Translational flows of an Oldroyd-B fluid with fractional derivatives

The objective of this paper is to study the unsteady flow of an Oldroyd-B fluid with fractional derivative model, between two infinite coaxial circular cylinders, using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, at time t=0⁺, applies a time dependent longitudinal shear stress to the fluid. Velocity field and the adequate shear stress are presented in series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional Maxwell, ordinary Maxwell, fractional second grade, ordinary second grade and Newtonian fluids performing the same motion are obtained as limiting cases of general solutions. In particular, the existing solutions for ordinary Oldroyd-B and second grade fluids are compared with the present solutions. Finally, the influence of the pertinent parameters on the fluid motion as well as a comparison between models is underlined by graphical illustrations.     

The impact of side walls on the MHD flow of a second-grade fluid through a porous medium

The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite plate is examined. Expressions for velocity and shear stress are determined with the help of integral transforms. In the absence of side walls, all the solutions that have been obtained are reduced to those corresponding to the motion over an infinite flat plate. The Newtonian solutions are also obtained as limiting case of the general solution. Finally, influence of magnetic and porosity parameter is graphically highlighted.

     

Thermal radiation and slip effects on MHD stagnation point flow of non-Newtonian nanofluid over a convective stretching surface

The present analysis examines the combine effects of thermal radiation and velocity slip along a convectively nonlinear stretching surface. Moreover, MHD effects are also considered near the stagnation point flow of Casson nanofluid. Slipped effects are considered with the porous medium to reduce the drag reduction at the surface of the sheet. Main structure of the system is based upon the system of partial differential equations attained in the form of momentum, energy, and concentration equations. To determine the similar solution system of PDEs is rehabilitated into the set of nonlinear ordinary differential equations (ODEs) by employing compatible similarity transformation. Important physical parameters are acquired through obtained differential equations. To determine the influence of emerging parameters, resulting set of ODE’s in term of unknown function of velocity, temperature, and concentration are successfully solved via Keller’s box-scheme. All the obtained unknown functions are discussed in detail after plotting the results against each physical parameter. To analyze the behavior at the surface: skin friction, local Nusselt and Sherwood numbers are also illustrated against the velocity ratio parameter A, Brownian motion Nb, thermophoresis Nt, and thermal radiation parameters R. Results obtained from the set of equations described that skin friction is decreasing function of A, and local Nusselt and Sherwood number demonstrate the significant influenced by Brownian motion Nb, thermophoresis Nt, and radiation parameters R.

     

Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder

The helical flow of an Oldroyd-B fluid with fractional derivatives, also named generalized Oldroyd-B fluid, in an infinite circular cylinder is studied using Hankel and Laplace transforms. The motion is due to the cylinder that, at time t=0⁺ begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Vt. The components of the velocity field and the resulting shear stresses are presented under integral and series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions, and are presented as sums of two terms, one of them being a similar solution for a Newtonian fluid. Similar solutions for generalized Maxwell fluids, as well as those for ordinary Oldroyd-B and Maxwell fluids are obtained as limiting cases of our general solutions. Furthermore, the solutions for Newtonian fluids performing the same motion, are also obtained as special cases of our solutions for α=β=1 and λ_r→λ.     

A high-shear, low Reynolds number microfluidic rheometer

We present a microfluidic rheometer that uses in situ pressure sensors to measure the viscosity of liquids at low Reynolds number. Viscosity is measured in a long, straight channel using a PDMS-based microfluidic device that consists of a channel layer and a sensing membrane integrated with an array of piezoresistive pressure sensors via plasma surface treatment. The micro-pressure sensor is fabricated using conductive particles/PDMS composites. The sensing membrane maps pressure differences at various locations within the channel in order to measure the fluid shear stress in situ at a prescribed shear rate to estimate the fluid viscosity. We find that the device is capable to measure the viscosity of both Newtonian and non-Newtonian fluids for shear rates up to 10⁴ s^?1 while keeping the Reynolds number well below 1.     

