scholarly journals Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 85-93
Author(s):  
S. Jayyousi Dajani ◽  
M. S. Abu Zaytoon ◽  
M. H. Hamdan
Keyword(s):  
Variable Viscosity ◽  
Fluid Pressure ◽  
Volume Averaging ◽  
Fluid Particle ◽  
Fluid Viscosity ◽  
Fluid Mixture ◽  
Intrinsic Volume ◽  
Mixture Flow ◽  
Particle Mixture ◽  
Pressure Dependent Viscosity

Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model

scholarly journals Effects of the Porous Microstructure on the Drag Coefficient in Flow of a Fluid with Pressure-Dependent Viscosity

2021 ◽  
Vol 15 ◽  
pp. 136-144
Author(s):  
M.S. Abu Zaytoon ◽  
S. Jayyousi Dajani ◽  
M.H. Hamdan
Keyword(s):  
Porous Structure ◽  
Drag Coefficient ◽  
Volume Averaging ◽  
Intrinsic Volume ◽  
Friction Factors ◽  
Pressure Dependent Viscosity ◽  
Variable Function ◽  
Porous Microstructure ◽  
Dependent Viscosity

Equations governing the flow of a fluid with pressure-dependent viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled and included in the pressure-dependent drag coefficient. Five friction factors relating to five different microstructures are used in this work

scholarly journals Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

Thermodynamic Properties of Fluids

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Mechanical Energy ◽  
Fluid Pressure ◽  
Fluid Flows ◽  
Thermal Conditions ◽  
Fluid Viscosity ◽  
Frozen Ground ◽  
Patterned Ground ◽  
Fluid Behavior ◽  
Fluid Properties ◽  
Convective Motions

Fluid behavior in many geological problems is strongly influenced by extant thermal conditions and flow of heat. Recall, for example, that the coefficient A in Glen’s law for ice (3.40) varies over three orders of magnitude with a change in temperature of 50 °C. The effect of this is to strongly modulate the rate of ice deformation for a given level of stress. Recall further that we introduced several fluid properties—fluid compressibility, for example—where we asserted that our purely mechanical developments were incomplete inasmuch as they did not treat effects of varying temperature. The reasons for this will become clear in this chapter, including why it is difficult to maintain isothermal conditions when the pressure of a fluid is changing. In addition, many geological problems involve fluid flows that are induced by effects of variations in thermal conditions over time and space. These include buoyancy-driven convective motions that arise from variations in fluid density associated with variations in temperature (Chapter 16). Specific examples include convective overturning in a magma chamber, which can significantly influence how crystallizing minerals are distributed; convective circulations of water and chemical solutions in a sedimentary basin, which can influence where rock materials are dissolved and where they are precipitated as cements within pores; and convective circulation of water within the active layer above seasonally frozen ground, which may influence where patterned ground develops in periglacial environments. These processes, and viscous flows in general, invariably involve conversions of mechanical energy to heat, or vice versa. So in considering problems involving heat energy, we should recall from introductory chemistry and physics that such conversions can involve work performed on the fluid or its surroundings, and anticipate that the effects of this ought be manifest in fluid behavior. This chapter, then, is concerned with fluid pressure, temperature, and density, and how these variables are related to heat, mechanical energy, and work. We will note in digressions how these macroscopic concepts, like fluid viscosity, often have clear interpretations at a molecular scale based on kinetic theory of matter.

Influence of Hydrodynamic Fluid Pressure and Shoe Tread Depth on Available Coefficient of Friction

2012 ◽  
Author(s):  
Gurjeet Singh ◽  
Kurt Beschorner
Keyword(s):  
Coefficient Of Friction ◽  
Hydrodynamic Lubrication ◽  
Fluid Pressure ◽  
Hydrodynamic Pressure ◽  
High Viscosity ◽  
Health Concern ◽  
Fluid Viscosity ◽  
Low Viscosity ◽  
The Coefficient Of Friction ◽  
Lubrication Mechanisms

