Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.     

Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium

Peristaltic transport of an incompressible viscous fluid in an inclined asymmetric channel through a porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The analytical solution has been obtained in the form of a stream function from which the axial velocity and pressure gradient have been derived. The results for the pressure drop and shear stress have also been computed numerically. The effects of various physical parameters are discussed through graphs and the phenomenon of trapping is also discussed. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.     

Stability of thermal convection of an Oldroyd-B fluid in a porous medium with Newtonian heating

A linear stability analysis determining the onset of oscillatory convection of an Oldroyd-B fluid in a bounded two-dimensional rectangular porous medium generated by Newtonian heating is conducted. Influences of viscoelastic parameters and Biot number on the onset of oscillatory convection, preferred modes and patterns of disturbed temperature contours are discussed.     

Experiment and Lattice Boltzmann numerical study on nanofluids flow in a micromodel as porous medium

Al₂O₃ nanofluids flow has been studied in etched glass micromodel which is idealization of porous media by using a pseudo 2D Lattice Boltzmann Method (LBM). The predictions were compared with experimental results. Pressure drop / flow rate relations have been measured for pure water and Al₂O₃ nanofluids. Because the size of Al₂O₃ nanoparticles is tiny enough to permit through the pore throats of the micromodel, blockage does not occur and the permeability is independent of the nanofluid volume fraction. Therefore, the nanofluid behaves as a single phase fluid, and a single phase LBM is able to simulate the results of this experiment. Although the flow in micromodels is 3D, we showed that 2D LBM can be used provided an effective viscous drag force, representing the effect of the third dimension, is considered. Good qualitative and quantitative agreement is seen between the numerical and experimental results.     

Convective heat transfer flow of nanofluid in a porous medium over wavy surface

In this letter, water base nanofluid flow over wavy surface in a porous medium of spherical packing beds is investigated. The copper oxides particles are taken into account. These properties are rehabilitated when fluid interacts with porous walls. For porous medium, Dupuit–Forchheimer model; an extension of Darcy's law model is utilized. The natures of velocity and temperature profiles of nanofluid are discussed graphically whereas the values of convection heat transfer coefficient in the presence of different nanoparticles concentrations in porous medium is presented in tabular form. The obtained results illustrate that convection heat transfer is improved by nanoparticles concentration but reduces when fluid attract to pores structured medium. On the other hand, when particles are added in fluid, convection heat transfer rate is improved but flow velocity is declined.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

Analysis of magnetohydrodynamic flow of a fractional viscous fluid through a porous medium

The aim of this paper is to investigate the exact general solutions of the incompressible viscous fluid flow by using the time-fractional Caputo–Fabrizio derivative. The flow of the fluid is subject to the motion of a plane wall, embedded in a porous medium under the influence of magnetic field. The corresponding non-dimensional governing fractional differential equation with appropriate initial and boundary conditions is solved by means of integral transforms namely, Laplace and Fourier transforms. Solutions are expressed as a sum of steady and transient parts, for the sinusoidal oscillations of the plane wall. The influence of involved physical parameters are discussed graphically. Specifically, it has been observed that the effective permeability K_eff reduces the time taken to reach the steady state.     

恒热流边界条件下流体横掠多孔介质中平板的边界层分析

基于Brinkman-Forchheimer-extended Darcy流动模型,对恒热流条件下流体横掠多孔介质中平板的强制对流进行了边界层分析。通过建立二维流动的连续方程、动量方程和考虑流体与多孔介质局部非热平衡时的能量方程,应用数量级分析和积分的方法对方程组进行简化和求解,得出了流体的速度分布、温度分布、速度边界层和温度边界层的厚度、对流传热的理论关联式。研究结果表明:恒热流条件下流体横掠多孔介质中平板的速度边界层与光板时完全不同,其在平板前端迅速增长,随后沿着流动方向变得非常平坦并趋于一定值;而温度边界层的厚度发展则与光板时类似,沿着流动方向不断增长,且与壁面处热流密度的大小无关。     

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.     

Lattice Boltzmann simulation for temperature-sensitive magnetic fluids in a porous square cavity

A lattice Boltzmann method is developed to simulate temperature-sensitive magnetic fluids in a porous cavity. In the simulation, the magnetic force, efficient gravity, viscous loss term and geometric loss term in porous medium are imported to the momentum equation. To test the reliability of the method, a validation with water in porous cavity is carried out. Good agreements with the previous results verify that the present lattice Boltzmann method is promising for simulation of magnetic fluids in porous medium. In this study, we investigate the change of magnetization with external magnetic field, and we present numerical results for the streamlines, isotherms, and magnetization at vertical or horizontal mid-profiles for different values of Ram. In addition, Nusselt numbers changing with magnetic Rayleigh numbers are also investigated.     