Double-diffusive and Soret-induced convection of a micropolar fluid in a vertical channel

This paper reports an investigation of the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel. Asymmetric temperature and concentration boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced convection are both considered. The governing parameters for the problem are the buoyancy ratio and the various material parameters of the micropolar fluid. The resulting non-dimensional boundary value problem is solved analytically in closed form using MAPLE software. A numerical solution of the time dependent governing equations is demonstrated to be in good agreement with the analytical model. The influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.     

New exact analytical solutions for Stokes’ first problem of Maxwell fluid with fractional derivative approach

The unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied using Fourier sine and Laplace transforms. The obtained solutions for the velocity field and shear stress, written in terms of generalized G functions, are presented as sum of the similar Newtonian solutions and the corresponding non-Newtonian contributions. The non-Newtonian contributions, as expected, tend to zero for λ→0. Furthermore, the solutions for ordinary Maxwell fluid, performing the same motion, are obtained as limiting cases of general solutions and verified by comparison with previously known results. Finally, the influence of the material and the fractional parameters on the fluid motion, as well as a comparison among fractional Maxwell, ordinary Maxwell and Newtonian fluids is also analyzed by graphical illustrations.     

A consideration on motion‐image‐quality improvement of LCDs and video systems

Abstract— The motion image quality of video systems with hold‐type displays, such as LCDs or OLEDs, were studied with regard to dynamic spatial frequency response and data from subjective evaluations on motion blur. The system parameters of motion image quality, or frame rate (F) and temporal aperture (A^t), were investigated and their required values were derived. A smaller temporal aperture and/or higher frame rate can improve the dynamic response and motion image quality, but the parameters required in order to maintain a good dynamic response for high motion image velocity seems very difficult to implement, such as a frame rate of 900 Hz. Therefore, the performance goal of video systems is set on “limit of acceptance” for motion image quality, as a compromise. An equation or the relational expression between motion image velocity and required parameter values is derived based on dynamic response and data from subjective evaluations found in published studies. Possible examples of parameter sets are obtained from the equation. Those are (F = 300 Hz, A_t = 5/6), (F = 240 Hz, A_t = 2/3), (F = 120 Hz, A_t = 1/3), and (F > 360 Hz, A_t = 1).     

Particle-Based Simulation of Fluids

Due to our familiarity with how fluids move and interact, as well as their complexity, plausible animation of fluidsremains a challenging problem. We present a particle interaction method for simulating fluids. The underlyingequations of fluid motion are discretized using moving particles and their interactions. The method allows simulationand modeling of mixing fluids with different physical properties, fluid interactions with stationary objects, andfluids that exhibit significant interface breakup and fragmentation. The gridless computational method is suitedfor medium scale problems since computational elements exist only where needed. The method fits well into thecurrent user interaction paradigm and allows easy user control over the desired fluid motion.     

Onset of double-diffusive convection of a sparsely packed micropolar fluid in a porous medium layer saturated with a nanofluid

The onset of convection of a sparsely packed micropolar fluid in a porous medium layer saturated by a nanofluid is examined by using a linear and nonlinear stability analyses. The Darcy–Brinkman–Forchheimer model is employed for the porous medium layer. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The critical Rayleigh number, wave number for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory, and the nonlinear analysis is made with minimal representation of the truncated Fourier series analysis involving only two terms. The effect of various parameters on the stationary and oscillatory convections is shown pictorially. The dependence of stationary or oscillatory convection on the porous parameter and parameters involved in micropolar fluids is also discussed. We also study the effect of time on transient Nusselt number and Sherwood number which are found to be oscillatory when time is small. However, when time becomes very large, both the transient Nusselt value and Sherwood value approach to their steady-state values.     

Determination of the flow curve of complex fluids using the Rabinowitsch–Mooney equation in sensorless microrheometer

In this work, we present a way to make rheological measurements on a microfluidic chip. The originality of our approach relies on the determination of the flow curve of a fluid using the Rabinowitsch–Mooney equation. For this purpose, we use a parallel flow between a reference fluid and a studied fluid to measure the pressure drop inside the channel. Using a Newtonian fluid of known viscosity, knowing the flow rates of the two liquids and measuring the geometrical features of the two-phase flow allows determining the pressure drop in the channel. The Rabinowitsch–Mooney equation is used to calculate the local shear rate and shear stress at the wall for the studied sample. We validate our method for several complex fluids.     

