On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

An experimental study of the effects of pulsating and steady internal fluid flow on an elastic tube subjected to external vibration

The results of an experimental study on both pulsating and steady Newtonian fluid flow in an initially stretched rubber tube subjected to external vibration are reported. A circulating loop system was designed to maintain constant hydrostatic pressure throughout the tests so that the influence of external excitation on the fluid flow could be properly distinguished. The effects of fluid flow velocity and initial stretch rates on the dynamic response and damping of the tube conveying fluid were examined, and it was observed that damping ratios increase with increasing flow velocities, and generally decrease with increasing initial stretch rates for the tube conveying fluid. It was also noted that dynamic responses increase with increasing initial stretch rates, and decrease with increasing flow velocities. The effect of external vibration on fluid flow rates is small in a tube with a thickness-to-radius ratio (D_out−D_in)/D_in=0.617. Fluid pressures vary, in terms of frequency and amplitude, with external vibration as well as Womersley number.     

MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative

This research article considers the exact solutions and theoretical aspects of the channel flow of a fractional viscous fluid which is electrically conducting and flowing through a porous medium. Joint Laplace and Fourier transform techniques are used to solve the momentum equation. The Caputo-Fabrizio time fractional derivative is used in the constitutive equations. Exact solutions for an arbitrary velocity are obtained, and then in the limiting cases over a bottom plate three types of flow are considered: that is, the impulsive, accelerating and oscillating motion of the fluid. The case where the flow of the fractional fluid is unaffected by the side walls, is correspondingly taken into account. For oscillating flow the solutions are separated into steady and transient parts for both sine and cosine oscillations. Moreover these solutions are captured graphically, and the effect of the Reynolds number “Re”, fractional parameter “α”, effective permeability “K_eff” and the time “t”, on the fluid's motion are observed.     

Thermoelastic vibrations of a semi-infinite strip

The forced vibrations of a thermoelastic strip (x₁ϵ [0, l], x₂ ⩾ 0) produced by a prescribed heating at the boundary x₂ = 0 are considered. The analysis is based on classical coupled thermoelastic theory (plane strain) and finite Fourier transforms. The solution of the problem under discussion is expressed in terms of the Lamé scalar and vector potentials.     

Numerical Investigation of Heat Transfer Characteristics of scCO2 Flowing in a Vertically-Upward Tube with High Mass Flux

In this work, the heat transfer characteristics of supercritical pressure CO₂ in vertical heating tube with 10 mm inner diameter under high mass flux were investigated by using an SST k-ω turbulent model. The influences of inlet temperature, heat flux, mass flux, buoyancy and flow acceleration on the heat transfer of supercritical pressure CO₂ were discussed. Our results show that the buoyancy and flow acceleration effect based on single phase fluid assumption fail to explain the current simulation results. Here, supercritical pseudo-boiling theory is introduced to deal with heat transfer of scCO₂. scCO₂ is treated to have a heterogeneous structure consisting of vapor-like fluid and liquid-like fluid. A physical model of scCO₂ heat transfer in vertical heating tube was established containing a gas-like layer near the wall and a liquid-like fluid layer. Detailed distribution of thermophysical properties and turbulence in radial direction show that scCO₂ heat transfer is greatly affected by the thickness of gas-like film, thermal properties of gas-like film and turbulent kinetic energy in the near-wall region. Buoyancy parameters Bu < 10⁻⁵, Bu* < 5.6 × 10⁻⁷ and flow acceleration parameter K_v < 3 × 10⁻⁶ in this paper, which indicate that buoyancy effect and flow acceleration effect has no influence on heat transfer of scCO₂ under high mass fluxes. This work successfully explains the heat transfer mechanism of supercritical fluid under high mass flux.     

Subsonic flapping flutter

A mathematical model of two-dimensional flow through a flexible channel is analyzed for its stability characteristics. Linear theory shows that fluid viscosity, modelled by a Darcy friction factor, induces flutter instability when the dimensionsless fluid speed, S, attains a critical flutter speed, S₀. This is in qualitative agreement with experimental results, and it is at variance with previous analytical studies where fluid viscosity was neglected and divergence instability was predicted. The critical flutter speed and the associated critical flutter frequency depend on three other dimensionless parameters: the ratio of fluid to wall damping; the ratio of wall to fluid mass; and the ratio of wall bending resistance to elastance. Non-linear theory predicts stable, finite amplitude flutter for S>S₀, which increases in frequency and amplitude as S increases. Both symmetric and antisymmetric modes of deformation are discussed.     

