimate of the electronic viscosity in the range between 6 × 10–3 kg m–1 s–1 and 3 × 10–4 kg m–1 s–1, versus 1 × 10–3 kg m–1 s–1 for water at room temperature.

Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media, and Nanofluids

Abstract: Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media, and Nanofluids addresses the wavy irregular surfaces in heat transfer devices. Fluid flow and heat transfer studies from wavy surfaces have received attention, since they add complexity and require special mathematical techniques. This book considers the flow and heat transfer characteristics from wavy surfaces, providing an understanding of convective behavioral changes.

Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions

Abstract: In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature.

Two analytical methods for time-fractional nonlinear coupled Boussinesq–Burger’s equations arise in propagation of shallow water waves

Abstract: In this paper, an analytical method based on the generalized Taylors series formula together with residual error function, namely residual power series method (RPSM), is proposed for finding the numerical solution of the coupled system of time–fractional nonlinear Boussinesq–Burger’s equations. The Boussinesq–Burger’s equations arise in studying the fluid flow in a dynamic system and describe the propagation of the shallow water waves. Subsequently, the approximate solutions of time-fractional nonlinear coupled Boussinesq–Burger’s equations obtained by RPSM are compared with the exact solutions as well as the solutions obtained by modified homotopy analysis transform method. Then, we provide a rigorous convergence analysis and error estimate of RPSM. Numerical simulations of the results are depicted through different graphical representations and tables showing that present scheme is reliable and powerful in finding the numerical solutions of coupled system of fractional nonlinear differential equations like Boussinesq–Burger’s equations.

Physical Fluid Dynamics

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Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives

Abstract: This paper presents a Caputo–Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo–Fabrizio time-fractional parameter \(\upalpha \), the material parameter \(\alpha _2 \), and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow.

Spin hydrodynamic generation

Abstract: Magnetohydrodynamic generators use magnetic fields to convert the kinetic energy of conducting fluids into electricity. Fluid motion is now shown to generate spin currents, which can induce electric voltages without applying magnetic fields. Magnetohydrodynamic generation1,2,3,4 is the conversion of fluid kinetic energy into electricity. Such conversion, which has been applied to various types of electric power generation, is driven by the Lorentz force acting on charged particles and thus a magnetic field is necessary3,4. On the other hand, recent studies of spintronics5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23 have revealed the similarity between the function of a magnetic field and that of spin–orbit interactions in condensed matter. This suggests the existence of an undiscovered route to realize the conversion of fluid dynamics into electricity without using magnetic fields. Here we show electric voltage generation from fluid dynamics free from magnetic fields; we excited liquid-metal flows in a narrow channel and observed longitudinal voltage generation in the liquid. This voltage has nothing to do with electrification or thermoelectric effects, but turned out to follow a universal scaling rule based on a spin-mediated scenario. The result shows that the observed voltage is caused by spin-current6 generation from a fluid motion: spin hydrodynamic generation. The observed phenomenon allows us to make mechanical spin-current and electric generators, opening a door to fluid spintronics.

Analysis of electrolyte transport through charged nanopores

Abstract: We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)JCPSA60021-960610.1063/1.1669814]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

Flow of a micropolar fluid due to a porous stretching sheet and heat transfer

Abstract: The present work investigates the micropolar fluid flow due to a permeable stretching sheet and the resulting heat transfer. Unlike the existing numerical works on the flow phenomenon in the literature, the prime interest here is to analytically work out shape of the solutions and identify whether they are unique. Indeed, unique solutions are detected and presented in the exact formulas for the associated boundary layer equations. Temperature field influenced by the microrotation is also mathematically resolved in the cases of constant wall temperature, constant heat flux and Newtonian heating. To discover the salient physical features of many mechanisms acting on the considered problem, it is adequate to have the analytical velocity and temperature fields and also closed-form skin friction/couple stress/heat transfer coefficients, all as given in the current paper. For instance, the practically significant rate of heat transfer is represented by a single formula valid for all three temperature cases.

Constructing higher-order hydrodynamics: The third order.

Abstract: Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the $\mathcal{N}=4$ supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.

Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs

Abstract: The state of the art of modeling fluid flow in shale reservoirs is dominated by dual-porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano-pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual-porosity models and Darcy’s law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of the complex flow mechanisms occurring in these reservoirs. This paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three porosity systems: inorganic matter, organic matter (mainly kerogen), and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nano-pores and micro-pores in kerogen are incorporated into the simulator. The multiple-porosity model is built upon a unique tool for simulating general multiple-porosity systems in which several porosity systems may be tied to each other through arbitrary connectivities. This new model allows us to better understand complex flow mechanisms and eventually is extended into the reservoir scale through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual-porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple-porosity simulation.

Flow and heat simultaneously induced by two stretchable rotating disks

Abstract: An exact solution for the steady state Navier-Stokes equations in cylindrical coordinates is presented in this work. It serves to investigate the fluid flow and heat transfer occurring between two stretchable disks rotating co-axially at constant distance apart. The governing equations of motion and energy are first transformed into a set of nonlinear differential equation system by the use of von Karman similarity transformations, which are later solved numerically. The small Reynolds number case allows us to extract closed-form solutions for the physical phenomenon. The effects of the same or opposite direction rotation, as well as the stretching parameter and the Reynolds number, are discussed on the flow and heat characteristics. The main physical implication of the results is that stretching action of a disk surface alters considerably the classical flow behavior occurring between two disks and the physically interesting quantities like the torque and heat transfer are elucidated in the presence of a new physical mechanism; that is the surface stretching in the current research.

Nonlinear Rayleigh–Taylor instability of the cylindrical fluid flow with mass and heat transfer

Abstract: The nonlinear Rayleigh–Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg–Landau equation. The F-expansion method is used to get exact solutions for a nonlinear Ginzburg–Landau equation. The region of solutions is displayed graphically.