Flow-induced deformation of compliant microchannels and its effect on pressure–flow characteristics

We report theoretical and experimental investigations of flow through compliant microchannels in which one of the walls is a thin PDMS membrane. A theoretical model is derived that provides an insight into the physics of the coupled fluid–structure interaction. For a fixed channel size, flow rate and fluid viscosity, a compliance parameter \(f_{\text{p}}\) is identified, which controls the pressure–flow characteristics. The pressure and deflection profiles and pressure–flow characteristics of the compliant microchannels are predicted using the model and compared with experimental data, which show good agreement. The pressure–flow characteristics of the compliant microchannel are compared with that obtained for an identical conventional (rigid) microchannel. For a fixed channel size and flow rate, the effect of fluid viscosity and compliance parameter \(f_{\text{p}}\) on the pressure drop is predicted using the theoretical model, which successfully confront experimental data. The pressure–flow characteristics of a non-Newtonian fluid (0.1 % polyethylene oxide solution) through the compliant and conventional (rigid) microchannels are experimentally measured and compared. The results reveal that for a given change in the flow rate, the corresponding modification in the viscosity due to the shear thinning effect determines the change in the pressure drop in such microchannels.     

On the influence of the wall shear stress vector form on hemodynamic indicators

Hemodynamic indicators such as the averaged wall shear stress (AWSS) and the oscillatory shear index (OSI) are well established to characterize areas of arterial walls with respect to the formation and progression of aneurysms. Here, we study two different forms for the wall shear stress vector from which AWSS and OSI are computed. One is commonly used as a generalization from the two-dimensional setting, the latter is derived from the full decomposition of the wall traction force given by the Cauchy stress tensor. We compare the influence of both approaches on hemodynamic indicators by numerical simulations under different computational settings. Namely, different (real and artificial) vessel geometries, and the influence of a physiological periodic inflow profile. The blood is modeled either as a Newtonian fluid or as a generalized Newtonian fluid with a shear rate dependent viscosity. Numerical results are obtained by using a stabilized finite element method. We observe profound differences in hemodynamic indicators computed by these two approaches, mainly at critical areas of the arterial wall.

     

A spreadsheet program to optimize kinetic parameters of organic matter from laboratory pyrolysis data

Transformation of sedimentary organic matter (OM) to hydrocarbons is best modeled by assuming the total reaction suite consists of parallel degradations of ‘i’ hypothetical components following the Arrhenius equation and first order kinetics. A kerogen can be defined by characterizing each constituent component by its activation energy (Ei) their initial potentials (Xios) and a single frequency factor (A). We present a user friendly Lotus 1-2-3 program to determine A, Ei and Xio distribution of OMs using a multiple linear regression utility and programmed macros. Rock Eval (RE) S₂ curves of three heating rates are required. Equally spaced time/temperature and peak height data for S₂ curves of ‘n’ temperature steps in increasing order of heating rates are the inputs for the program. The fraction of hydrocarbon generated (f) from 19 hypothetical components of Ei 30, 32,34…78 Kcal/mole for ‘n’ temperature/time steps, by using frequency factor (A) value and assuming Xios=1, are calculated and set up in a ‘n×19’ matrix (matrix M). The fraction of total hydrocarbon generated (f) at ‘n’ temperature steps, obtained from the observed peak heights, are set up in a ‘n×1’ matrix (matrix L). Matrix M is suitably reduced by the program to ‘n×k’ matrix (matrix N) where ‘k’ is a variable, facilitating matrix inversion. Regressing matrix N against matrix L by the program, gives the Xios for ‘k’ Ei components along with a standard error (ERR) of Y estimates and R². Xios and A are then optimized iteratively by varying A values and selecting the solution associated with the lowest ERR value. Results of applying the program on data sets of two widely different types of samples from Indian basins are shown. They match the results obtained from the more sophisticated proprietary software.     