MHD mixed convection flow and heat transfer in a porous medium

The effects of a steady two-dimensional laminar MHD mixed convection flow and heat transfer against a heated vertical semi-infinite permeable surface in a porous medium are discussed. The coupled nonlinear partial differential equations describing the conservation of mass, momentum, and energy are solved by a perturbation technique. The results are presented to illustrate the influence of Hartmann number (M), Prandtl number (Pr), permeability parameter (K _p ), suction/blowing parameter (f _w ), heat generation/absorption coefficient (?), and mixed convection or buoyancy parameter (γ). The effects of different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are discussed with the help of figures.     

Natural convection with damped thermal flux in a vertical circular cylinder

Natural convection flows of an incompressible Newtonian fluid inside a circular cylinder are studied. The heat transfer process is described by a generalized fractional constitutive equation for the thermal flux-temperature gradient. Caputo time-fractional derivative operator, which provides the damping of thermal flux, is considered into the studied model.Analytical solutions to the fluid temperature, thermal flux, fluid velocity and volume flow rate are obtained with the integral transforms method (Laplace transform and finite Hankel transform).Temperature behaviors for small and large values of the time t, as well as the post-transient and transient velocity components are determined. The influence of the memory parameter (the order of the time-fractional derivative) on the temperature, thermal flux, velocity and the volume flow rate is numerically and graphically studied.     

Influence of metallic nanoparticles in water driven along a wavy circular cylinder

In the present study, simultaneous effects of metallic nanoparticles and magnetohydrodynamic due to stagnation point flow of nanofluid along a wave circular cylinder is presented. The effect of induced magnetic field is incorporated to deal the boundary and thermal boundary layer domain. Mathematical modelling for momentum and energy equation is constructed that is based upon three different kinds of nanoparticles namely: copper (Cu), Titanium di oxide (TiO₂), and alumina (Al₂O₃) within the working fluid water. Each mixture is analysed at the individual level and made comparison amongst all the mixture to examine the resistance and thermal conductivity of nanofluid within the boundary layer region. The solutions are exposed via boundary value problem using shooting method along with the Runge-Kutta-Fehlberg method. The characteristics of emerging parameters for the fluid flow and heat transfer are discussed through graphs and tables. The effects of ϕ (nanoparticle volume fraction) on heat transfer and shear stress at the wall are analysed in detail. It is finally concluded that by increasing the ratio of nanoparticles there is a significant increase in the temperature but slight decrease in the velocity profile.     

Flow and heat transfer over a rotating porous disk in a nanofluid

The steady flow of an incompressible viscous fluid due to a rotating disk in a nanofluid is studied. The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction parameter φ and suction/injection parameter h₀. Two models for the effective thermal conductivity of the nanofluid, namely the Maxwell-Garnett model and the Patel model, are considered. It is found that for the Patel model, the heat transfer rate at the surface increases for both suction and injection, whereas different behaviors are observed for the Maxwell-Garnett model, i.e. increasing the values of φ leads to a decrease in the heat transfer rate at the surface for suction, but increases for injection. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Two-dimensional Euler flows in slowly deforming domains

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow compared to the fluid motion. The Eulerian flow is found to remain approximately steady throughout the evolution. At leading order, the velocity field depends instantaneously on the shape of the domain boundary, and it is determined by the steadiness and vorticity-preservation conditions. This is made explicit by reformulating the problem in terms of an area-preserving diffeomorphism g_Λ which transports the vorticity. The first-order correction to the velocity field is linear in the boundary velocity, and we show how it can be computed from the time derivative of g_Λ.The evolution of the Lagrangian position of fluid particles is also examined. Thanks to vorticity conservation, this position can be specified by an angle-like coordinate along vorticity contours. An evolution equation for this angle is derived, and the net change in angle resulting from a cyclic deformation of the domain boundary is calculated. This includes a geometric contribution which can be expressed as the integral of a certain curvature over the interior of the circuit that is traced by the parameters defining the deforming boundary.A perturbation approach using Lie series is developed for the computation of both the Eulerian flow and geometric angle for small deformations of the boundary. Explicit results are presented for the evolution of nearly axisymmetric flows in slightly deformed discs.     

