Linear Momentum Equations Research Articles

Micropolar Fluids Using B-spline Divergence Conforming Spaces

We discretized the two-dimensional linear momentum, microrotation, energy and mass conservation equations from micropolar fluids theory, with the finite element method, creating divergence conforming spaces based on B-spline basis functions to obtain pointwise divergence free solutions [8]. Weak boundary conditions were imposed using Nitsche's method for tangential conditions, while normal conditions were imposed strongly.Once the exact mass conservation was provided by the divergence free formulation, we focused on evaluating the differences between micropolar fluids and conventional fluids, to show the advantages of using the micropolar fluid model to capture the features of complex fluids. A square and an arc heat driven cavities were solved as test cases. A variation of the parameters of the model, along with the variation of Rayleigh number were performed for a better understanding of the system.The divergence free formulation was used to guarantee an accurate solution of the flow. This formulation was implemented using the framework PetIGA as a basis, using its parallel stuctures to achieve high scalability. The results of the square heat driven cavity test case are in good agreement with those reported earlier.

Numerical Simulation on Buoyancy-driven Heat Transfer Enhancement of Nanofluids in an Inclined Triangular Enclosure

Heat transfer enhancement in a two-dimensional inclined lid-driven triangular enclosure utilizing nanofluids is investigated numerically for various pertinent parameters. The present model is developed to analyze the heat transfer performance of nanofluids inside an enclosure taking into account the solid volume fraction δ, variable velocity and thermal boundary conditions. Fluid mechanics and conjugate heat transfer, described in terms of continuity, linear momentum and energy equations. The transport equations are solved numerically using the Galerkin finite element method. Results are obtained for a wide range of parameters such as the Grashof numbers. Copper-water nanofluids is used with Prandtl number, Pr = 6.2 and solid volume fraction δ is varied from 0% - 20%. The streamlines, isotherm plots and heat transfer correlation of the average Nusselt number at the hot surface as well as average fluid temperature in the enclosure is presented and discussed in detailed. It is found that heat transfer increased by 28% as volume fraction δ increases from 0% to 20% at Gr =105. Moreover, the variation of the average Nusselt number and average fluid temperature in the cavity is linear with the solid volume fraction.

Modeling fluid–structure interaction by the particle finite element method in OpenSees

The OpenSees finite element software framework is extended for simulating fluid–structure interaction (FSI) by the particle finite element method (PFEM). At high levels of the framework, new classes handle meshing and interface detection of the fluid and structure domains and implement the fractional step method in order to solve the governing equations of linear momentum and mass conservation. At lower levels of the framework, new finite element and pressure constraint classes assemble fluid contributions to the global system of equations. Verification and validation examples are presented along with a demonstrative example of wave loading on a coastal structure modeled using geometrically nonlinear frame elements with material nonlinear fiber sections. The extension of OpenSees for FSI allows analysts to simulate the complex phenomena of wave loading on structural models as well as the response of these models to sequential natural hazards such as earthquake induced tsunamis.

Intestinal Flow of a Couple Stress Nanofluid in Arteries

The current article discusses the influence of nanofluid on the peristaltic flow of an incompressible couple stress fluid in a two-dimensional uniform tube. The problem formulation is accessible in an upsurge structure of orientation for equations of momentum, energy, and concentrations. The continuity, linear momentum, energy, and nanoparticle equations lead to the mathematical development. HPM is used to get the solutions for velocity, temperature, nanoparticle, and pressure gradient. The solutions contain the Brownian motion number N(b), thermophoresis number N(t), local temperature Grashof number B(r), and local nanoparticle Grashof number G(r). The physical features of different embedded parameters are analyzed and discussed physically in detail.

A Magneto-convection Over a Semi -infinite Porous Plate with Heat Generation

Convective flow through porous media is a branch of research undergoing rapid growth in fluid mechanics and heat transfer. This is quite natural because of its important applications in environmental, geophysical and energy related engineering problems. Prominent applications are the utilization of geothermal energy, the control of pollutant spread in ground water, the design of nuclear reactors, solar power collectors and the heat transfer associated with the deep storage of nuclear waste. The study of heat generation in moving fluids is important in problems dealing with chemical reactions and those concerned with dissociating fluids. Heat generation effects may alter the temperature distribution and this in turn can affect the particle deposition rate in nuclear reactors, electronic chips and semi conductor wafers. Although exact modeling of internal heat generation is quite difficult, some simple mathematical models can be used to express its general behaviour for most physical situations. The objective of this work is to investigate the effects of internal heat generation on an unsteady two-dimensional magnetohydrodynamic free convection flow of a viscous, incompressible fluid free convection flow past a semi-infinite vertical porous plate embedded in a porous medium, in the presence of variable suction. The equations of continuity, linear momentum and energy, which govern the flow field, are transformed to a system of ordinary differential equations by perturbation technique. The resulting equations are solved analytically to obtain the solutions for the velocity and temperature fields. The behavior of the velocity, temperature, skin-friction and Nusselt number have been discussed for variations in the physical parameters.

