Sink flow analysis

The sink flow analysis, which assumes a purely extensional flow (i.e., no shear component), was presented by Metzner and Metzner (1970) to evaluate the extensional viscosity from orifice Apen measurements. For an axisymmetric contraction, the flow into the orifice is analogous to a point sink for a planar contraction flow, the analogy is with a line sink (Batchelor, 1967). In the case of axisymmetric contraction (Figure 7.8.1), the use of spherical coordinates and continuity gives the velocity components... 

Other kinematical problems associated with the sink flow analysis are discussed by Denn (1977) and Cogswell (1978). 

Several different analyses have been presented to estimate the extensional viscosity from Apen measurements. The three major approaches are discussed below sink flow (Metzner and Metzner, 1970), Cogswell s analysis (1972), and Binding s analysis (1988). 

DecoveTj of Capital. In Figure 1, the annual book depreciation is used to retire the fixed capital investment. Whereas this accounting model does not correspond to the typical money flow, it is one possible model for recovery of capital. This model assumes that the investment is reduced each year by the amount of the annual depreciation. Another model (22) assumes that a uniform yearly book depreciation payment is made to an interest-bear sinking fund that accumulates to the depreciable fixed capital amount at the end of the venture. Using this second model, the investment is outstanding throughout the lifetime of the project. This also does not correspond to the actual money flow in most cases. ProfitabiUty analysis utilizes a third model based on discounted cash flows. 

Lelea D, Nishio S, Takano K (2004) The experimental research on micro-tube heat transfer and fluid flow of distilled water. Int J Heat Mass Transfer 47 2817-2830 Li J, Peterson GP, Cheng P (2004) Three-dimensional analysis of heat transfer in a micro-heat sink with single phase flow. Int J Heat Mass Transfer 47 4215-4231 Lin TY, Yang CY (2007) An experimental investigation by method of fluid crystal thermography. Int. J. Heat Mass Transfer 50(23-24) 4736-4742... 

A life cycle assessment (LCA), also known as life cycle analysis, of a product or process begins with an inventory of the energy and environmental flows associated with a product from "cradle to grave" and provides information on the raw materials used from the environment, energy resources consumed, and air, water, and solid waste emissions generated. GHGs and other wastes, sinks, and emissions may then be assessed (Sheehan et ah, 1998). The net GHG emissions calculated from an LCA are usually reported per imit of product or as the carbon footprint. 

Analysis (a) Assume that the heat exchangers are isobaric, and turbine and pump are isentropic. (b) Input heat source fluid = water, P5 = 200 bars, V5=lbar, xg = 0, and pg = 200 bars heat sink fluid = water, X7 = 0, p7 = 0.02bar, Xg=l, and pg = 0.02bar heat exchangers are counter-flow type and steam cycle fluid = water, Xi=0, pi = lbar, V3 = 1, p3 = 117.6bars, and mdot= 1 kg/sec, as shown in Fig. 7.21a. 

As illustrated in Fig. 5.2, the classic Jeffery-Hamel flow concerns two-dimensional radial flow in a wedge-shaped region between flat inclined walls. The flow may be directed radially outward (as illustrated) or radially inward. The flow is assumed to originate in a line source or terminate in a line sink. Velocity at the solid walls obeys a no-slip condition. In practice, there must be an entry region where the flow adjusts from the line source to the channel-confined flow with no-slip walls. The Jeffery-Hamel analysis applies to the channel after this initial adjustment is accomplished. 

Figure 5.7 illustrates a spherical variation of the Jeffery-Hamel flow. Here the flow either originates or terminates in a point source or sink. As in the wedge flow (Section 5.2) the analysis here considers steady, incompressible, constant-property flow. 

In a steady state continuous distillation with the assumption of a well mixed liquid and vapour on the plates, the holdup has no effect on the analysis (modelling of such columns does not usually include column holdup) since any quantity of liquid holdup in the system has no effect on the mass flows in the system (Rose, 1985). Batch distillation however is inherently an unsteady state process and the liquid holdup in the system become sinks (accumulators) of material which affect the rate of change of flows and hence the whole dynamic response of the system. 

Another problem of significance is the optimum policy of water recycling. This subject is in itself substantial and cannot be handled here. An economical approach involves optimal allocation of streams, both as flow rates and contaminant concentration. The analysis may be performed systematically with tools based on the concept of water pinch and mass-exchange networks . This subject is treated thoroughly in specialized works, as in the books of El-Halwagi [19] and Smith [20]. A source-sink mapping technique developed around the acrylonitrile plant may be found in the book of Allen and Shoppard [21]. 

The above theoretical analysis of penetrable roughnesses and their interaction with the flow was based on the introduction of a distributed momentum sink (i.e. the force) and heat and mass sources, and was sufficient for discovering some important features of the phenomenon under consideration. It was a simplified consideration with mainly constant coefficients. However, in order to be applied to real environmental and engineering problems, realistic exchange coefficients are to be known. 

An analysis [238] of different simulation calculations of flow conditions in baffled vessels with turbine stirrers proposed in the literature resulted in a number of inconsistencies and provoked the question of whether it was permissible to simplify the three dimensional flow by an axially symmetrical approximation. The results obtained for a turbulent 3-D single phase flow, showed that the standard k-s-model did not produce a satisfactory result, due to the strongly pronounced velocity gradients in the turbulence field in the immediate proximity of the stirrer. In particular, the necessary assumption of a momentum sink for the baffles averaged over the circumference of the tank led to misrepresentation of the tangential flow field. 

Sensible heat and the latent heat of freeing are removed from the water at the liquid/solid interface. Under the prevailing static conditions heat will pass from the water to the cold sink by conduction. The resistance to this heat flow initially, will be a combination of the thermal resistances in the liquid and due to the cold solid. Immediately a layer of ice be ns to form on the cold surface a further resistance is added to the other thermal resistances. As further heat is extracted from the water, the ice layer thickens representing an advancing boundary between the solid ice and the liquid water, i.e. a transient condition. The transient condition, coupled with complex geometries and different forms of ice structure dependent in turn on the rate of cooling, constitute severe problems of mathematical analysis. 

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