The 3rd flow component as a QGP signal

Earlier fluid dynamical calculations with QGP show a softening of the directed flow while with hadronic matter this effect is absent. On the other hand, we indicated that a third flow component shows up in the reaction plane as an enhanced emission, which is orthogonal to the directed flow. This is not shadowed by the deflected projectile and target, and shows up at measurable rapidities, y _CM=1?2. To study the formation of this effect initial stages of relativistic heavy ion collisions are studied. An effective string rope model is presented for heavy ion collisions at RHIC energies. Our model takes into account baryon recoil for both target and projectile, arising from the acceleration of partons in an effective field. The typical field strength (string tension) for RHIC energies is about 5–12 GeV/fm, what allows us to talk about “string ropes”. The results show that QGP forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. The produced initial state can be used as an initial condition for further hydrodynamical calculations. Such initial conditions lead to the creation of third flow component. Recent v ₁ measurements are promising that this effect can be used as a diagnostic tool of the QGP.     

A nonlinear scenario for development of vortex layer instability in gravity field

A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t ₀ ? t)^?1, where t ₀ is the collapse time.     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

The initial stage in the nonlinear motion of a domain wall in garnet films

A study of the domain-wall motion in single-crystal garnet films of the YBiFeGa system with a perpendicular magnetic anisotropy, activated by a constant in-plane bias field H _p parallel to the wall plane and a pulsed drive field H _g of an amplitude corresponding to the nonlinear region of the domain-wall velocity vs. the H _g relation is reported. The earlier data suggesting the existence of an initial phase of motion, where the wall is accelerated to a high instantaneous velocity, have been confirmed. The wall behavior in the initial phase has been shown to be affected by the field H _p and the drive-field pulse rise time. A possible mechanism of the wall structure transformation after the application of the H _g pulse is considered. It has been established that the dependence of the wall velocity on H _p in the saturation region disagrees with theory.     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.     

Buoyancy-assisted mixed convective flow over backward-facing step in a vertical duct using nanofluids

Laminar mixed convective buoyancy assisting flow through a two-dimensional vertical duct with a backward-facing step using nanofluids as a medium is numerically simulated using finite volume technique. Different types of nanoparticles such as Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂ and TiO₂ with 5 % volume fraction are used. The wall downstream of the step was maintained at a uniform wall temperature, while the straight wall that forms the other side of the duct was maintained at constant temperature equivalent to the inlet fluid temperature. The walls upstream of the step and the backward-facing step were considered as adiabatic surfaces. The duct has a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The downstream wall was fixed at uniform wall temperature 0 ?? ??T?? 30 °C, which was higher than the inlet flow temperature. The Reynolds number in the range of 75 ?? Re ?? 225 was considered. It is found that a recirculation region was developed straight behind the backward-facing step which appeared between the edge of the step and few millimeters before the corner which connect the step and the downstream wall. In the few millimeters gap between the recirculation region and the downstream wall, a U-turn flow was developed opposite to the recirculation flow which mixed with the unrecirculated flow and traveled along the channel. Two maximum and one minimum peaks in Nusselt number were developed along the heated downstream wall. It is inferred that Au nanofluid has the highest maximum peaks while diamond nanofluid has the highest minimum peak. Nanofluids with a higher Prandtl number have a higher peak of Nusselt numbers after the separation and the recirculation flow disappeared.     

Field dependence of uniform magnon energies in lamellar CoCl2 and CoBr2 by AFMR experiments

AFMR experiments in the frequency range 77<v<600 GHz and in the magnetic field range 0<H<75 kG on antiferromagnetic CoCl₂ and CoBr₂ single crystals at 4.2 K are reported. The waves propagate along the c axis of the crystals and the steady magnetic field is in the plane of the layers, which is also the easy plane of the spins.The influence of a rotation of the field in the easy magnetization plane is investigated, showing the existence of antiferromagnetic domains.The results of the field dependence of uniform magnon energies are reported in detail for the two compounds CoCl₂ and CoBr₂. In CoBr₂, the two magnon modes at zero field are non degenerate, their frequencies are v₁(0) = 60 GHzandv₂(0) = 675 GHz, and the field required for saturation is H_s⊥ = 74.2 kG.     

Heat transfer analysis for stretching flow over a curved surface with magnetic field

The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.     

Analysis of peristaltic flow of Jeffrey six constant nano fluid in a vertical non-uniform tube

Peristaltic flow of non-Newtonian nano fluid through a non-uniform surface has been investigated in this paper. The fluid motion along the wall of the surface is caused by the sinusoidal wave traveling with constant speed. The governing equations are converted into cylindrical coordinate system and assuming low Reynolds number and long wave length partial differential equations are simplified. Analytically solutions of the problem are obtained by utilizing the homotopy perturbation method (HPM). In order to insight the impact of embedded parameters on temperature, concentration and velocity some graphs are plotted for different peristaltic waves. At the end, some observations were made from the graphical presentation that velocity, pressure rise and nano particle concentration are increasing function of thermophoresis parameter N_t while temperature and frictional forces show opposite trend.