Exact solutions for the unsteady rotating flows of a generalized Maxwell fluid with oscillating pressure gradient between coaxial cylinders

This paper deals with the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field and the adequate shear stress are determined by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform. The exact solutions are presented by integral and series form in terms of the generalized G and Mittag-Leffler functions. The similar solutions can be easily obtained for ordinary Maxwell and Newtonian fluids as limiting cases. Finally, the influence of the relaxation time and the fractional parameter on the fluid dynamic characteristics, as well as a comparison between models, is shown by graphical illustrations.     

Particle behavior in a vertical channel with thermal convection in the low Grashof number regime

In the present study the motion of isothermal circular particles in a two-dimensional vertical channel with hot and cold isothermal conditions at the left and right walls in the presence of thermal convection was investigated. An isothermal circular particle for a particle to fluid density ratio ρ_r = ρ_p/ρ_f = of 1.00232 where ρ_p and ρ_f denote the particle and the fluid densities, respectively, was considered. Numerical simulations were carried out using the direct forcing/fictitious domain (DF/FD) method to investigate the solid motion in a fluid with a Prandtl number of 0.7 for different Grashof numbers ranging from 0 to 50. Under the conditions of the present problem, the particle motion is mainly governed by the thermal convection between the side walls of the channel and the particle, and by the wall confinement. The results of the present study indicate that three regimes of particle behavior can be identified in the present range of Grashof numbers regardless of the cold and hot thermal boundary conditions of the particle. In the first regime, the particle exhibits steady settling behavior; in the second regime, it undergoes a transient overshoot before the steady settling; in the third regime, the particle motion is submerged in the thermal levitation.     

Two-layered micropolar fluid flow through stenosed artery: Effect of peripheral layer thickness

An unsteady analysis of a two-layered blood flow through a flexible artery under stenotic conditions has been carried out in the present study where the flowing blood is represented by the two-fluid model, consisting of a core region of suspension of all erythrocytes assumed to be Eringen’s micropolar fluid and a plasma layer free from cells of any kind as a Newtonian fluid. The artery has been treated as an elastic (moving wall) cylindrical tube. The equations governing the unsteady flow mechanism subject to pulsatile pressure gradient, has been solved numerically using finite difference scheme by exploiting the appropriate physically realistic prescribed conditions. An extensive quantitative analysis has been performed through numerical computations in order to estimate the effect of different micropolar fluid parameters and the Reynolds number on the flow velocity, the flux, the resistive impedance and the wall shear stress together with their dependencies with time, the input pressure gradient and the severity of the stenosis. The graphical representations of these results do illustrate the flow characteristics of blood under stenotic conditions with proper scientific reasoning and hence validate the applicability of the model under consideration. Special emphasis has duly been made to compare the present theoretical results with the existing ones including experimental results and good agreement between them has been achieved both qualitatively and quantitatively.     

Approximation of time-dependent,multi-component,viscoelastic fluid flow

In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling equations for the individual fluids are combined into a single system of equations using a continuum surface model. The numerical approximation is stabilized by using an SUPG approximation for the constitutive equation. Under a small data assumption on the true solution, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of the mesh parameter h, the time discretization parameter Δt, and the SUPG coefficient ν are also derived. Numerical simulations of viscoelastic fluid flow involving two immiscible fluids are also presented.     

Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular porous channel

In the present work, the characteristics of physical model unsteady nanofluid flow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two-dimensional flow model of nanofluid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary differential equations (ODEs). Then, the obtained nonlinear system of ODEs is solved via wavelet collocation method. The effect of various emerging parameters, such as nanoparticle volume fraction, Reynolds number (Re), and expansion ratio have been analyzed on velocity and temperature profiles. Numerical results have been presented in form of figures and tables. For some special cases, the obtained numerical results are compared with exact one and found that the results are good in agreement with exact solutions.

     

Stability radii of differential algebraic equations with structured perturbations

This paper deals with a formula for computing stability radii of a differential algebraic equation of the form AX^′(t)−BX(t)=0, where A,B are constant matrices. A computable formula for the complex stability radius is given and a key difference between the ordinary differential equation (ODEs for short) and the differential algebraic equation (DAEs for short) is pointed out. A special case where the real stability radius and the complex one are equal is considered.