Unsteady buoyancy-driven heat transfer enhancement of nanofluids in an inclined triangular enclosure

Heat transfer enhancement in a two-dimensional inclined lid-driven triangular enclosure utilizing nanofluids is investigated numerically for various pertinent parameters. The present model is developed to analyze unsteady heat transfer performance of nanofluids inside an enclosure taking into account the solid volume fraction δ, variable velocity and variable thermal boundary conditions. Fluid mechanics and conjugate heat transfer described in terms of continuity, linear momentum and energy equations. The transport equations are solved numerically using the Galerkin finite element method. Results are obtained for a wide range of parameters such as the Grashof numbers (103≤Gr≤106), and time step (0.01≤τ≤1). Copper-water nanofluids is used with Prandtl number, Pr=6.2 and solid volume fraction δ is varied from 0% to 25%. The streamlines, isotherm plots and heat transfer correlation of the average Nusselt number at the hot surface as well as average fluid temperature in the enclosure is presented and discussed in detail. It is found that heat transfer increased by 31.85% as volume fraction δ increases from 0% to 25% at Gr=105 for τ=0.01. Moreover, the variation of the average Nusselt number and average fluid temperature in the cavity is linear with the solid volume fraction.

A hyperbolic model of chemotaxis

The motion of cells, within the extracellular liquid, is induced by a chemical attractant. Here the cell population, the attractant, and the liquid are modelled within continuum mechanics as a mixture of three constituents. The active character of the cells is expressed by a body force proportional to the gradient of the attractant density. The balance equations of mass and linear momentum are developed and the density of cell population is shown to satisfy a hyperbolic equation. The characteristic features of previous models of chemotaxis are also investigated and evidence is given to the assumptions that lead to parabolic equations.

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

SUMMARYThe accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.

Transmission loss analysis of single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) circular chamber mufflers by using Green’s function method

A Green’s function solution method is implemented to study sound attenuation in single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) circular chamber mufflers. The mufflers are modeled as piston driven rigid circular chambers containing a stationary fluid. The pistons are assumed to perform simple harmonic motion with uniform velocities. Velocity potential in the chamber is derived as a superposition of three dimensional velocity potential due to each piston. Pressure field in the chamber is calculated from the velocity potential through conservation of linear momentum equation. Acoustic pressure acting on each piston is calculated by averaging over the surface of the piston. Transmission loss (TL) is evaluated from incident and transmitted acoustic energy. TL curves for various inlet/outlet orientations derived from this method is validated with results obtained from the literature. The effect of locations of inlet/outlet on TL is studied.

Mixed convection heat and mass transfer in peristaltic flow with chemical reaction and inclined magnetic field

A mathematical model is constructed to investigate the mixed convective heat and mass transfer effects on peristaltic flow of magnetohydrodynamic pseudoplastic fluid in a symmetric channel. An analysis has been carried out to examine the impact of an inclined magnetic field and chemical reaction in presence of heat sink/source. Mechanics of flow and heat/mass transfer described in terms of continuity, linear momentum, energy and concentration equations are predicted by using long wavelength and low Reynolds number. Expressions for stream function, temperature, concentration and pressure gradient are derived. Numerical simulation is performed for the rise in pressure per wave length. Effects of several physical parameters on the flow quantities are analyzed.

Heat Transfer Enhancement of Nanofluids in a Lid-Driven Triangular Enclosure having a Discrete Heater

In the present study, the behaviour of nanofluids is investigated numerically in a lid-driven triangular enclosure which has a partially heated on bottom side to gain insight into convective recirculation and flow processes induced by a nanofluid. The present model is developed to examine the behaviour of nanofluids taking into account the heater length. Fluid mechanics and conjugate heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the Galerkin finite element method. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. Numerical results are obtained for a wide range of parameters such as the Richardson number, and heater length. Copper-water nanofluids is used with Prandtl number, Pr = 6.2. The streamlines, isotherm plots and the variation of the average Nusselt number at the hot surface as well as average fluid temperature in the enclosure is presented and discussed in detailed.

Numerical prediction of buoyancy driven micropolar fluid flow within uniformly heated eccentric annulus

In this paper, the problem of buoyancy driven micropolar fluid flow within an annulus formed between two circular concentric/eccentric tubes has been numerically investigated using Fourier spectral method. The annulus inner wall is uniformly heated and maintained at constant heat flux while the outer wall is cooled and kept at constant temperature. The full governing equations of linear momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by modified Rayleigh number Ra, Prandtl number Pr, radius ratio Rr, eccentricity, e and material parameters of Micropolar fluid. The material parameters are dimensionless spin gradient viscosity λ, dimensionless micro-inertia density B and dimensionless vortex viscosity D. The study considered a range of modified Ra up to 105 and is carried out at three values of Pr, namely Pr=0.1,1.0 and 7.0, and at three values of parameter D, namely, D=2,4,8 while the eccentricity is varied between −0.65 and +0.65. The radius ratio is fixed at 2.6 while the material parameters B and λ are assigned the value of 1. The effect of the controlling parameters on flow and thermal fields has been investigated with emphasis on the effect of these parameters on local and mean inner wall temperatures. The study has shown that for certain controlling parameters the steady mean temperature of inner wall of the annulus is maximum at a certain eccentricity. The study has also shown that as the parameter D increases the steady mean inner wall temperature increases. Moreover, the study has shown that as the Pr increases the mean inner wall temperature decreases.

