Fluid properties laminar flow

Much of the research activity in this area has related to heat transfer to inelastic non-Newtonian fluids in laminar flow in circular and non-circular ducts. In recent years, some consideration has also been given to heat transfer to/from non-Newtonian fluids in vessels fitted with coils and jackets, but little information is available on the operation of heat exchange equipment with non-Newtonian fluids. Consequently, this chapter is concerned mainly with the prediction of heat transfer rates for flow in circular tubes. Heat transfer in external (boundary layer) flows is discussed in Chapter 7, whereas the cooling/heating of non-Newtonian fluids in stirred vessels is dealt with in Chapter 8. First of all, however, the thermo-physical properties of the commonly used non-Newtonian materials will be described. 

Laminar flow in tubes. A large portion of the experimental investigations have been concerned with heat transfer of non-Newtonian fluids in laminar flow through cylindrical tubes. The physical properties that are needed for heat transfer coefficients are density, heat capacity, thermal conductivity, and the rheological constants K and n or K and n. 

Viscosity is defined as the property which determines the resistance to motion when a sheering force is exerted on the fluid under laminar flow conditions. 

The first term (AQ) is the pressure drop due to laminar flow, and the FQ term is the pressure drop due to turbulent flow. The A and F factors can be determined by well testing, or from the fluid and reservoir properties, if known. 

It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a flowing liquid with laminar flow. This makes it possible to compute properties not measurable in a static fluid, such as the viscosity. Nonequilibrium simulations give rise to additional technical difficulties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work. 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

But in order to prediet ly, knowledge of cdoo is required as a funetion of the fluid properties and partiele eharaeteristie dimension, viz. the partiele Reynolds number. This is straightforward for partieles experieneing laminar flow for whieh there exists an analytieal solution. In turbulent eonditions, however, the flow is mueh more eomplex and analytieal solutions are not available. Fortunately, in these eases resort ean be made to semi-empirieal (or semi-theoretieal) formulae or eharts that eorrelate reported experimental data over a wide range of eonditions. 

Equation 5.2 is found to hold well for non-Newtonian shear-thinning suspensions as well, provided that the liquid flow is turbulent. However, for laminar flow of the liquid, equation 5.2 considerably overpredicts the liquid hold-up e/,. The extent of overprediction increases as the degree of shear-thinning increases and as the liquid Reynolds number becomes progressively less. A modified parameter X has therefore been defined 16 171 for a power-law fluid (Chapter 3) in such a way that it reduces to X both at the superficial velocity uL equal to the transitional velocity (m )f from streamline to turbulent flow and when the liquid exhibits Newtonian properties. The parameter X is defined by the relation... 

Chapter 7 deals with the practical problems. It contains the results of the general hydrodynamical and thermal characteristics corresponding to laminar flows in micro-channels of different geometry. The overall correlations for drag and heat transfer coefficients in micro-channels at single- and two-phase flows, as well as data on physical properties of selected working fluids are presented. The correlation for boiling heat transfer is also considered. 

Hetsroni et al. (2005) evaluated the effect of inlet temperature, channel size and fluid properties on energy dissipation in the flow of a viscous fluid. For fully developed laminar flow in circular micro-channels, they obtained an equation for the adiabatic increase of the fluid temperature due to viscous dissipation ... 

The quasi-one-dimensional model of laminar flow in a heated capillary is presented. In the frame of this model the effect of channel size, initial temperature of the working fluid, wall heat flux and gravity on two-phase capillary flow is studied. It is shown that hydrodynamical and thermal characteristics of laminar flow in a heated capillary are determined by the physical properties of the liquid and its vapor, as well as the heat flux on the wall. 

To describe the velocity profile in laminar flow, let us consider a hemisphere of radius a, which is mounted on a cylindrical support as shown in Fig. 2 and is rotating in an otherwise undisturbed fluid about its symmetric axis. The fluid domain around the hemisphere may be specified by a set of spherical polar coordinates, r, 8, , where r is the radial distance from the center of the hemisphere, 0 is the meridional angle measured from the axis of rotation, and (j> is the azimuthal angle. The velocity components along the r, 8, and (j> directions, are designated by Vr, V9, and V. It is assumed that the fluid is incompressible with constant properties and the Reynolds number is sufficiently high to permit the application of boundary layer approximation [54], Under these conditions, the laminar boundary layer equations describing the steady-state axisymmetric fluid motion near the spherical surface may be written as ... 

Laminar flow (LF) is also a form of tubular flow, and is the flow model for an LFR. It is described in Section 2.5. LF occurs at low Reynolds numbers, and is characterized by a lack of mixing in both axial and radial directions. As a consequence, fluid properties vary in both directions. There is a distribution of residence times, since the fluid velocity varies as a parabolic function of radial position. 

No methods appear to be available for the precise prediction of pressure drop when a non-Newtonian fluid is being heated or cooled, but Vaughn (V2) has shown that the procedure recommended most recently by McAdams (M4, p. 149) for Newtonian fluids is slightly conservative when applied to pressure-drop data on the heating of non-Newtonian solutions in laminar flow. McAdams has suggested evaluation of the fluid properties at a film temperature [Pg.116]

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

The most general equations for the laminar flow of a viscous incompressible fluid of constant physical properties are the Navier-Stokes equations. In terms of the rectangular coordinates x, y, z, these may be written ... 

A rotated disc in a fluid behaves as a pump which draws fluid towards the disc and throws it out radially, Fig. 5.17. Flow to a rotated disc has the surprising property that, under laminar flow conditions, the film thickness is uniform across the whole of the disc surface, excluding edge eifects, and the film thickness (5) is rigorously calculable using fluid mechanics theory [22]. ft is given by Equation 5.12 where D is the diffusion coefficient in cm2 s-1, v is the kinematic viscosity in cm2 s 1 and a> is the rotation speed in rad s-1 ... 

Hydrodynamic focusing Hydrodynamic focusing is the property of laminar flow in a stream of increasing velocity that maintains particles in the narrowing central core of a column of fluid. 

The thickness of the liquid film on the rotor packing helps determine mass transfer rates. Film thickness can be shown to be inversely proportional to rotor speed to the 0.8 power (17). Visual measurements using a video camera attached to the rotor show a water film thickness of 20-80 microns on foam metal packing and 10 microns on wire gauze packing (15). Theoretical models estimate similar film thickness values (13,18,19). Film flow is expected to be laminar. In addition to rotor speed, liquid flow rate and fluid properties affect the film thickness (14). 

A characteristic of micro channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Just considering the laminar flow would deliver an extremely wide residence-time distribution. The near wall flow is close to stagnation because a fluid element at the wall of the channel is, by definition, fixed to the wall for an endlessly long time, in contrast to the fast core flow. The phenomenon that prevents such a behavior is the known dispersion effect and is demonstrated in Figure 3.88. 

Solution This flow is z-axisymmetric. We, thus, select a cylindrical coordinate system, and make the following simplifying assumptions Newtonian and incompressible fluid with constant thermophysical properties no slip at the wall of the orifice die steady-state fully developed laminar flow adiabatic boundaries and negligible of heat conduction. 

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