scholarly journals Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

2021 ◽  
Vol 11 (21) ◽  
pp. 10352
Author(s):  
Juliana Bertoco ◽  
Rosalía T. Leiva ◽  
Luís L. Ferrás ◽  
Alexandre M. Afonso ◽  
Antonio Castelo
Keyword(s):  
Numerical Study ◽  
Creeping Flow ◽  
Model Parameters ◽  
Channel Inlet ◽  
Parallel Plates ◽  
Development Length ◽  
Governing Equations ◽  
Flow Limit ◽  
The Finite Difference Method ◽  
Elasticity Number

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

Numerical Study of Wave Slamming on a Rectangular Slab

2012 ◽  
Vol 204-208 ◽  
pp. 4971-4977
Author(s):  
Ya Mei Lan ◽  
Wen Hua Guo ◽  
Yong Guo Li
Keyword(s):  
Numerical Study ◽  
Navier Stokes ◽  
Governing Equations ◽  
Reflected Waves ◽  
Rans Equations ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
Wave Slamming ◽  
Numerical Wave ◽  
Rectangular Slab

The CFD software FLUENT was used as the foundation to develop the numerical wave flume, in which the governing equations are the Reynolds-averaged Navier-Stokes (RANS) equations and the standard k~ε turbulence model. The wave generating and absorbing were introduced into the RANS equations as the source terms using the relaxation approach. A new module of the wave generating and absorbing function, which is suitable for FLUENT based on the volume of fluid method (VOF), was established. Within the numerical wave flume, the reflected waves from the model within the computation domain can be absorbed effectively before second reflection appears due to the wave generating boundary. The computational results of the wave pressures on the bottom of the rectangular slab were validated for the different relative clearance by the experimental data. Good agreements were found.

A Numerical Study of Sensitivity Coefficients for a Model of Amyloid Precursor Protein and Tubulin-Associated Unit Protein Transport and Agglomeration in Neurons at the Onset of Alzheimer's Disease

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Amyloid Precursor Protein ◽  
Tau Protein ◽  
Protein Transport ◽  
Numerical Study ◽  
Amyloid Β ◽  
Precursor Protein ◽  
Model Parameters ◽  
In The Beginning

Modeling of intracellular processes occurring during the development of Alzheimer's disease (AD) can be instrumental in understanding the disease and can potentially contribute to finding treatments for the disease. The model of intracellular processes in AD, which we previously developed, contains a large number of parameters. To distinguish between more important and less important parameters, we performed a local sensitivity analysis of this model around the values of parameters that give the best fit with published experimental results. We show that the influence of model parameters on the total concentrations of amyloid precursor protein (APP) and tubulin-associated unit (tau) protein in the axon is reciprocal to the influence of the same parameters on the average velocities of the same proteins during their transport in the axon. The results of our analysis also suggest that in the beginning of AD the aggregation of amyloid-β and misfolded tau protein have little effect on transport of APP and tau in the axon, which suggests that early damage in AD may be reversible.

Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling

2016 ◽  
Vol 26 (5) ◽  
pp. 1567-1579 ◽  
Author(s):  
Ahmada Omar Ali ◽  
Oluwole Daniel Makinde ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Couette Flow ◽  
Numerical Study ◽  
Integration Scheme ◽  
Parallel Plates ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Mhd Couette Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel. Design/methodology/approach – The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme. Findings – Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods. Practical implications – This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems. Originality/value – Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

Numerical Study on Heat Transfer Characteristics From Parallel Plates With Cavities Swept by a Visco-Elastic Fluid

2010 ◽  
Author(s):  
Hiroshi Suzuki ◽  
Shinpei Maeda ◽  
Yoshiyuki Komoda
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Thermal Field ◽  
Numerical Study ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Heat Transfer Characteristics ◽  
Elastic Fluid ◽  
Heat Transfer Augmentation

Two-dimensional numerical computations have been performed in order to investigate the development characteristics of flow and thermal field in a flow between parallel plates swept by a visco-elastic fluid. In the present study, the effect of the cavity number in the domain and of Reynolds number was focused on when the geometric parameters were set constant. From the results, it is found that the flow penetration into the cavities effectively causes the heat transfer augmentation in the cavities in any cavity region compared with that of water case. It is also found that the development of thermal field in cases of the present visco-elastic fluid is quicker compared with that of water cases. The present heat transfer augmentation technique using Barus effect of a visco-elastic fluid is effective in the range of low Reynolds number.