On the solution of magneto-hydrodynamics three-dimensional flow due to a stretching sheet in a porous medium using the successive linearization method

In this paper, we propose a new application of the successive linearization method for solving a system of nonlinear third order equations that govern the steady of laminar three dimensional flow for an incompressible, viscous fluid past a stretching sheet. A comparison is made with results from existing methods reported in the literature to test the validity, accuracy and convergence of the method. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods. Also, the effects of the physical parameters the fluid velocity are depicted graphically and are analyzed in detail.     

The effects of porosity and permeability on fluid flow and heat transfer of multi walled carbon nano-tubes suspended in oil (MWCNT/Oil nano-fluid) in a microchannel filled with a porous medium

The forced convection heat transfer and laminar flow in a two-dimensional microchannel filled with a porous medium is numerically investigated. The nano-particles which have been used are multi walled carbon nano-tubes (MWCNT) suspended in oil as the based fluid. The assumption of no-slip condition between the base fluid and nano-particles as well as the thermal equilibrium between them allows us to study the nanofluid in a single phase. The nanofluid flow through the microchannel has been modeled using the Darcy–Forchheimer equation. It is also assumed that there is a thermal equilibrium between the solid phase and the nanofluid for energy transfer. The walls of the microchannel are under the influence of a fluctuating heat flux. Also, the slip velocity boundary condition has been assumed along the walls. The effects of Darcy number, porosity and slip coefficients and Reynolds number on the velocity and temperature profiles and Nusselt number will be studied in this research.     

A class of stochastic evolutions that scale to the porous medium equation

A class of reversible Markov jump processes on a periodic lattice is described and a result about their scaling behavior stated: Under diffusion scaling, the empirical measure converges to a solution of the porous medium equation on thed-dimensional torus. The process can be viewed as a randomly interacting configuration of sticks that evolves through exchanges of stick pieces between nearest neighbors through a zero-range pressure mechanism, with conservation of total stick length.     

Scaling approach of the convective drying of a porous medium

We propose a simplified, theoretical approach of the evolution of liquid distribution during the convective drying of a granular packing. In the absence of gravity effects three regimes are distinguished according to the relative importance of surface evaporation, capillarity or evaporation from the interior of the sample. The evolution of the drying rate as a function of the saturation can be inferred from the characteristic velocities associated to each of these effects. We also carried out drying experiments of bead packings saturated with ethanol, at four different velocities of the boundary convection current, and with bead size ranging from 4.5 to 100 μm. The drying curves exhibit different regimes with a scaling as a function of particle radius and current velocity as predicted by the theory. Received 7 June 1999 and Received in final form 25 October 1999     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

MRI measurements of CO2 hydrate dissociation rate in a porous medium

After obtaining experimental data of CO₂ hydrate formation and dissociation in a porous medium using magnetic resonance imaging (MRI), the purpose of this study was to analyze the different dissociation rate of CO₂ hydrate using two heating rates. Images were obtained by using a fast spin-echo sequence, and the field of view was set to 40×40×40 mm. The vessel pressure was monitored during hydrate formation and dissociation, which was used to compare with MRI mean intensity. The result indicated that the MRI could visualize hydrate formation and dissociation, and the MRI mean intensity of water was in good agreement with the vessel pressure changes. The hydrate formation and dissociation rates were also quantified using the MRI mean intensity of water. The experimental results showed that the higher heating rate caused the rapid hydrate dissociation.     

Stability analysis of a Maxwell fluid in a porous medium heated from below

Based on a modified-Darcy–Brinkman–Maxwell model, stability analysis of a horizontal layer of Maxwell fluid in a porous medium heated from below is performed. By solving the eigenvalue problems, the critical Rayleigh number, wave number and frequency for overstability are determined. It is found that the critical Rayleigh number for overstability decreases as the relaxation time increases and the elasticity of a Maxwell fluid has a destabilizing effect on the fluid layer in porous media. On the other hand, the critical Rayleigh number for overstability increases by increasing the porous parameter which acts to stabilize the system. In limiting cases, some previous results for viscoelastic fluids in nonporous media are recovered from our results.     

Oblique stagnation slip flow of a micropolar fluid towards a stretching/shrinking surface: A stability analysis

A numerical solution is obtained for the steady oblique stagnation-point flow of a micropolar fluid over a stretching or shrinking surface with velocity slip condition. Results are obtained for representative values of slip parameter, micropolar parameter and stretching/shrinking parameter for strong particle interaction micropolar fluid. Dual solutions are found for the case of shrinking surface. An analysis of stability of these dual solutions shows that the solution branch that proceeds to large stretching case is stable. The streamlines are not symmetric for the oblique stagnation-point flow and reversed flow are observed near to the shrinking surface. The streamlines plots show that increase of slip parameter will reduce/eliminate the existing of rotating flow near the surface that caused by the shrinking effect.     

A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method

In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.