Mixed Convection Heat Transfer in Micropolar Nanofluid over a Vertical Slender Cylinder

Analysis is carried for the problem of boundary layer steady flow and heat transfer of a micropolar fluid containing nanoparticles over a vertical cylinder. The governing partial differential equations of linear momentum, angular momentum, heat transfer and nano concentration are reduced to nonlinear coupled ordinary differential equations by applying the boundary layer approximations and a suitable similarity transformation. These nonlinear coupled ordinary differential equations, subject to the appropriate boundary conditions, are then solved by using the homotopy analysis method. The effects of the physical parameters on the flow, heat transfer and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed.

Evaluation of Tsunami Loads on Wood-Frame Walls at Full Scale

The performance of full-scale light-frame wood walls subjected to wave loading was examined using the Large Wave Flume of the Network for Earthquake Engineering (NEES) Tsunami Facility at Oregon State University. The hydrodynamic conditions (water level and bore speed) and structural response (horizontal force, pressure, and deflection) were observed for a range of incident tsunami heights and for several wood wall framing configurations. The walls were tested at the same cross-shore location with a dry-bed condition. For each tsunami wave height tested, the force and pressure profiles showed a transient peak force followed by a period of sustained quasi-static force. The ratio of the transient force to quasi-static force was 2.2. These experimental values were compared with the predicted values using the linear momentum equation, and it was found that the equation predicted the measured forces on the vertical wall within an accuracy of approximately 20% without using a momentum correction coefficient. The experiments also showed that the more flexible 2×4 wall resulted in lower peak forces when compared with 2×6 walls subjected to similar tsunami heights. However, the 2×6 walls were able to withstand larger waves before failure.

MHD Mixed Convection Flow over a Permeable Vertical Plate with Buoyancy and Soret Effects

This study examines the problem of steady, MHD, mixed convection flow of an incompressible viscous fluid past a semi-infinite vertical permeable plate with slip condition at the boundary layer. The flow field is exposed to the influence of buoyancy, Ohmic heating and Soret effects. The governing equations include the continuity, linear momentum, energy and mass transfer equations which are solved analytically by using perturbation method. The results of this parametric study on the velocity, temperature and concentration distributions are shown graphically and the physical aspects of the problem are highlighted and discussed. The effect of shear stress, rate of heat and mass transfer coefficients at the channel walls are displayed in tables.

Wave propagation in 3-D poroelastic media including gradient effects

In the framework of the theory of mixtures, the governing equations of motion of a fluid-saturated poroelastic medium including microstructural (for both the solid and the fluid) and micro-inertia (for the solid) effects are derived. This is accomplished by appropriately combining the conservation of mass and linear momentum equations with the constitutive equations for both the solid and the fluid constituents. The solid is assumed to be gradient elastic, that is, its stress tensor depends on the strain and the second gradient of strain tensor. The fluid is assumed to have an analogous behavior, that is, its stress tensor depends on the pressure and the second gradient of pressure. A micro-inertia term in the form of the second gradient of the acceleration of the solid is also included in the equations of motion. The equations of motion in three dimensions are seven equations with seven unknowns, the six displacement components for the solid and the fluid and the pore-fluid pressure. Because of the microstructural effects, the order of these equations is two degrees higher than in the classical case. Application of the divergence and the rot operations on these equations enable one to study the propagation of plane harmonic waves in the infinitely extended medium separately in the form of dilatational and rotational dispersive waves. The effects of the microstructure and the micro-inertia on the dispersion curves are determined and discussed.

HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION

The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of magnetic field parameter (Ha) , micropolar spin gradient viscosity parameter (Γ) and unsteadiness parameter (S) on linear and angular velocity (micro-rotation) are presented graphically, for specified values of the micropolar vortex viscosity parameter (R), Darcy number (Da i.e. permeability parameter) and medium porosity parameter (ε). Increasing magnetic field (Ha) serves to decelerate both the linear and angular velocity i.e. enhances lubrication. The excellent potential of HAM in bio-lubrication flows is highlighted.

EFFECT OF AN INDUCED MAGNETIC FIELD ON PERISTALTIC FLOW OF NON-NEWTONIAN FLUID IN A CURVED CHANNEL

The purpose of this study is to discuss the influence of induced magnetic field on the peristaltic flow of an incompressible third-grade fluid in a curved channel. The problem formulation is presented in a wave frame of reference. The continuity, linear momentum, and induction equations lead to the mathematical development. The relations of stream function, pressure gradient, magnetic force function, induced magnetic field, and current density are developed. The effects of embedded parameters are explained by plots.

The Shear-Driven Fluid Motion Using Oscillating Boundaries

A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (Cd) on wind velocity can be predicted, while both a(z) and Cd must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.