Slip and fall accidents are a major occupational health concern. Identifying the lubrication mechanisms affecting shoe-floor-contaminant friction under biofidelic (testing conditions that mimic human slipping) conditions is critical to identifying unsafe surfaces and designing a slip-resistant work environment. The purpose of this study is to measure the effects of varying tread design, tread depth and fluid viscosity on underfoot hydrodynamic pressure, the load supported by the fluid (i.e. load carrying capacity), and the coefficient of friction (COF) during a simulated slip. A single vinyl floor material and two shoe types (work shoe and sportswear shoe) with three different tread depths (no tread, half tread and full tread) were tested under two lubrication conditions: 1) 90% glycerol and 10% water (219 cP) and 2) 1.5% Detergent-98.5% (1.8cP) water solutions. Hydrodynamic pressures were measured with a fluid pressure sensor embedded in the floor and a forceplate was used to measure the friction and normal forces used to calculate coefficient of friction. The study showed that hydrodynamic pressure developed when high viscosity fluids were combined with no tread and resulted in a major reduction of COF (0.005). Peak hydrodynamic pressures (and load supported by the fluid) for the no tread-high viscous conditions were 234 kPa (200.5 N) and 87.63 kPa (113.3 N) for the work and sportswear shoe, respectively. Hydrodynamic pressures were negligible when at least half the tread was present or when a low viscosity fluid was used despite the fact that many of these conditions also resulted in dangerously low COF values. The study suggests that hydrodynamic lubrication is only relevant when high viscous fluids are combined with little or no tread and that other lubrication mechanisms besides hydrodynamic effects are relevant to slipping like boundary lubrication.

scholarly journals The Flow of a Variable Viscosity Fluid down an Inclined Plane with a Free Surface

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
M. S. Tshehla
Keyword(s):  
Free Surface ◽  
Variable Viscosity ◽  
Convective Heating ◽  
Fluid Viscosity ◽  
Inclined Plane ◽  
Flow Equations ◽  
Variation Parameter ◽  
Viscosity Variation ◽  
Viscosity Fluid ◽  
Variable Viscosity Fluid

The effect of a temperature dependent variable viscosity fluid flow down an inclined plane with a free surface is investigated. The fluid film is thin, so that lubrication approximation may be applied. Convective heating effects are included, and the fluid viscosity decreases exponentially with temperature. In general, the flow equations resulting from the variable viscosity model must be solved numerically. However, when the viscosity variation is small, then an asymptotic approximation is possible. The full solutions for the temperature and velocity profiles are derived using the Runge-Kutta numerical method. The flow controlling parameters such as the nondimensional viscosity variation parameter, the Biot and the Brinkman numbers, are found to have a profound effect on the resulting flow profiles.

Effects of capillary number, Bond number, and gas solubility on water saturation of sand specimens

2013 ◽  
Vol 50 (2) ◽  
pp. 133-144 ◽  
Author(s):  
Bruce L. Kutter
Keyword(s):  
Capillary Number ◽  
Water Saturation ◽  
Fluid Pressure ◽  
Infiltration Rate ◽  
Capillary Forces ◽  
Bond Number ◽  
Pore Fluid ◽  
Degree Of Saturation ◽  
Fluid Viscosity ◽  
Viscous Forces

To better understand how to prepare completely water-saturated specimens or centrifuge models from dry sand, the mechanisms of the infiltration and filling of pores in sand are studied. Complete saturation has been shown by others to be especially important in studies involving the triggering of liquefaction. This paper discusses how the degree of saturation obtained during infiltration increases with the “Bond number”, Bo (ratio of body forces and capillary forces), and the “capillary number”, Ca (ratio of viscous forces and capillary forces), as well as the solubility of gas bubbles in the pore fluid. Bo is varied by changing the particle size, fluid density, and centrifugal acceleration. Ca is varied by changing the fluid viscosity and infiltration rate. The dissolution of gas is encouraged by replacing pore air by CO2 (56 times more soluble in water than N2), by de-airing the liquid prior to infiltration or by increasing the pore fluid pressure after infiltration. Infiltration experiments performed at 1g and in a centrifuge are presented. A new technique for measuring the degree of saturation is also presented. Quantitative pressure–saturation relations are presented for different gasses, illustrating the importance of replacement of air by CO2. Spinning a specimen in a centrifuge during infiltration is also useful for speeding up the saturation process and for achieving higher degrees of saturation.

