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Preliminary Concepts
Published in Hillel Rubin, Joseph Atkinson, Environmental Fluid Mechanics, 2001
In addition to Ri, another parameter of interest is the Reynolds number, Re, which is the inverse of the last term on the right-hand side of Eq. (13.3.41). When Re is large, there is generally forced convection. The nondimensional pressure term is called either a Cauchy number or an Euler number, but this term is generally not of major interest in the analysis of convection. One further dimensionless number arising from a nondimensional representation of the temperature equation (13.3.39) is the Prandtl number, Pr=v/kT. This gives the relative importance of momentum diffusion, compared with heat diffusion. Including the nondimensional temporal term, a simple dimensional analysis suggests solutions of the form
Hydrostatics and Hydraulics
Published in W. David Yates, Safety Professional’s Reference and Study Guide, 2020
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents perpendicular to the direction of flow; neither are there eddies or swirls of fluids. In laminar flow, the motion of the particles of fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.
Hydrostatics and Hydraulics
Published in W. David Yates, Safety Professional’s, 2015
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents perpendicular to the direction of flow; neither are there eddies or swirls of fluids. In laminar flow, the motion of the particles of fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.
A comprehensive two-phase flow model for unidirectional sheet-flows
Published in Journal of Hydraulic Research, 2018
The sheet-flow regime of sediment transport occurs when the fluid flow is strong enough to mobilize a thick and dense layer of particles on the top of the sediment bed. Provided that the particles are light enough or the shearing is strong enough, sediment particles can be entrained in suspension to form a suspension layer above the sheet layer. It is widely accepted that both intergranular interactions and turbulent processes are key mechanisms in momentum diffusion and dilatancy effects (e.g. Bagnold, 1956; Jenkins & Hanes, 1998). In this paper, we focus on uniform and steady sheet-flows of well-sorted particles in which the slope is sufficiently low to neglect the body force acting on the particles.
Numerical modeling of bioconvection and heat transfer analysis of Prandtl nanofluid in an inclined stretching sheet: A finite difference scheme
Published in Numerical Heat Transfer, Part A: Applications, 2023
The thermophoresis is a phenomenon in which the fluid particles migrate from a higher temperature region to lower temperature region and is illustrated in Figure 6(a–b). Due to this, the fluid particle is dragged away from the heated surface due to which both temperature and motile density decreases. Additionally, increasing causes the fluid particles to accelerate quickly, which increases their kinetic energy and promotes the boundary layer to thicken. In reality, the random acceleration of the fluid particle decreases as the quantity of grows, movement of the fluid particles from higher to lower regions improves fast. Hence decrease in the and is observed. Increasing must increase the velocity distribution. But, in this case, reverse trend is witnessed. This is due to the fact the Brownian motion is dominating the thermophoretic effect. The Prandtl fluid parameter (), which is a dimensionless number, describes how important momentum diffusion (viscosity) and temperature diffusion (thermal conductivity) are in a fluid in relation to one another. It describes the difference between a fluid’s capacity to carry heat and motion. When the Prandtl fluid parameter is high, momentum diffusion is less important than heat diffusion. In this case, convective heat transmission is reduced as heat transfer processes have a greater influence on determining flow velocity. Additionally, can increase the thickness of the thermal boundary layer, which indicates that the thermal effects and temperature gradients affect the temperature distribution close to solid surfaces by penetrating further into the fluid.