scholarly journals Numerical Study of MHD Flow and Heat Transfer Through Porous Medium Between Two Parallel Plates With Hall and Ion Slip Effects

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Numerical Study ◽  
Mhd Flow ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Slip Effects ◽  
Ion Slip ◽  
Temperature And Pressure

This paper studies the effects of Hall and ion slip on two dimensional incompressible flow and heat transfer of an electrically conducting viscous fluid in a porous medium between two parallel plates, generated due to periodic suction and injection at the plates. The flow field, temperature and pressure are assumed to be periodic functions in ti e ω and the plates are kept at different but constant temperatures. A numerical solution for the governing nonlinear ordinary differential equations is obtained using quasilinearization method. The graphs for velocity, temperature distribution and skin friction are presented for different values of the fluid and geometric parameters.

Micropolar Fluid Flow Between Two Inclined Parallel Plates

2017 ◽  
Author(s):  
Abbas Hazbavi ◽  
Sajad Sharhani
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Micropolar Fluid ◽  
Constant Heat Flux ◽  
Hydrodynamic Characteristics ◽  
Parallel Plates ◽  
Governing Equations ◽  
Micropolar Fluid Flow ◽  
Flow Through ◽  
The Magnetic Field

In this study, the hydrodynamic characteristics are investigated for magneto-micropolar fluid flow through an inclined channel of parallel plates with constant pressure gradient. The lower plate is maintained at constant temperature and upper plate at a constant heat flux. The governing equations which are continuity, momentum and energy are are solved numerically by Explicit Runge-Kutta. The effect of characteristic parameters is discussed on velocity and microrotation in different diagrams. The nonlinear parameter affected the velocity microrotation diagrams. An increase in the value of Hartmann number slows down the movement of the fluid in the channel. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Also the effect of pressure gradient is investigated on velocity and microrotation in different diagrams.

Numerical study of Zika model as a mosquito-borne virus with non-singular fractional derivative

2021 ◽  
Author(s):  
Sachin Kumar ◽  
Dia Zeidan
Keyword(s):  
Fractional Derivative ◽  
Zika Virus ◽  
Numerical Study ◽  
Asymptomatic Carrier ◽  
Virus Transmission ◽  
Model Parameters ◽  
Human Society ◽  
Sexual Interaction ◽  
Virus Model ◽  
Global Threat

Zika virus infection, which is closely related to dengue, is becoming a global threat to human society. The transmission of the Zika virus from one human to another is spread by bites of Aedes mosquitoes. Recent studies also reveal the fact that the Zika virus can be transmitted by sexual interaction. In this paper, we use the fractional derivative with Mittag–Leffler non-singular kernel to study Zika virus transmission dynamics. This fractional is also known as the Atangana–Baleanu Caputo (ABC) derivative which is employed for the resulting system of ordinary differential equations. We investigate the proposed Zika virus model by using the Legendre spectral method. The model parameters are estimated and validated numerically by investigating the effect of fractional order exponent on various cases such as Susceptible human, infected human, asymptomatic carrier, exposed human, and recovered human. Numerical results obtained with the proposed method have been compared with exact solutions, showing in all parameters a very satisfactory agreement.

scholarly journals Transient free convection in an inclined square porous cavity filled with a nanofluid using LTNE and Buongiorno’s models

2018 ◽  
Vol 240 ◽  
pp. 03014
Author(s):  
Mikhail Sheremet ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Inclination Angle ◽  
Equilibrium Temperature ◽  
Brownian Diffusion ◽  
Governing Equations ◽  
Nanofluid Flow ◽  
Porous Cavity ◽  
Flow And Heat Transfer ◽  
The Finite Difference Method ◽  
Porous Enclosure

The combined effect of Brownian diffusion, thermophoresis and cavity inclination angle on natural convective heat transfer in an inclined porous enclosure has been studied numerically. Fluid containing nanoparticles of low concentration circulates inside the cavity under the effect of the buoyancy force. Governing equations with corresponding boundary conditions formulated using the non-dimensional stream function and vorticity variables have been solved by the finite difference method. An influence of the cavity inclination angle, Darcy and Nield numbers on nanofluid flow and heat transfer has been investigated. It has been found that high Nield numbers illustrate more equilibrium temperature distribution inside the porous cavity.

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