Internal Flows

Let us start with a model situation there is a single bubble in the liquid, the gas is insoluble, and there is no flow. Internal pressure Pint in the equilibrium bubble is in this case counterbalanced by external pressure Pext and surface Laplace pressure PL = 2a/r (a is surface tension) ... 

For computational purposes it is useful to distinguish the directed edges associated with the external inputs and outputs, which are usually specified, from those associated with the flows internal to the network. Denoting the net output from vertex i by and including henceforth only the internal edges in the incidence matrix M, we may restate Eq. (7) as... 

If the pipe fluid continues to flow, internal convection is often sufficient to prevent failure, with the temperature reaching equilibrium below the failure temperature. However, this is not invariably the case. 

J C Leung, "Simplified Vent Sizing Methods Incorporating Two-phase Flow", International Symposium on Runaway Reactions and Pressure Relief Design, 200-236, AlChE, 1995, ISBN 0-8169-0676-9... 

The plutonium solution concentration was determined by alpha counting 0.5-ml. aliquots evaporated to dryness on planchets. Gas flow internal proportional counting was used with 90% argon-10 % methane gas and Nuclear Measurement Corp. counters. 

The QRRK model postulates that vibrational energy can freely flow (internally) from one vibrational mode in the molecule to another. This is a very significant assumption. For a collection of harmonic oscillators, energy in a particular vibrational mode will stay in that mode it cannot flow into other vibrational modes of the system. That is, a system of harmonic oscillators is uncoupled. 

According to its working principles, the nozzle shown in Fig. 7.5 should be classified as a three-flow internal-external mixing nozzle Berman and co-workers called it a complete external mixing type . 

Patankar, S.V. and Spalding, D.B.A. Calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal for Heat and Mass Transfer, 1972. 15, 1787-1806. 

External Flow Internal Flow External and internal flows. 

The resistance of melt flow exhibited within a body of material identifies its viscosity. It relates to plastic melt flow which in turn relates to the processing behavior of plastic. During melt flow internal friction occurs when one layer of fluid is caused to move in relationship to another layer.487 Ordinary viscosity is the internal friction or resistance of a plastic to flow. It is the constant ratio of shearing stress to the rate of shear. Shearing is the motion of a fluid, layer by layer, like the movement of a deck of cards. 

The latter include the discounted cash flow, internal rate of retnm. discounted pay-out time, economic cost price etc. 

V. Gnielinski. New Equations for Heal and Mass Transfer in Turbulent Pipe and Channel Flow. International Chemical Engineering 16 (1976), pp. 359-368. 

C- A. Sleicher and M. W. Rouse. A Convenient Correlation for Heal Transfer to Constant and Variable Property Fluids in Turbulent Pipe Flow. International Journal of Heat Mass Transfer 18 (1975), pp. 1429-1435. 

Jones, J., Owen C., and Zuber, N. (1975) The Interrelation between Void Fraction Fluctuations and Flow Patterns in Two-Phase Flow, International Journal of Multiphase Flow, Vol. 2(3), pp. 273-306. 

Mudde RF, Simonin O (1999) Two- and three-dimensional simnlations of a bubble plume using a two-fluid model. Chem Eng Sci 54 5061-5069 Natarajan VVR, Hunt ML (1998) Kinetic theory analysis of heat transfer in granular flows. International Journal of Heat and Mass Transfer, 41 1929-1944, 1998. 

Antal SP, Ettorre SM, Kunz RF, Podowski MZ (2000) Development of a Next Generation Computer Code for the Prediction of Multicomponent Multiphase Flows. International Meeting on Trends in Numerical and Physical Modeling for Industrial Multiphase Flow, Cargese, Prance, September 27-29... 

Effect of rotation rate. This is one parameter which does not have an analogous counterpart in batch column operation. Therefore, this parameter provides additional flexibility when optimizing a separation performed in an annular chromatograph. The rotation rate does not influence the solute residence time in the unit nor does it influence the relative time scales for flow, internal diffusion or external mass transfer. However, the rotation rate does influence the angular distance that a solute traverses in a given time. The result of a slower rotation rate is to decrease both the peak variance and the displacement for each solute and therefore again the resolution between proteins changes less than either mi/mo or a. ... 

Ammar, Y. Reeks, M. 2009 Agglomeration of inertial particles in a random rotating symmetric straining flow. International Journal of Multiphase Flow 35, 840-853. 

Cook, T. L. Harlow, E H. 1986 Vortices in bubbly two-phase flow. International Journal of Multiphase Flow 12, 35-61. 

Lasheras, J. C., Eastwood, C., Marttnez-Bazan, C. Montanes, G. L. 2002 A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow. International Journal of Multiphase Flow 28, 247-278. 

Sachdev, J. S., Groth, C. P. T. Gottueb, J. J. 2007 Numerical solution scheme for inert, disperse, and dilute gas-particle flows. International Journal of Multiphase Flow 33, 282-299. 

Sato, Y. Sekoguchi, K. 1975 Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95. 

The plutonium concentration in the ambient sorbing solutions was determined by alpha counting an evaporated aliquot in a gas flow internal proportional counter, also previously described (I). The amount... 

R.F. Barron, X.M. Wang, R.O. Warrington, and T.A. Ameel, The Graetz problem extended to slip flow. International Journal of Heat and Mass Transfer AQ, 1817-1823 (1997). 

A. Beskok, G.E. Kamiadakis, and W. Trimmer, Rarefaction, compressibility effects in gas microflows. Journal of Fluids Engineering 118, 448 56 (1996). W. Sun, S. Kakac, and A. Guvenc Yazicioglu, A numerical study of singlephase convective heat transfer in microtubes for shp flow. International Journal of Thermal Sciences 46, 1084-94 (2007). 

For this type of system, diffusion alone is not sufficient to achieve suitable mixing. Therefore, it was proposed to inject the droplets into a pressure driven flow in a serpentine channel, as shown in Fig. 7.8 [103, 104]. Flows internal to the drop were caused by changing the geometry of the channels, and resulted in intra-drop mixing. 

Internal Flow. Internally finned circular tubes are commercially available in aluminum and copper (or copper alloys). For laminar flow, the following correlations are available [113] Spiral-Fin Tubes. 

Perkin Elmer introduced, in 1984, a Stabilized Temperature Platform Furnace (STPF) (Figure 49). There are two inert gas flows (internal and external). The heating rate of the furnace is high (about 2000 Ks ), which allows the use of lower atomization temperatures. After the thermal pretreatment a small temperature step (<1600 K) is used in order to prevent the atomization of the sample before the equilibrium has been reached. 

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