An Alternative to API 14E Erosional Velocity Limits for Sand-Laden Fluids

2000 ◽  
Vol 122 (2) ◽  
pp. 71-77 ◽  
Author(s):  
Mamdouh M. Salama
Keyword(s):  
Flow Velocity ◽  
Flow Loop ◽  
Fluid Mixture ◽  
Mixture Flow ◽  
Empirical Constant ◽  
Mixture Density ◽  
S Factor ◽  
Piping Systems ◽  
Pipe Geometry ◽  
Alternative Equation

The current practice for eliminating erosional problems in piping systems is to limit the flow velocity Ve to that established by the recommended practice API RP 14E based on an empirical constant (C-factor) and the fluid mixture density ρm as follows: Ve=C/ρm. The API criterion is specified for clean service (noncorrosive and sand-free), and it is noted that the C-factor should be reduced if sand or corrosive conditions are present. The validity of the equation has been challenged on the basis that the API RP 14E limits on the C-factor can be very conservative for clean service and is not applicable for conditions when corrosion or sand are present. Extensive effort has been devoted to develop an alternative approach for establishing erosional velocity limits for sand-laden fluids. Unfortunately, none of these proposals have been adopted as a standard practice because of their complexity. This paper will review the results of these studies and proposes an alternative equation that is as simple as the API 14E equation. This alternative equation has the following form: Ve=SDρm/W. The value of the S-factor depends on the pipe geometry, i.e., bend, tee, contraction, expansion, etc. Using the units for mixture flow velocity Ve in m/s, fluid mixture density ρm in kg/m3, pipe diameter (D) in mm and sand production W in kg/day, the value of the S-factor is 0.05 for pipe bends. The accuracy of the proposed equation for predicting erosion in pipe bends for fluids containing sand is demonstrated by a comparison with several multi-phase flow loop tests that cover a broad range of liquid-gas ratios and sand concentrations. [S0195-0738(00)00202-8]

Chemically Reacting MHD Mixed Convection Variable Viscosity Blasius Flow Embedded in a Porous Medium

2017 ◽  
Vol 374 ◽  
pp. 83-91 ◽  
Author(s):  
Oluwole Daniel Makinde ◽  
S.R. Mishra
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Skin Friction ◽  
Sherwood Number ◽  
Variable Viscosity ◽  
Fluid Viscosity ◽  
Reaction Heat ◽  
Blasius Flow

In this paper, the combined effects of magnetic field, buoyancy forces, nth order chemical reaction, heat source, viscous dissipation, Joule heating and variable viscosity on mixed convection Blasius flow of a conducting fluid over a convectively heated permeable plate embedded in a porous medium is investigated. The fluid properties are assumed to be constant except for the density variation with the temperature and reacting chemical species concentration. The nonlinear governing differential equations were obtained and solved numerically using the Runge-Kutta-Fehlberg method with shooting technique. The dimensionless velocity, temperature and concentration profiles are shown graphically. The effects of pertinent parameters on the skin friction, Nusselt number and Sherwood number are examined. It is found that skin friction decreases while Nusselt number and Sherwood number increase with a decrease in the fluid viscosity in the presence of magnetic field.

scholarly journals Impacts of Thermal Conductivity and Variable Viscosity on the Dissipative Heat and Species Transport of MHD Flow in Porous Media

2021 ◽  
pp. 1-10
Author(s):  
M. A. Mohammed ◽  
J. F. Baiyeri ◽  
T. O. Ogunbayo ◽  
O. A. Esan
Keyword(s):  
Magnetic Field ◽  
Variable Viscosity ◽  
Flow In Porous Media ◽  
Wall Friction ◽  
Working Fluid ◽  
Fluid Viscosity ◽  
Moving Plate ◽  
Temperature Function ◽  
Flowing Liquid ◽  
Dissipative Heat

The investigation of dissipative heat and species diffusion of a conducting liquid under the combined influence of buoyancy forces in a moving plate is examined in the existence of magnetic field. The flowing liquid heat conductivity and viscosity are taken to be linearly varied as a temperature function. The governing derivative equations of the problem are changed to anon-linear coupled ordinary derivative equations by applying similarity quantities. The dimensionless model is solved using shooting technique along with the Runge-Kutta method. The outcomes for the flow wall friction, heat gradient and species wall gradient are offered in table and qualitatively explained. The study revealed that the Newtonian fluid viscosity can be enhanced by increasing the fluid flow medium porosity and the magnetic field strength. Hence, the study will improve the industrial usage of Newtonian working fluid.

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